exec.tex

%!TEX root = std.tex
\rSec0[exec]{Execution control library}

\rSec1[exec.general]{General}

\pnum
This Clause describes components
supporting execution of function objects\iref{function.objects}.

\pnum
The following subclauses describe
the requirements, concepts, and components
for execution control primitives as summarized in \tref{exec.summary}.

\begin{libsumtab}{Execution control library summary}{exec.summary}
\ref{exec.sched}     & Schedulers   & \tcode{<execution>} \\
\ref{exec.recv}      & Receivers    & \\
\ref{exec.opstate}   & Operation states & \\
\ref{exec.snd}       & Senders & \\
\end{libsumtab}

\pnum
\tref{exec.pos} shows
the types of customization point objects\iref{customization.point.object}
used in the execution control library.

\begin{floattable}{Types of customization point objects in the execution control library}{exec.pos}{lx{0.23\hsize}x{0.45\hsize}}
\topline
\lhdr{Customization point} & \chdr{Purpose} & \rhdr{Examples} \\
\lhdr{object type} & &  \\
\capsep
core &
  provide core execution functionality, and connection between core components &
  e.g., \tcode{connect}, \tcode{start} \\
completion functions &
  called by senders to announce the completion of the work (success, error, or cancellation) &
  \tcode{set_value}, \tcode{set_error}, \tcode{set_stopped} \\
senders &
  allow the specialization of the provided sender algorithms &
  \begin{itemize}
  \item sender factories (e.g., \tcode{schedule}, \tcode{just}, \tcode{read_env})
  \item sender adaptors (e.g., \tcode{continues_on}, \tcode{then}, \tcode{let_value})
  \item sender consumers (e.g., \tcode{sync_wait})
  \end{itemize}
    \\
queries &
  allow querying different properties of objects &
  \begin{itemize}
  \item general queries (e.g., \tcode{get_allocator}, \tcode{get_stop_token})
  \item environment queries (e.g., \tcode{get_scheduler}, \tcode{get_delegation_scheduler})
  \item scheduler queries (e.g., \tcode{get_forward_progress_guarantee})
  \item sender attribute queries (e.g., \tcode{get_completion_scheduler})
  \end{itemize}
    \\
\end{floattable}

\pnum
This clause makes use of the following exposition-only entities.

\pnum
For a subexpression \tcode{expr},
let \tcode{\exposid{MANDATE-NOTHROW}(expr)} be
expression-equivalent to \tcode{expr}.

\mandates
\tcode{noexcept(expr)} is \tcode{true}.

\pnum
\begin{codeblock}
namespace std {
  template<class T>
    concept @\defexposconcept{movable-value}@ =                                     // \expos
      @\libconcept{move_constructible}@<decay_t<T>> &&
      @\libconcept{constructible_from}@<decay_t<T>, T> &&
      (!is_array_v<remove_reference_t<T>>);
}
\end{codeblock}

\pnum
For function types \tcode{F1} and \tcode{F2} denoting
\tcode{R1(Args1...)} and \tcode{R2(Args2...)}, respectively,
\tcode{\exposid{MATCHING-SIG}(F1, F2)} is \tcode{true} if and only if
\tcode{\libconcept{same_as}<R1(Args1\&\&...), R2(Args2\&\&...)>}
is \tcode{true}.

\pnum
For a subexpression \tcode{err},
let \tcode{Err} be \tcode{decltype((err))} and
let \tcode{\exposid{AS-EXCEPT-PTR}(err)} be:
\begin{itemize}
\item
\tcode{err} if \tcode{decay_t<Err>} denotes the type \tcode{exception_ptr}.

\expects
\tcode{!err} is \tcode{false}.
\item
Otherwise,
\tcode{make_exception_ptr(system_error(err))}
if \tcode{decay_t<Err>} denotes the type \tcode{error_code}.
\item
Otherwise, \tcode{make_exception_ptr(err)}.
\end{itemize}

\pnum
For a subexpression \tcode{expr},
let \tcode{\exposid{AS-CONST}(expr)} be expression-equivalent to
\begin{codeblock}
[](const auto& x) noexcept -> const auto& { return x; }(expr)
\end{codeblock}

\rSec1[exec.queryable]{Queries and queryables}

\rSec2[exec.queryable.general]{General}

\pnum
A \defnadj{queryable}{object} is
a read-only collection of key/value pair
where each key is a customization point object known as a \defn{query object}.
A \defn{query} is an invocation of a query object
with a queryable object as its first argument and
a (possibly empty) set of additional arguments.
A query imposes syntactic and semantic requirements on its invocations.

\pnum
Let \tcode{q} be a query object,
let \tcode{args} be a (possibly empty) pack of subexpressions,
let \tcode{env} be a subexpression
that refers to a queryable object \tcode{o} of type \tcode{O}, and
let \tcode{cenv} be a subexpression referring to \tcode{o}
such that \tcode{decltype((cenv))} is \tcode{const O\&}.
The expression \tcode{q(env, args...)} is equal to\iref{concepts.equality}
the expression \tcode{q(cenv, args...)}.

\pnum
The type of a query expression cannot be \tcode{void}.

\pnum
The expression \tcode{q(env, args...)} is
equality-preserving\iref{concepts.equality} and
does not modify the query object or the arguments.

\pnum
If the expression \tcode{env.query(q, args...)} is well-formed,
then it is expression-equivalent to \tcode{q(env, args...)}.

\pnum
Unless otherwise specified,
the result of a query is valid as long as the queryable object is valid.

\rSec2[exec.queryable.concept]{\tcode{queryable} concept}

\begin{codeblock}
namespace std {
  template<class T>
    concept @\defexposconcept{queryable}@ = @\libconcept{destructible}@<T>;   // \expos
}
\end{codeblock}

\pnum
The exposition-only \exposconcept{queryable} concept specifies
the constraints on the types of queryable objects.

\pnum
Let \tcode{env} be an object of type \tcode{Env}.
The type \tcode{Env} models \exposconcept{queryable}
if for each callable object \tcode{q} and a pack of subexpressions \tcode{args},
if \tcode{requires \{ q(env, args...) \}} is \tcode{true} then
\tcode{q(env, args...)} meets any semantic requirements imposed by \tcode{q}.

\rSec1[exec.async.ops]{Asynchronous operations}

\pnum
An \defnadj{execution}{resource} is a program entity that manages
a (possibly dynamic) set of execution agents\iref{thread.req.lockable.general},
which it uses to execute parallel work on behalf of callers.
\begin{example}
The currently active thread,
a system-provided thread pool, and
uses of an API associated with an external hardware accelerator
are all examples of execution resources.
\end{example}
Execution resources execute asynchronous operations.
An execution resource is either valid or invalid.

\pnum
An \defnadj{asynchronous}{operation} is
a distinct unit of program execution that
\begin{itemize}
\item
is explicitly created;
\item
can be explicitly started once at most;
\item
once started, eventually completes exactly once
with a (possibly empty) set of result datums and
in exactly one of three \defnx{dispositions}{disposition}:
success, failure, or cancellation;
\begin{itemize}
\item
A successful completion, also known as a \defnadj{value}{completion},
can have an arbitrary number of result datums.
\item
A failure completion, also known as an \defnadj{error}{completion},
has a single result datum.
\item
A cancellation completion, also known as a \defnadj{stopped}{completion},
has no result datum.
\end{itemize}
An asynchronous operation's \defnadj{async}{result}
is its disposition and its (possibly empty) set of result datums.
\item
can complete on a different execution resource
than the execution resource on which it started; and
\item
can create and start other asynchronous operations
called \defnadj{child}{operations}.
A child operation is an asynchronous operation
that is created by the parent operation and,
if started, completes before the parent operation completes.
A \defnadj{parent}{operation} is the asynchronous operation
that created a particular child operation.
\end{itemize}
\begin{note}
An asynchronous operation can execute synchronously;
that is, it can complete during the execution of its start operation
on the thread of execution that started it.
\end{note}

\pnum
An asynchronous operation has associated state
known as its \defnadj{operation}{state}.

\pnum
An asynchronous operation has an associated environment.
An \defn{environment} is a queryable object\iref{exec.queryable}
representing the execution-time properties of the operation's caller.
The caller of an asynchronous operation is
its parent operation or the function that created it.

\pnum
An asynchronous operation has an associated receiver.
A \defn{receiver} is an aggregation of three handlers
for the three asynchronous completion dispositions:
\begin{itemize}
\item a value completion handler for a value completion,
\item an error completion handler for an error completion, and
\item a stopped completion handler for a stopped completion.
\end{itemize}
A receiver has an associated environment.
An asynchronous operation's operation state owns the operation's receiver.
The environment of an asynchronous operation
is equal to its receiver's environment.

\pnum
For each completion disposition, there is a \defnadj{completion}{function}.
A completion function is
a customization point object\iref{customization.point.object}
that accepts an asynchronous operation's receiver as the first argument and
the result datums of the asynchronous operation as additional arguments.
The value completion function invokes
the receiver's value completion handler with the value result datums;
likewise for the error completion function and the stopped completion function.
A completion function has
an associated type known as its \defnadj{completion}{tag}
that is the unqualified type of the completion function.
A valid invocation of a completion function is called
a \defnadj{completion}{operation}.

\pnum
The \defn{lifetime of an asynchronous operation},
also known as the operation's \defn{async lifetime},
begins when its start operation begins executing and
ends when its completion operation begins executing.
If the lifetime of an asynchronous operation's associated operation state
ends before the lifetime of the asynchronous operation,
the behavior is undefined.
After an asynchronous operation executes a completion operation,
its associated operation state is invalid.
Accessing any part of an invalid operation state is undefined behavior.

\pnum
An asynchronous operation shall not execute a completion operation
before its start operation has begun executing.
After its start operation has begun executing,
exactly one completion operation shall execute.
The lifetime of an asynchronous operation's operation state can end
during the execution of the completion operation.

\pnum
A \defn{sender} is a factory for one or more asynchronous operations.
\defnx{Connecting}{connect} a sender and a receiver creates
an asynchronous operation.
The asynchronous operation's associated receiver is equal to
the receiver used to create it, and
its associated environment is equal to
the environment associated with the receiver used to create it.
The lifetime of an asynchronous operation's associated operation state
does not depend on the lifetimes of either the sender or the receiver
from which it was created.
A sender is started when it is connected to a receiver and
the resulting asynchronous operation is started.
A sender's async result is the async result of the asynchronous operation
created by connecting it to a receiver.
A sender sends its results by way of the asynchronous operation(s) it produces,
and a receiver receives those results.
A sender is either valid or invalid;
it becomes invalid when its parent sender (see below) becomes invalid.

\pnum
A \defn{scheduler} is an abstraction of an execution resource
with a uniform, generic interface for scheduling work onto that resource.
It is a factory for senders
whose asynchronous operations execute value completion operations
on an execution agent belonging to
the scheduler's associated execution resource.
A \defn{schedule-expression} obtains such a sender from a scheduler.
A \defn{schedule sender} is the result of a schedule expression.
On success, an asynchronous operation produced by a schedule sender executes
a value completion operation with an empty set of result datums.
Multiple schedulers can refer to the same execution resource.
A scheduler can be valid or invalid.
A scheduler becomes invalid when the execution resource to which it refers
becomes invalid,
as do any schedule senders obtained from the scheduler, and
any operation states obtained from those senders.

\pnum
An asynchronous operation has one or more associated completion schedulers
for each of its possible dispositions.
A \defn{completion scheduler} is a scheduler
whose associated execution resource is used to execute
a completion operation for an asynchronous operation.
A value completion scheduler is a scheduler
on which an asynchronous operation's value completion operation can execute.
Likewise for error completion schedulers and stopped completion schedulers.

\pnum
A sender has an associated queryable object\iref{exec.queryable}
known as its \defnx{attributes}{attribute}
that describes various characteristics of the sender and
of the asynchronous operation(s) it produces.
For each disposition,
there is a query object for reading the associated completion scheduler
from a sender's attributes;
i.e., a value completion scheduler query object
for reading a sender's value completion scheduler, etc.
If a completion scheduler query is well-formed,
the returned completion scheduler is unique
for that disposition for any asynchronous operation the sender creates.
A schedule sender is required to have a value completion scheduler attribute
whose value is equal to the scheduler that produced the schedule sender.

\pnum
A \defn{completion signature} is a function type
that describes a completion operation.
An asynchronous operation has a finite set of possible completion signatures
corresponding to the completion operations
that the asynchronous operation potentially evaluates\iref{basic.def.odr}.
For a completion function \tcode{set},
receiver \tcode{rcvr}, and
pack of arguments \tcode{args},
let \tcode{c} be the completion operation \tcode{set(rcvr, args...)}, and
let \tcode{F} be
the function type \tcode{decltype(auto(set))(decltype((args))...)}.
A completion signature \tcode{Sig} is associated with \tcode{c}
if and only if
\tcode{\exposid{MATCHING-SIG}(Sig, F)} is \tcode{true}\iref{exec.general}.
Together, a sender type and an environment type \tcode{Env} determine
the set of completion signatures of an asynchronous operation
that results from connecting the sender with a receiver
that has an environment of type \tcode{Env}.
The type of the receiver does not affect
an asynchronous operation's completion signatures,
only the type of the receiver's environment.
A \defnadj{non-dependent}{sender} is a sender type
whose completion signatures are knowable
independent of an execution environment.

\pnum
A sender algorithm is a function that takes and/or returns a sender.
There are three categories of sender algorithms:
\begin{itemize}
\item
A \defn{sender factory} is a function
that takes non-senders as arguments and that returns a sender.
\item
A \defn{sender adaptor} is a function
that constructs and returns a parent sender
from a set of one or more child senders and
a (possibly empty) set of additional arguments.
An asynchronous operation created by a parent sender is
a parent operation to the child operations created by the child senders.
\item
A \defn{sender consumer} is a function
that takes one or more senders and
a (possibly empty) set of additional arguments, and
whose return type is not the type of a sender.
\end{itemize}

\rSec1[execution.syn]{Header \tcode{<execution>} synopsis}

\indexheader{execution}%
\begin{codeblock}
namespace std {
  // \ref{execpol.type}, execution policy type trait
  template<class T> struct is_execution_policy;                 // freestanding
  template<class T> constexpr bool @\libglobal{is_execution_policy_v}@ =      // freestanding
      is_execution_policy<T>::value;
}

namespace std::execution {
  // \ref{execpol.seq}, sequenced execution policy
  class sequenced_policy;

  // \ref{execpol.par}, parallel execution policy
  class parallel_policy;

  // \ref{execpol.parunseq}, parallel and unsequenced execution policy
  class parallel_unsequenced_policy;

  // \ref{execpol.unseq}, unsequenced execution policy
  class unsequenced_policy;

  // \ref{execpol.objects}, execution policy objects
  inline constexpr sequenced_policy            seq{ @\unspec@ };
  inline constexpr parallel_policy             par{ @\unspec@ };
  inline constexpr parallel_unsequenced_policy par_unseq{ @\unspec@ };
  inline constexpr unsequenced_policy          unseq{ @\unspec@ };
}

namespace std {
  // \ref{exec.general}, helper concepts
  template<class T>
    concept @\exposconceptnc{movable-value}@ = @\seebelownc@;                          // \expos

  template<class From, class To>
    concept @\defexposconceptnc{decays-to}@ = @\libconcept{same_as}@<decay_t<From>, To>;             // \expos

  template<class T>
    concept @\defexposconceptnc{class-type}@ = @\exposconceptnc{decays-to}@<T, T> && is_class_v<T>;      // \expos

  // \ref{exec.queryable}, queryable objects
  template<class T>
    concept @\exposconceptnc{queryable}@ = @\seebelownc@;                              // \expos

  // \ref{exec.queries}, queries
  struct @\libglobal{forwarding_query_t}@ { @\unspec@ };
  struct @\libglobal{get_allocator_t}@ { @\unspec@ };
  struct @\libglobal{get_stop_token_t}@ { @\unspec@ };

  inline constexpr forwarding_query_t @\libglobal{forwarding_query}@{};
  inline constexpr get_allocator_t @\libglobal{get_allocator}@{};
  inline constexpr get_stop_token_t @\libglobal{get_stop_token}@{};

  template<class T>
    using stop_token_of_t = remove_cvref_t<decltype(get_stop_token(declval<T>()))>;

  template<class T>
    concept @\defexposconceptnc{forwarding-query}@ = forwarding_query(T{});           // \expos
}

namespace std::execution {
  // \ref{exec.queries}, queries
  struct @\libglobal{get_domain_t}@ { @\unspec@ };
  struct @\libglobal{get_scheduler_t}@ { @\unspec@ };
  struct @\libglobal{get_delegation_scheduler_t}@ { @\unspec@ };
  struct @\libglobal{get_forward_progress_guarantee_t}@ { @\unspec@ };
  template<class CPO>
    struct @\libglobal{get_completion_scheduler_t}@ { @\unspec@ };
  struct get_await_completion_adaptor_t { @\unspec@ };

  inline constexpr get_domain_t @\libglobal{get_domain}@{};
  inline constexpr get_scheduler_t @\libglobal{get_scheduler}@{};
  inline constexpr get_delegation_scheduler_t @\libglobal{get_delegation_scheduler}@{};
  enum class forward_progress_guarantee;
  inline constexpr get_forward_progress_guarantee_t @\libglobal{get_forward_progress_guarantee}@{};
  template<class CPO>
    constexpr get_completion_scheduler_t<CPO> @\libglobal{get_completion_scheduler}@{};
  inline constexpr get_await_completion_adaptor_t get_await_completion_adaptor{};

  struct @\libglobal{get_env_t}@ { @\unspec@ };
  inline constexpr get_env_t @\libglobal{get_env}@{};

  template<class T>
    using @\libglobal{env_of_t}@ = decltype(get_env(declval<T>()));

  // \ref{exec.prop}, class template \tcode{prop}
  template<class QueryTag, class ValueType>
    struct prop;

  // \ref{exec.env}, class template \tcode{env}
  template<@\exposconcept{queryable}@... Envs>
    struct env;

  // \ref{exec.domain.default}, execution domains
  struct default_domain;

  // \ref{exec.sched}, schedulers
  struct @\libglobal{scheduler_t}@ {};

  template<class Sch>
    concept @\libconcept{scheduler}@ = @\seebelow@;

  // \ref{exec.recv}, receivers
  struct @\libglobal{receiver_t}@ {};

  template<class Rcvr>
    concept @\libconcept{receiver}@ = @\seebelow@;

  template<class Rcvr, class Completions>
    concept @\libconcept{receiver_of}@ = @\seebelow@;

  struct @\libglobal{set_value_t}@ { @\unspec@ };
  struct @\libglobal{set_error_t}@ { @\unspec@ };
  struct @\libglobal{set_stopped_t}@ { @\unspec@ };

  inline constexpr set_value_t @\libglobal{set_value}@{};
  inline constexpr set_error_t @\libglobal{set_error}@{};
  inline constexpr set_stopped_t @\libglobal{set_stopped}@{};

  // \ref{exec.opstate}, operation states
  struct @\libglobal{operation_state_t}@ {};

  template<class O>
    concept @\libconcept{operation_state}@ = @\seebelow@;

  struct @\libglobal{start_t}@;
  inline constexpr start_t @\libglobal{start}@{};

  // \ref{exec.snd}, senders
  struct @\libglobal{sender_t}@ {};

  template<class Sndr>
    inline constexpr bool enable_sender = @\seebelow@;

  template<class Sndr>
    concept @\libconcept{sender}@ = @\seebelow@;

  template<class Sndr, class... Env>
    concept @\libconcept{sender_in}@ = @\seebelow@;

  template<class Sndr>
    concept @\libconcept{dependent_sender}@ = @\seebelow@;

  template<class Sndr, class Rcvr>
    concept @\libconcept{sender_to}@ = @\seebelow@;

  template<class... Ts>
    struct @\exposidnc{type-list}@;                                           // \expos

  template<class... Ts>
    using @\exposidnc{decayed-tuple}@ = tuple<decay_t<Ts>...>;                // \expos

  template<class... Ts>
    using @\exposidnc{variant-or-empty}@ = @\seebelownc@;                         // \expos

  template<class Sndr, class Env = env<>,
           template<class...> class Tuple = @\exposid{decayed-tuple}@,
           template<class...> class Variant = @\exposid{variant-or-empty}@>
      requires @\libconcept{sender_in}@<Sndr, Env>
    using value_types_of_t = @\seebelow@;

  template<class Sndr, class Env = env<>,
           template<class...> class Variant = @\exposid{variant-or-empty}@>
      requires @\libconcept{sender_in}@<Sndr, Env>
    using error_types_of_t = @\seebelow@;

  template<class Sndr, class Env = env<>>
      requires @\libconcept{sender_in}@<Sndr, Env>
    constexpr bool sends_stopped = @\seebelow@;

  template<class Sndr, class... Env>
    using @\exposidnc{single-sender-value-type}@ = @\seebelownc@;                 // \expos

  template<class Sndr, class... Env>
    concept @\exposconcept{single-sender}@ = @\seebelow@; // \expos

  template<@\libconcept{sender}@ Sndr>
    using tag_of_t = @\seebelow@;

  // \ref{exec.snd.transform}, sender transformations
  template<class Domain, @\libconcept{sender}@ Sndr, @\exposconcept{queryable}@... Env>
      requires (sizeof...(Env) <= 1)
    constexpr @\libconcept{sender}@ decltype(auto) transform_sender(
      Domain dom, Sndr&& sndr, const Env&... env) noexcept(@\seebelow@);

  // \ref{exec.snd.transform.env}, environment transformations
  template<class Domain, @\libconcept{sender}@ Sndr, @\exposconcept{queryable}@ Env>
    constexpr @\exposconcept{queryable}@ decltype(auto) transform_env(
      Domain dom, Sndr&& sndr, Env&& env) noexcept;

  // \ref{exec.snd.apply}, sender algorithm application
  template<class Domain, class Tag, @\libconcept{sender}@ Sndr, class... Args>
    constexpr decltype(auto) apply_sender(
      Domain dom, Tag, Sndr&& sndr, Args&&... args) noexcept(@\seebelow@);

  // \ref{exec.connect}, the connect sender algorithm
  struct @\libglobal{connect_t}@;
  inline constexpr connect_t @\libglobal{connect}@{};

  template<class Sndr, class Rcvr>
    using @\libglobal{connect_result_t}@ =
      decltype(connect(declval<Sndr>(), declval<Rcvr>()));

  // \ref{exec.factories}, sender factories
  struct @\libglobal{just_t}@ { @\unspec@ };
  struct @\libglobal{just_error_t}@ { @\unspec@ };
  struct @\libglobal{just_stopped_t}@ { @\unspec@ };
  struct @\libglobal{schedule_t}@ { @\unspec@ };

  inline constexpr just_t @\libglobal{just}@{};
  inline constexpr just_error_t @\libglobal{just_error}@{};
  inline constexpr just_stopped_t @\libglobal{just_stopped}@{};
  inline constexpr schedule_t @\libglobal{schedule}@{};
  inline constexpr @\unspec@ @\libglobal{read_env}@{};

  template<@\libconcept{scheduler}@ Sch>
    using @\libglobal{schedule_result_t}@ = decltype(schedule(declval<Sch>()));

  // \ref{exec.adapt}, sender adaptors
  template<@\exposconcept{class-type}@ D>
    struct @\libglobal{sender_adaptor_closure}@ { };

  struct @\libglobal{starts_on_t}@ { @\unspec@ };
  struct @\libglobal{continues_on_t}@ { @\unspec@ };
  struct @\libglobal{on_t}@ { @\unspec@ };
  struct @\libglobal{schedule_from_t}@ { @\unspec@ };
  struct @\libglobal{then_t}@ { @\unspec@ };
  struct @\libglobal{upon_error_t}@ { @\unspec@ };
  struct @\libglobal{upon_stopped_t}@ { @\unspec@ };
  struct @\libglobal{let_value_t}@ { @\unspec@ };
  struct @\libglobal{let_error_t}@ { @\unspec@ };
  struct @\libglobal{let_stopped_t}@ { @\unspec@ };
  struct @\libglobal{bulk_t}@ { @\unspec@ };
  struct @\libglobal{bulk_chunked_t}@ { @\unspec@ };
  struct @\libglobal{bulk_unchunked_t}@ { @\unspec@ };
  struct @\libglobal{when_all_t}@ { @\unspec@ };
  struct @\libglobal{when_all_with_variant_t}@ { @\unspec@ };
  struct @\libglobal{into_variant_t}@ { @\unspec@ };
  struct @\libglobal{stopped_as_optional_t}@ { @\unspec@ };
  struct @\libglobal{stopped_as_error_t}@ { @\unspec@ };
  struct @\libglobal{associate_t}@ { @\unspec@ };
  struct @\libglobal{spawn_future_t}@ { @\unspec@ };

  inline constexpr @\unspec@ @\libglobal{write_env}@{};
  inline constexpr @\unspec@ @\libglobal{unstoppable}@{};
  inline constexpr starts_on_t @\libglobal{starts_on}@{};
  inline constexpr continues_on_t @\libglobal{continues_on}@{};
  inline constexpr on_t @\libglobal{on}@{};
  inline constexpr schedule_from_t @\libglobal{schedule_from}@{};
  inline constexpr then_t @\libglobal{then}@{};
  inline constexpr upon_error_t @\libglobal{upon_error}@{};
  inline constexpr upon_stopped_t @\libglobal{upon_stopped}@{};
  inline constexpr let_value_t @\libglobal{let_value}@{};
  inline constexpr let_error_t @\libglobal{let_error}@{};
  inline constexpr let_stopped_t @\libglobal{let_stopped}@{};
  inline constexpr bulk_t @\libglobal{bulk}@{};
  inline constexpr bulk_chunked_t @\libglobal{bulk_chunked}@{};
  inline constexpr bulk_unchunked_t @\libglobal{bulk_unchunked}@{};
  inline constexpr when_all_t @\libglobal{when_all}@{};
  inline constexpr when_all_with_variant_t @\libglobal{when_all_with_variant}@{};
  inline constexpr into_variant_t @\libglobal{into_variant}@{};
  inline constexpr stopped_as_optional_t @\libglobal{stopped_as_optional}@{};
  inline constexpr stopped_as_error_t @\libglobal{stopped_as_error}@{};
  inline constexpr associate_t @\libglobal{associate}@{};
  inline constexpr spawn_future_t @\libglobal{spawn_future}@{};

  // \ref{exec.cmplsig}, completion signatures
  template<class Fn>
    concept @\exposconceptnc{completion-signature}@ = @\seebelownc@;                   // \expos

  template<@\exposconcept{completion-signature}@... Fns>
    struct @\libglobal{completion_signatures}@;

  template<class Sigs>
    concept @\exposconceptnc{valid-completion-signatures}@ = @\seebelownc@;            // \expos

  struct dependent_sender_error : exception {};

  // \ref{exec.getcomplsigs}, get completion signatures
  template<class Sndr, class... Env>
    consteval auto get_completion_signatures() -> @\exposconcept{valid-completion-signatures}@ auto;

  template<class Sndr, class... Env>
      requires @\libconcept{sender_in}@<Sndr, Env...>
    using completion_signatures_of_t = decltype(get_completion_signatures<Sndr, Env...>());

  // \ref{exec.run.loop}, run_loop
  class run_loop;
}

namespace std::this_thread {
  // \ref{exec.consumers}, consumers
  struct @\libglobal{sync_wait_t}@ { @\unspec@ };
  struct @\libglobal{sync_wait_with_variant_t}@ { @\unspec@ };

  inline constexpr sync_wait_t @\libglobal{sync_wait}@{};
  inline constexpr sync_wait_with_variant_t @\libglobal{sync_wait_with_variant}@{};
}

namespace std::execution {
  // \ref{exec.consumers}, consumers
  struct @\libglobal{spawn_t}@ { @\unspec@ };
  inline constexpr spawn_t spawn{};

  // \ref{exec.as.awaitable}, coroutine utility \tcode{as_awaitable}
  struct @\libglobal{as_awaitable_t}@ { @\unspec@ };
  inline constexpr as_awaitable_t @\libglobal{as_awaitable}@{};

  // \ref{exec.with.awaitable.senders}, coroutine utility \tcode{with_awaitable_senders}
  template<@\exposconcept{class-type}@ Promise>
    struct with_awaitable_senders;

  // \ref{exec.scope.concepts}, scope concepts
  template<class Token>
    concept @\libconcept{scope_token}@ = @\seebelow@;

  // \ref{exec.scope.simple.counting}, simple counting scope
  class simple_counting_scope;

  // \ref{exec.scope.counting}, counting scope
  class counting_scope;
}

namespace std::execution {
  // \ref{exec.par.scheduler}, parallel scheduler
  class @\libglobal{parallel_scheduler}@ { @\unspec@ };
  parallel_scheduler get_parallel_scheduler();
}

// \ref{exec.sysctxrepl}, namespace \tcode{system_context_replaceability}
namespace std::execution::@\libglobal{system_context_replaceability}@ {
  struct receiver_proxy;
  struct bulk_item_receiver_proxy;
  struct parallel_scheduler_backend;

  shared_ptr<parallel_scheduler_backend> query_parallel_scheduler_backend();
}

namespace std::execution {
  // \ref{exec.affine.on}, coroutine utility \tcode{affine_on}
  struct @\libglobal{affine_on_t}@ { @\unspec@ };
  inline constexpr affine_on_t @\libglobal{affine_on}@{};

  // \ref{exec.inline.scheduler}, inline scheduler
  class @\libglobal{inline_scheduler}@;

  // \ref{exec.task.scheduler}, task scheduler
  class @\libglobal{task_scheduler}@;

  template<class E>
  struct @\libglobal{with_error}@ {
    using type = remove_cvref_t<E>;
    type error;
  };
  template<class E>
    with_error(E) -> with_error<E>;

  template<@\libconcept{scheduler}@ Sch>
  struct change_coroutine_scheduler {
    using type = remove_cvref_t<Sch>;
    type scheduler;
  };
  template<@\libconcept{scheduler}@ Sch>
    change_coroutine_scheduler(Sch) -> change_coroutine_scheduler<Sch>;

  // \ref{exec.task}, class template \tcode{task}
  template<class T, class Environment>
    class @\libglobal{task}@;
}
\end{codeblock}

\pnum
The exposition-only type \tcode{\exposid{variant-or-empty}<Ts...>}
is defined as follows:
\begin{itemize}
\item
If \tcode{sizeof...(Ts)} is greater than zero,
\tcode{\exposid{variant-or-empty}<Ts...>} denotes \tcode{variant<Us...>}
where \tcode{Us...} is the pack \tcode{decay_t<Ts>...}
with duplicate types removed.
\item
Otherwise, \tcode{\exposid{variant-or-empty}<Ts...>} denotes
the exposition-only class type:
\begin{codeblock}
namespace std::execution {
  struct @\exposidnc{empty-variant}@ {        // \expos
    @\exposidnc{empty-variant}@() = delete;
  };
}
\end{codeblock}
\end{itemize}

\pnum
For type \tcode{Sndr} and pack of types \tcode{Env},
let \tcode{CS} be \tcode{completion_signatures_of_t<Sndr, Env...>}.
Then \tcode{\exposid{single-sender-value-type}<Sndr, Env...>} is ill-formed
if \tcode{CS} is ill-formed or
if \tcode{sizeof...(Env) > 1} is \tcode{true};
otherwise, it is an alias for:
\begin{itemize}
\item
\tcode{\exposid{gather-signatures}<set_value_t, CS, decay_t, type_identity_t>}
if that type is well-formed,
\item
Otherwise, \tcode{void}
if \tcode{\exposid{gather-signatures}<set_value_t, CS, tuple, variant>} is
\tcode{variant<tuple<>>} or \tcode{variant<>},
\item
Otherwise, \tcode{\exposid{gather-signatures}<set_value_t, CS, \exposid{decayed-tuple}, type_identity_t>}
if that\linebreak{} type is well-formed,
\item
Otherwise, \tcode{\exposid{single-sender-value-type}<Sndr, Env...>} is ill-formed.
\end{itemize}

\pnum
The exposition-only concept \exposconcept{single-sender} is defined as follows:
\begin{codeblock}
namespace std::execution {
  template<class Sndr, class... Env>
    concept @\defexposconcept{single-sender}@ = @\libconcept{sender_in}@<Sndr, Env...> &&
      requires {
        typename @\exposid{single-sender-value-type}@<Sndr, Env...>;
      };
}
\end{codeblock}

\pnum
A type satisfies and models the exposition-only concept
\defexposconcept{valid-completion-signatures} if
it is a specialization of the \tcode{completion_signatures} class template.

\rSec1[exec.queries]{Queries}

\rSec2[exec.fwd.env]{\tcode{forwarding_query}}

\pnum
\tcode{forwarding_query} asks a query object
whether it should be forwarded through queryable adaptors.

\pnum
The name \tcode{forwarding_query} denotes a query object.
For some query object \tcode{q} of type \tcode{Q},
\tcode{forwarding_query(q)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{\exposid{MANDATE-NOTHROW}(q.query(forwarding_query))}
if that expression is well-formed.

\mandates
The expression above has type \tcode{bool} and
is a core constant expression if \tcode{q} is a core constant expression.
\item
Otherwise, \tcode{true} if \tcode{\libconcept{derived_from}<Q, forwarding_query_t>} is \tcode{true}.
\item
Otherwise, \tcode{false}.
\end{itemize}

\rSec2[exec.get.allocator]{\tcode{get_allocator}}

\pnum
\tcode{get_allocator} asks a queryable object for its associated allocator.

\pnum
The name \tcode{get_allocator} denotes a query object.
For a subexpression \tcode{env},
\tcode{get_allocator(env)} is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(env).query(get_allocator))}.

\mandates
If the expression above is well-formed,
its type satisfies
\exposconcept{simple-allocator}\iref{allocator.requirements.general}.

\pnum
\tcode{forwarding_query(get_allocator)} is a core constant expression and
has value \tcode{true}.

\rSec2[exec.get.stop.token]{\tcode{get_stop_token}}

\pnum
\tcode{get_stop_token} asks a queryable object for an associated stop token.

\pnum
The name \tcode{get_stop_token} denotes a query object.
For a subexpression \tcode{env},
\tcode{get_stop_token(env)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(env).query(get_stop_token))}
if that expression is well-formed.

\mandates
The type of the expression above satisfies \libconcept{stoppable_token}.

\item
Otherwise, \tcode{never_stop_token\{\}}.
\end{itemize}

\pnum
\tcode{forwarding_query(get_stop_token)} is a core constant expression and
has value \tcode{true}.

\rSec2[exec.get.env]{\tcode{execution::get_env}}

\pnum
\tcode{execution::get_env} is a customization point object.
For a subexpression \tcode{o},
\tcode{execution::get_env(o)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(o).get_env())}
if that expression is well-formed.

\mandates
The type of the expression above satisfies
\exposconcept{queryable}\iref{exec.queryable}.
\item
Otherwise, \tcode{env<>\{\}}.
\end{itemize}

\pnum
The value of \tcode{get_env(o)} shall be valid while \tcode{o} is valid.

\pnum
\begin{note}
When passed a sender object,
\tcode{get_env} returns the sender's associated attributes.
When passed a receiver,
\tcode{get_env} returns the receiver's associated execution environment.
\end{note}

\rSec2[exec.get.domain]{\tcode{execution::get_domain}}

\pnum
\tcode{get_domain} asks a queryable object
for its associated execution domain tag.

\pnum
The name \tcode{get_domain} denotes a query object.
For a subexpression \tcode{env},
\tcode{get_domain(env)} is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(env).query(get_domain))}.

\pnum
\tcode{forwarding_query(execution::get_domain)} is
a core constant expression and has value \tcode{true}.

\rSec2[exec.get.scheduler]{\tcode{execution::get_scheduler}}

\pnum
\tcode{get_scheduler} asks a queryable object for its associated scheduler.

\pnum
The name \tcode{get_scheduler} denotes a query object.
For a subexpression \tcode{env},
\tcode{get_scheduler(env)} is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(env).query(get_scheduler))}.

\mandates
If the expression above is well-formed,
its type satisfies \libconcept{scheduler}.

\pnum
\tcode{forwarding_query(execution::get_scheduler)} is
a core constant expression and has value \tcode{true}.

\rSec2[exec.get.delegation.scheduler]{\tcode{execution::get_delegation_scheduler}}

\pnum
\tcode{get_delegation_scheduler} asks a queryable object for a scheduler
that can be used to delegate work to
for the purpose of forward progress delegation\iref{intro.progress}.

\pnum
The name \tcode{get_delegation_scheduler} denotes a query object.
For a subexpression \tcode{env},
\tcode{get_delegation_scheduler(env)} is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(env).query(get_delegation_scheduler))}.

\mandates
If the expression above is well-formed,
its type satisfies \libconcept{scheduler}.

\pnum
\tcode{forwarding_query(execution::get_delegation_scheduler)} is
a core constant expression and has value \tcode{true}.

\rSec2[exec.get.fwd.progress]{\tcode{execution::get_forward_progress_guarantee}}

\begin{codeblock}
namespace std::execution {
  enum class @\libglobal{forward_progress_guarantee}@ {
    concurrent,
    parallel,
    weakly_parallel
  };
}
\end{codeblock}

\pnum
\tcode{get_forward_progress_guarantee} asks a scheduler about
the forward progress guarantee of execution agents
created by that scheduler's associated execution resource\iref{intro.progress}.

\pnum
The name \tcode{get_forward_progress_guarantee} denotes a query object.
For a subexpression \tcode{sch}, let \tcode{Sch} be \tcode{decltype((sch))}.
If \tcode{Sch} does not satisfy \libconcept{scheduler},
\tcode{get_forward_progress_guarantee} is ill-formed.
Otherwise,
\tcode{get_forward_progress_guarantee(sch)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{\exposid{MANDATE-NOTHROW}(\exposid{AS-CONST}(sch).query(get_forward_progress_guarantee))},
if that expression is well-formed.

\mandates
The type of the expression above is \tcode{forward_progress_guarantee}.
\item
Otherwise, \tcode{forward_progress_guarantee::weakly_parallel}.
\end{itemize}

\pnum
If \tcode{get_forward_progress_guarantee(sch)} for some scheduler \tcode{sch}
returns \tcode{forward_progress_guaran\-tee::concurrent},
all execution agents created by that scheduler's associated execution resource
shall provide the concurrent forward progress guarantee.
If it returns \tcode{forward_progress_guarantee::parallel},
all such execution agents
shall provide at least the parallel forward progress guarantee.

\rSec2[exec.get.compl.sched]{\tcode{execution::get_completion_scheduler}}

\pnum
\tcode{get_completion_scheduler<\exposid{completion-tag>}} obtains
the completion scheduler associated with a completion tag
from a sender's attributes.

\pnum
The name \tcode{get_completion_scheduler} denotes a query object template.
For a subexpression \tcode{q},
the expression \tcode{get_completion_scheduler<\exposid{completion-tag}>(q)}
is ill-formed if \exposid{completion-tag} is not one of
\tcode{set_value_t}, \tcode{set_error_t}, or \tcode{set_stopped_t}.
Otherwise, \tcode{get_completion_scheduler<\exposid{completion-tag}>(q)}
is expression-equivalent to
\begin{codeblock}
@\exposid{MANDATE-NOTHROW}@(@\exposid{AS-CONST}@(q).query(get_completion_scheduler<@\exposid{completion-tag}@>))
\end{codeblock}
\mandates
If the expression above is well-formed,
its type satisfies \libconcept{scheduler}.

\pnum
Let \exposid{completion-fn} be a completion function\iref{exec.async.ops};
let \exposid{completion-tag} be
the associated completion tag of \exposid{completion-fn};
let \tcode{args} be a pack of subexpressions; and
let \tcode{sndr} be a subexpression
such that \tcode{\libconcept{sender}<decltype((sndr))>} is \tcode{true} and
\tcode{get_completion_scheduler<\exposid{completion-tag}>(get_env(sndr))}
is well-formed and denotes a scheduler \tcode{sch}.
If an asynchronous operation
created by connecting \tcode{sndr} with a receiver \tcode{rcvr}
causes the evaluation of \tcode{\exposid{completion-fn}(rcvr, args...)},
the behavior is undefined
unless the evaluation happens on an execution agent
that belongs to \tcode{sch}'s associated execution resource.

\pnum
The expression
\tcode{forwarding_query(get_completion_scheduler<\exposid{completion-tag}>)}
is a core constant expression and has value \tcode{true}.

\rSec2[exec.get.await.adapt]{\tcode{execution::get_await_completion_adaptor}}

\pnum
\tcode{get_await_completion_adaptor} asks a queryable object for
its associated awaitable completion adaptor.

\pnum
The name \tcode{get_await_completion_adaptor} denotes a query object.
For a subexpression \tcode{env},
\begin{codeblock}
get_await_completion_adaptor(env)
\end{codeblock}
is expression-equivalent to
\begin{codeblock}
@\exposidnc{MANDATE-NOTHROW}@(@\exposid{AS-CONST}@(env).query(get_await_completion_adaptor))
\end{codeblock}

\pnum
\tcode{forwarding_query(execution::get_await_completion_adaptor)}
is a core constant expression and has value \tcode{true}.

\rSec1[exec.sched]{Schedulers}

\pnum
The \libconcept{scheduler} concept defines
the requirements of a scheduler type\iref{exec.async.ops}.
\tcode{schedule} is a customization point object
that accepts a scheduler.
A valid invocation of \tcode{schedule} is a schedule-expression.
\begin{codeblock}
namespace std::execution {
  template<class Sch>
    concept @\deflibconcept{scheduler}@ =
      @\libconcept{derived_from}@<typename remove_cvref_t<Sch>::scheduler_concept, scheduler_t> &&
      @\exposconcept{queryable}@<Sch> &&
      requires(Sch&& sch) {
        { schedule(std::forward<Sch>(sch)) } -> @\libconcept{sender}@;
        { auto(get_completion_scheduler<set_value_t>(
            get_env(schedule(std::forward<Sch>(sch))))) }
              -> @\libconcept{same_as}@<remove_cvref_t<Sch>>;
      } &&
      @\libconcept{equality_comparable}@<remove_cvref_t<Sch>> &&
      @\libconcept{copyable}@<remove_cvref_t<Sch>>;
}
\end{codeblock}

\pnum
Let \tcode{Sch} be the type of a scheduler and
let \tcode{Env} be the type of an execution environment
for which \tcode{\libconcept{sender_in}<schedule_result_t<Sch>, Env>}
is satisfied.
Then \tcode{\exposconcept{sender-in-of}<schedule_result_t<Sch>, Env>}
shall be modeled.

\pnum
No operation required by
\tcode{\libconcept{copyable}<remove_cvref_t<Sch>>} and
\tcode{\libconcept{equality_comparable}<remove_cvref_t<Sch>>}
shall exit via an exception.
None of these operations,
nor a scheduler type's \tcode{schedule} function,
shall introduce data races
as a result of potentially concurrent\iref{intro.races} invocations
of those operations from different threads.

\pnum
For any two values \tcode{sch1} and \tcode{sch2}
of some scheduler type \tcode{Sch},
\tcode{sch1 == sch2} shall return \tcode{true}
only if both \tcode{sch1} and \tcode{sch2} share
the same associated execution resource.

\pnum
For a given scheduler expression \tcode{sch},
the expression
\tcode{get_completion_scheduler<set_value_t>(get_env(schedule(sch)))}
shall compare equal to \tcode{sch}.

\pnum
For a given scheduler expression \tcode{sch},
if the expression \tcode{get_domain(sch)} is well-formed,
then the expression \tcode{get_domain(get_env(schedule(sch)))}
is also well-formed and has the same type.

\pnum
A scheduler type's destructor shall not block
pending completion of any receivers
connected to the sender objects returned from \tcode{schedule}.
\begin{note}
The ability to wait for completion of submitted function objects
can be provided by the associated execution resource of the scheduler.
\end{note}

\rSec1[exec.recv]{Receivers}

\rSec2[exec.recv.concepts]{Receiver concepts}

\pnum
A receiver represents the continuation of an asynchronous operation.
The \libconcept{receiver} concept defines
the requirements for a receiver type\iref{exec.async.ops}.
The \libconcept{receiver_of} concept defines
the requirements for a receiver type that is usable as
the first argument of a set of completion operations
corresponding to a set of completion signatures.
The \tcode{get_env} customization point object is used to access
a receiver's associated environment.
\begin{codeblock}
namespace std::execution {
  template<class Rcvr>
    concept @\deflibconcept{receiver}@ =
      @\libconcept{derived_from}@<typename remove_cvref_t<Rcvr>::receiver_concept, receiver_t> &&
      requires(const remove_cvref_t<Rcvr>& rcvr) {
        { get_env(rcvr) } -> @\exposconcept{queryable}@;
      } &&
      @\libconcept{move_constructible}@<remove_cvref_t<Rcvr>> &&       // rvalues are movable, and
      @\libconcept{constructible_from}@<remove_cvref_t<Rcvr>, Rcvr>;   // lvalues are copyable

  template<class Signature, class Rcvr>
    concept @\defexposconcept{valid-completion-for}@ =                 // \expos
      requires (Signature* sig) {
        []<class Tag, class... Args>(Tag(*)(Args...))
            requires @\exposconcept{callable}@<Tag, remove_cvref_t<Rcvr>, Args...>
        {}(sig);
      };

  template<class Rcvr, class Completions>
    concept @\defexposconcept{has-completions}@ =                      // \expos
      requires (Completions* completions) {
        []<@\exposconcept{valid-completion-for}@<Rcvr>...Sigs>(completion_signatures<Sigs...>*)
        {}(completions);
      };

  template<class Rcvr, class Completions>
    concept @\deflibconcept{receiver_of}@ =
      @\libconcept{receiver}@<Rcvr> && @\exposconcept{has-completions}@<Rcvr, Completions>;
}
\end{codeblock}

\pnum
Class types that are marked \tcode{final} do not model the \libconcept{receiver} concept.

\pnum
Let \tcode{rcvr} be a receiver and
let \tcode{op_state} be an operation state associated with
an asynchronous operation created by connecting \tcode{rcvr} with a sender.
Let \tcode{token} be a stop token equal to
\tcode{get_stop_token(get_env(rcvr))}.
\tcode{token} shall remain valid
for the duration of the asynchronous operation's lifetime\iref{exec.async.ops}.
\begin{note}
This means that, unless it knows about further guarantees
provided by the type of \tcode{rcvr},
the implementation of \tcode{op_state} cannot use \tcode{token}
after it executes a completion operation.
This also implies that any stop callbacks registered on token
must be destroyed before the invocation of the completion operation.
\end{note}

\rSec2[exec.set.value]{\tcode{execution::set_value}}

\pnum
\tcode{set_value} is a value completion function\iref{exec.async.ops}.
Its associated completion tag is \tcode{set_value_t}.
The expression \tcode{set_value(rcvr, vs...)}
for a subexpression \tcode{rcvr} and
pack of subexpressions \tcode{vs} is ill-formed
if \tcode{rcvr} is an lvalue or an rvalue of const type.
Otherwise, it is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(rcvr.set_value(vs...))}.

\rSec2[exec.set.error]{\tcode{execution::set_error}}

\pnum
\tcode{set_error} is an error completion function\iref{exec.async.ops}.
Its associated completion tag is \tcode{set_error_t}.
The expression \tcode{set_error(rcvr, err)}
for some subexpressions \tcode{rcvr} and \tcode{err} is ill-formed
if \tcode{rcvr} is an lvalue or an rvalue of const type.
Otherwise, it is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(rcvr.set_error(err))}.

\rSec2[exec.set.stopped]{\tcode{execution::set_stopped}}

\pnum
\tcode{set_stopped} is a stopped completion function\iref{exec.async.ops}.
Its associated completion tag is \tcode{set_stopped_t}.
The expression \tcode{set_stopped(rcvr)}
for a subexpression \tcode{rcvr} is ill-formed
if \tcode{rcvr} is an lvalue or an rvalue of const type.
Otherwise, it is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(rcvr.set_stopped())}.

\rSec1[exec.opstate]{Operation states}

\rSec2[exec.opstate.general]{General}

\pnum
The \libconcept{operation_state} concept defines
the requirements of an operation state type\iref{exec.async.ops}.
\begin{codeblock}
namespace std::execution {
  template<class O>
    concept @\deflibconcept{operation_state}@ =
      @\libconcept{derived_from}@<typename O::operation_state_concept, operation_state_t> &&
      requires (O& o) {
        start(o);
      };
}
\end{codeblock}

\pnum
If an \libconcept{operation_state} object is destroyed
during the lifetime of its asynchronous operation\iref{exec.async.ops},
the behavior is undefined.
\begin{note}
The \libconcept{operation_state} concept does not impose requirements
on any operations other than destruction and \tcode{start},
including copy and move operations.
Invoking any such operation on an object
whose type models \libconcept{operation_state} can lead to undefined behavior.
\end{note}

\pnum
The program is ill-formed
if it performs a copy or move construction or assignment operation on
an operation state object created by connecting a library-provided sender.

\rSec2[exec.opstate.start]{\tcode{execution::start}}

\pnum
The name \tcode{start} denotes a customization point object
that starts\iref{exec.async.ops}
the asynchronous operation associated with the operation state object.
For a subexpression \tcode{op},
the expression \tcode{start(op)} is ill-formed
if \tcode{op} is an rvalue.
Otherwise, it is expression-equivalent to
\tcode{\exposid{MANDATE-NOTHROW}(op.start())}.

\pnum
If \tcode{op.start()} does not start\iref{exec.async.ops}
the asynchronous operation associated with the operation state \tcode{op},
the behavior of calling \tcode{start(op)} is undefined.

\rSec1[exec.snd]{Senders}

\rSec2[exec.snd.general]{General}

\pnum
Subclauses \ref{exec.factories} and \ref{exec.adapt} define
customizable algorithms that return senders.
Each algorithm has a default implementation.
Let \tcode{sndr} be the result of an invocation of such an algorithm or
an object equal to the result\iref{concepts.equality}, and
let \tcode{Sndr} be \tcode{decltype((sndr))}.
Let \tcode{rcvr} be a receiver of type \tcode{Rcvr}
with associated environment \tcode{env} of type \tcode{Env}
such that \tcode{\libconcept{sender_to}<Sndr, Rcvr>} is \tcode{true}.
For the default implementation of the algorithm that produced \tcode{sndr},
connecting \tcode{sndr} to \tcode{rcvr} and
starting the resulting operation state\iref{exec.async.ops}
necessarily results in the potential evaluation\iref{basic.def.odr} of
a set of completion operations
whose first argument is a subexpression equal to \tcode{rcvr}.
Let \tcode{Sigs} be a pack of completion signatures corresponding to
this set of completion operations, and
let \tcode{CS} be
the type of the expression \tcode{get_completion_signatures<Sndr, Env>()}.
Then \tcode{CS} is
a specialization of
the class template \tcode{completion_signatures}\iref{exec.cmplsig},
the set of whose template arguments is \tcode{Sigs}.
If none of the types in \tcode{Sigs} are dependent on the type \tcode{Env}, then
the expression \tcode{get_completion_signatures<Sndr>()} is well-formed and
its type is \tcode{CS}.
If a user-provided implementation of the algorithm
that produced \tcode{sndr} is selected instead of the default:

\begin{itemize}
\item
Any completion signature
that is in the set of types
denoted by \tcode{completion_signatures_of_t<Sndr, Env>} and
that is not part of \tcode{Sigs} shall correspond to
error or stopped completion operations,
unless otherwise specified.

\item
If none of the types in \tcode{Sigs} are dependent on the type \tcode{Env}, then
\tcode{completion_signatures_of_t<Sndr>} and
\tcode{completion_signatures_of_t<Sndr, Env>}
shall denote the same type.
\end{itemize}

\rSec2[exec.snd.expos]{Exposition-only entities}

\pnum
Subclause \ref{exec.snd} makes use of the following exposition-only entities.

\pnum
\indexlibraryglobal{\exposid{FWD-ENV}}%
For a queryable object \tcode{env},
\tcode{\exposid{FWD-ENV}(env)} is an expression
whose type satisfies \exposconcept{queryable}
such that for a query object \tcode{q} and
a pack of subexpressions \tcode{as},
the expression \tcode{\exposid{FWD-ENV}(env).query(q, as...)} is ill-formed
if \tcode{forwarding_query(q)} is \tcode{false};
otherwise, it is expression-equivalent to \tcode{env.query(q, as...)}.
\indexlibraryglobal{\exposid{FWD-ENV-T}}%
The type \tcode{\exposid{FWD-ENV-T}(Env)} is
\tcode{decltype(\exposid{FWD-ENV}(declval<Env>()))}.

\pnum
For a query object \tcode{q} and a subexpression \tcode{v},
\tcode{\exposid{MAKE-ENV}(q, v)} is an expression \tcode{env}
whose type satisfies \exposconcept{queryable}
such that the result of \tcode{env.query(q)} has
a value equal to \tcode{v}\iref{concepts.equality}.
Unless otherwise stated,
the object to which \tcode{env.query(q)} refers remains valid
while \tcode{env} remains valid.

\pnum
For two queryable objects \tcode{env1} and \tcode{env2},
a query object \tcode{q}, and
a pack of subexpressions \tcode{as},
\tcode{\exposid{JOIN-ENV}(env1, env2)} is an expression \tcode{env3}
whose type satisfies \exposconcept{queryable}
such that \tcode{env3.query(q, as...)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{env1.query(q, as...)} if that expression is well-formed,
\item
otherwise, \tcode{env2.query(q, as...)} if that expression is well-formed,
\item
otherwise, \tcode{env3.query(q, as...)} is ill-formed.
\end{itemize}

\pnum
The results of \exposid{FWD-ENV}, \exposid{MAKE-ENV}, and \exposid{JOIN-ENV}
can be context-dependent;
i.e., they can evaluate to expressions
with different types and value categories
in different contexts for the same arguments.

\pnum
For a scheduler \tcode{sch},
\tcode{\exposid{SCHED-ATTRS}(sch)} is an expression \tcode{o1}
whose type satisfies \exposconcept{queryable}
such that \tcode{o1.query(get_completion_scheduler<Tag>)} is
an expression with the same type and value as \tcode{sch}
where \tcode{Tag} is one of \tcode{set_value_t} or \tcode{set_stopped_t}, and
such that \tcode{o1.query(get_domain)} is expression-equivalent to
\tcode{sch.query(get_domain)}.
\tcode{\exposid{SCHED-ENV}(sch)} is an expression \tcode{o2}
whose type satisfies \exposconcept{queryable}
such that \tcode{o2.query(get_scheduler)} is a prvalue
with the same type and value as \tcode{sch}, and
such that \tcode{o2.query(get_domain)} is expression-equivalent to
\tcode{sch.query(get_domain)}.

\pnum
For two subexpressions \tcode{rcvr} and \tcode{expr},
\tcode{\exposid{SET-VALUE}(rcvr, expr)} is expression-equivalent to
\tcode{(expr, set_value(std::move(rcvr)))}
if the type of \tcode{expr} is \tcode{void};
otherwise, \tcode{set_value(std::move(rcvr), expr)}.
\tcode{\exposid{TRY-EVAL}(rcvr, expr)} is equivalent to:
\begin{codeblock}
try {
  expr;
} catch(...) {
  set_error(std::move(rcvr), current_exception());
}
\end{codeblock}
if \tcode{expr} is potentially-throwing; otherwise, \tcode{expr}.
\tcode{\exposid{TRY-SET-VALUE}(rcvr, expr)} is
\begin{codeblock}
@\exposid{TRY-EVAL}@(rcvr, @\exposid{SET-VALUE}@(rcvr, expr))
\end{codeblock}
except that \tcode{rcvr} is evaluated only once.

\begin{itemdecl}
template<class Default = default_domain, class Sndr>
  constexpr auto @\exposid{completion-domain}@(const Sndr& sndr) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\tcode{\exposid{COMPL-DOMAIN}(T)} is the type of the expression
\tcode{get_domain(get_completion_scheduler<T>(get_env(sndr)))}.

\pnum
\effects
If all of the types
\tcode{\exposid{COMPL-DOMAIN}(set_value_t)},
\tcode{\exposid{COMPL-DOMAIN}(set_error_t)}, and\linebreak
\tcode{\exposid{COMPL-DOMAIN}(set_stopped_t)} are ill-formed,
\tcode{completion-domain<Default>(sndr)} is
a default-constructed prvalue of type \tcode{Default}.
Otherwise, if they all share a common type\iref{meta.trans.other}
(ignoring those types that are ill-formed),
then \tcode{\exposid{completion-domain}<Default>(sndr)} is
a default-constructed prvalue of that type.
Otherwise, \tcode{\exposid{completion-domain}<Default>(sndr)} is ill-formed.
\end{itemdescr}

\begin{itemdecl}
template<class Tag, class Env, class Default>
  constexpr decltype(auto) @\exposid{query-with-default}@(
    Tag, const Env& env, Default&& value) noexcept(@\seebelow@);
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{e} be the expression \tcode{Tag()(env)}
if that expression is well-formed;
otherwise, it is \tcode{static_cast<Default>(std::forward<Default>(value))}.

\pnum
\returns
\tcode{e}.

\pnum
\remarks
The expression in the noexcept clause is \tcode{noexcept(e)}.
\end{itemdescr}

\begin{itemdecl}
template<class Sndr>
  constexpr auto @\exposid{get-domain-early}@(const Sndr& sndr) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
return Domain();
\end{codeblock}
where \tcode{Domain} is
the decayed type of the first of the following expressions that is well-formed:
\begin{itemize}
\item \tcode{get_domain(get_env(sndr))}
\item \tcode{\exposid{completion-domain}(sndr)}
\item \tcode{default_domain()}
\end{itemize}
\end{itemdescr}

\begin{itemdecl}
template<class Sndr, class Env>
  constexpr auto @\exposid{get-domain-late}@(const Sndr& sndr, const Env& env) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{itemize}
\item
If \tcode{\exposconcept{sender-for}<Sndr, continues_on_t>} is \tcode{true}, then
\begin{codeblock}
return Domain();
\end{codeblock}
where \tcode{Domain} is the type of the following expression:
\begin{codeblock}
[] {
  auto [_, sch, _] = sndr;
  return @\exposid{query-with-default}@(get_domain, sch, default_domain());
}();
\end{codeblock}
\begin{note}
The \tcode{continues_on} algorithm works
in tandem with \tcode{schedule_from}\iref{exec.schedule.from}
to give scheduler authors a way to customize both
how to transition onto (\tcode{continues_on}) and off of (\tcode{schedule_from})
a given execution context.
Thus, \tcode{continues_on} ignores the domain of the predecessor and
uses the domain of the destination scheduler to select a customization,
a property that is unique to \tcode{continues_on}.
That is why it is given special treatment here.
\end{note}
\item
Otherwise,
\begin{codeblock}
return Domain();
\end{codeblock}
where \tcode{Domain} is the first of the following expressions
that is well-formed and whose type is not \tcode{void}:
\begin{itemize}
\item \tcode{get_domain(get_env(sndr))}
\item \tcode{\exposid{completion-domain}<void>(sndr)}
\item \tcode{get_domain(env)}
\item \tcode{get_domain(get_scheduler(env))}
\item \tcode{default_domain()}
\end{itemize}
\end{itemize}
\end{itemdescr}

\pnum
\begin{codeblock}
template<@\exposconcept{callable}@ Fun>
  requires is_nothrow_move_constructible_v<Fun>
struct @\exposid{emplace-from}@ {
  Fun @\exposid{fun}@;                                                      // \expos
  using type = @\exposid{call-result-t}@<Fun>;

  constexpr operator type() && noexcept(@\exposconcept{nothrow-callable}@<Fun>) {
    return std::move(fun)();
  }

  constexpr type operator()() && noexcept(@\exposconcept{nothrow-callable}@<Fun>) {
    return std::move(fun)();
  }
};
\end{codeblock}
\begin{note}
\exposid{emplace-from} is used to emplace non-movable types
into \tcode{tuple}, \tcode{optional}, \tcode{variant}, and similar types.
\end{note}

\pnum
\begin{codeblock}
struct @\exposid{on-stop-request}@ {
  inplace_stop_source& @\exposid{stop-src}@;       // \expos
  void operator()() noexcept { @\exposid{stop-src}@.request_stop(); }
};
\end{codeblock}

\pnum
\begin{codeblock}
template<class T@$_0$@, class T@$_1$@, @$\dotsc$,@ class T@$_n$@>
struct @\exposid{product-type}@ {       // \expos
  T@$_0$@ t@$_0$@;                // \expos
  T@$_1$@ t@$_1$@;                // \expos
    @\vdots@
  T@$_n$@ t@$_n$@;                // \expos

  template<size_t I, class Self>
  constexpr decltype(auto) @\exposid{get}@(this Self&& self) noexcept;      // \expos

  template<class Self, class Fn>
  constexpr decltype(auto) @\exposid{apply}@(this Self&& self, Fn&& fn)     // \expos
    noexcept(@\seebelow@);
};
\end{codeblock}

\pnum
\begin{note}
\exposid{product-type} is presented here in pseudo-code form
for the sake of exposition.
It can be approximated in standard \Cpp{} with a tuple-like implementation
that takes care to keep the type an aggregate
that can be used as the initializer of a structured binding declaration.
\end{note}
\begin{note}
An expression of type \exposid{product-type} is usable as
the initializer of a structured binding declaration\iref{dcl.struct.bind}.
\end{note}

\begin{itemdecl}
template<size_t I, class Self>
constexpr decltype(auto) @\exposid{get}@(this Self&& self) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto& [...ts] = self;
return std::forward_like<Self>(ts...[I]);
\end{codeblock}
\end{itemdescr}

\begin{codeblock}
template<class Self, class Fn>
constexpr decltype(auto) @\exposid{apply}@(this Self&& self, Fn&& fn) noexcept(@\seebelow@);
\end{codeblock}

\begin{itemdescr}
\pnum
\constraints
The expression in the \tcode{return} statement below is well-formed.

\pnum
\effects
Equivalent to:
\begin{codeblock}
auto& [...ts] = self;
return std::forward<Fn>(fn)(std::forward_like<Self>(ts)...);
\end{codeblock}

\pnum
\remarks
The expression in the \tcode{noexcept} clause is \tcode{true}
if the \tcode{return} statement above is not potentially throwing;
otherwise, \tcode{false}.
\end{itemdescr}

\pnum
Let \exposconcept{valid-specialization} be the following concept:
\begin{codeblock}
namespace std::execution {
  template<template<class...> class T, class... Args>
  concept @\defexposconceptnc{valid-specialization}@ =                                // \expos
    requires { typename T<Args...>; };
}
\end{codeblock}

\begin{itemdecl}
template<class Tag, class Data = @\seebelow@, class... Child>
  constexpr auto @\exposid{make-sender}@(Tag tag, Data&& data, Child&&... child);
\end{itemdecl}

\begin{itemdescr}
\pnum
\mandates
The following expressions are \tcode{true}:
\begin{itemize}
\item \tcode{\libconcept{semiregular}<Tag>}
\item \tcode{\exposconcept{movable-value}<Data>}
\item \tcode{(\libconcept{sender}<Child> \&\& ...)}
\item%
\tcode{\libconcept{dependent_sender}<Sndr> || \libconcept{sender_in}<Sndr>},
where \tcode{Sndr} is \tcode{\exposid{basic-sender}<Tag, Data,\linebreak{}Child...>}
as defined below.

 \recommended
If evaluation of \tcode{\libconcept{sender_in}<Sndr>} results in
an uncaught exception from
the evaluation of \tcode{get_completion_signatures<Sndr>()},
the implementation should include information about that exception in
the resulting diagnostic.
\end{itemize}

\pnum
\returns
A prvalue of
type \tcode{\exposid{basic-sender}<Tag, decay_t<Data>, decay_t<Child>...>}
that has been direct-list-initialized with the forwarded arguments,
where \exposid{basic-sender} is the following exposition-only class template except as noted below.
\end{itemdescr}

\pnum
\remarks
The default template argument for the \tcode{Data} template parameter
denotes an unspecified empty trivially copyable class type
that models \libconcept{semiregular}.

\begin{codeblock}
namespace std::execution {
  template<class Tag>
  concept @\defexposconceptnc{completion-tag}@ =                                      // \expos
    @\libconcept{same_as}@<Tag, set_value_t> || @\libconcept{same_as}@<Tag, set_error_t> || @\libconcept{same_as}@<Tag, set_stopped_t>;

  template<class Sndr, class Rcvr>                              // \expos
  using @\exposid{state-type}@ = decay_t<@\exposid{call-result-t}@<
    decltype(@\exposid{impls-for}@<tag_of_t<Sndr>>::@\exposid{get-state}@), Sndr, Rcvr&>>;

  template<class Index, class Sndr, class Rcvr>                 // \expos
  using @\exposid{env-type}@ = @\exposid{call-result-t}@<
    decltype(@\exposid{impls-for}@<tag_of_t<Sndr>>::@\exposid{get-env}@), Index,
    @\exposid{state-type}@<Sndr, Rcvr>&, const Rcvr&>;

  template<class Sndr>
  using @\exposidnc{data-type}@ = decltype(declval<Sndr>().template @\exposidnc{get}@<1>());                // \expos

  template<class Sndr, size_t I = 0>
  using @\exposidnc{child-type}@ = decltype(declval<Sndr>().template @\exposidnc{get}@<I+2>());             // \expos

  template<class Sndr>
  using @\exposidnc{indices-for}@ = remove_reference_t<Sndr>::@\exposidnc{indices-for}@;                    // \expos

  template<class Sndr, class Rcvr>
  struct @\exposidnc{basic-state}@ {                                          // \expos
    @\exposid{basic-state}@(Sndr&& sndr, Rcvr&& rcvr) noexcept(@\seebelow@)
      : @\exposid{rcvr}@(std::move(rcvr))
      , @\exposid{state}@(@\exposid{impls-for}@<tag_of_t<Sndr>>::@\exposid{get-state}@(std::forward<Sndr>(sndr), @\exposid{rcvr}@)) { }

    Rcvr @\exposidnc{rcvr}@;                                                  // \expos
    @\exposidnc{state-type}@<Sndr, Rcvr> @\exposidnc{state}@;                               // \expos
  };
}
\end{codeblock}

\pnum
The expression in the \tcode{noexcept} clause of
the constructor of \exposid{basic-state} is
\begin{codeblock}
is_nothrow_move_constructible_v<Rcvr> &&
@\exposconcept{nothrow-callable}@<decltype(@\exposid{impls-for}@<tag_of_t<Sndr>>::@\exposid{get-state}@), Sndr, Rcvr&> &&
(@\libconcept{same_as}@<@\exposid{state-type}@<Sndr, Rcvr>, @\exposid{get-state-result}@> ||
 is_nothrow_constructible_v<@\exposid{state-type}@<Sndr, Rcvr>, @\exposid{get-state-result}@>)
\end{codeblock}
where \exposid{get-state-result} is
\begin{codeblock}
@\exposid{call-result-t}@<decltype(@\exposid{impls-for}@<tag_of_t<Sndr>>::@\exposid{get-state}@), Sndr, Rcvr&>.
\end{codeblock}

\pnum
\begin{codeblock}
namespace std::execution {
  template<class Sndr, class Rcvr, class Index>
    requires @\exposconcept{valid-specialization}@<@\exposid{env-type}@, Index, Sndr, Rcvr>
  struct @\exposidnc{basic-receiver}@ {                                       // \expos
    using receiver_concept = receiver_t;

    using @\exposidnc{tag-t}@ = tag_of_t<Sndr>;                               // \expos
    using @\exposidnc{state-t}@ = @\exposidnc{state-type}@<Sndr, Rcvr>;                     // \expos
    static constexpr const auto& @\exposidnc{complete}@ = @\exposidnc{impls-for}@<@\exposidnc{tag-t}@>::@\exposidnc{complete}@;         // \expos

    template<class... Args>
      requires @\exposconcept{callable}@<decltype(@\exposid{complete}@), Index, @\exposid{state-t}@&, Rcvr&, set_value_t, Args...>
    void set_value(Args&&... args) && noexcept {
      @\exposid{complete}@(Index(), op->@\exposid{state}@, op->@\exposid{rcvr}@, set_value_t(), std::forward<Args>(args)...);
    }

    template<class Error>
      requires @\exposconcept{callable}@<decltype(@\exposid{complete}@), Index, @\exposid{state-t}@&, Rcvr&, set_error_t, Error>
    void set_error(Error&& err) && noexcept {
      @\exposid{complete}@(Index(), op->@\exposid{state}@, op->@\exposid{rcvr}@, set_error_t(), std::forward<Error>(err));
    }

    void set_stopped() && noexcept
      requires @\exposconcept{callable}@<decltype(@\exposid{complete}@), Index, @\exposid{state-t}@&, Rcvr&, set_stopped_t> {
      @\exposid{complete}@(Index(), op->@\exposid{state}@, op->@\exposid{rcvr}@, set_stopped_t());
    }

    auto get_env() const noexcept -> @\exposid{env-type}@<Index, Sndr, Rcvr> {
      return @\exposid{impls-for}@<tag-t>::@\exposid{get-env}@(Index(), op->@\exposid{state}@, op->@\exposid{rcvr}@);
    }

    @\exposidnc{basic-state}@<Sndr, Rcvr>* @\exposidnc{op}@;                                // \expos
  };
}
\end{codeblock}

\begin{codeblock}
namespace std::execution {
  constexpr auto @\exposidnc{connect-all}@ = @\seebelownc@;                       // \expos

  template<class Sndr, class Rcvr>
  using @\exposidnc{connect-all-result}@ = @\exposidnc{call-result-t}@<                     // \expos
    decltype(@\exposid{connect-all}@), @\exposid{basic-state}@<Sndr, Rcvr>*, Sndr, @\exposid{indices-for}@<Sndr>>;
}
\end{codeblock}

\pnum
The object \exposid{connect-all} is initialized with
a callable object equivalent to the following lambda:
\begin{itemdecl}
[]<class Sndr, class Rcvr, size_t... Is>(
  @\exposid{basic-state}@<Sndr, Rcvr>* op, Sndr&& sndr, index_sequence<Is...>) noexcept(@\seebelow@)
    -> decltype(auto) {
    auto& [_, data, ...child] = sndr;
    return @\exposid{product-type}@{connect(
      std::forward_like<Sndr>(child),
      @\exposid{basic-receiver}@<Sndr, Rcvr, integral_constant<size_t, Is>>{op})...};
  }
\end{itemdecl}

\begin{itemdescr}
\pnum
\constraints
The expression in the \tcode{return} statement is well-formed.

\pnum
\remarks
The expression in the \tcode{noexcept} clause is \tcode{true}
if the \tcode{return} statement is not potentially throwing;
otherwise, \tcode{false}.
\end{itemdescr}

\pnum
\begin{codeblock}
namespace std::execution {
  template<class Sndr, class Rcvr>
    requires @\exposconcept{valid-specialization}@<@\exposid{state-type}@, Sndr, Rcvr> &&
             @\exposconcept{valid-specialization}@<@\exposid{connect-all-result}@, Sndr, Rcvr>
  struct @\exposidnc{basic-operation}@ : @\exposidnc{basic-state}@<Sndr, Rcvr> {            // \expos
    using operation_state_concept = operation_state_t;
    using @\exposidnc{tag-t}@ = tag_of_t<Sndr>;                               // \expos

    @\exposidnc{connect-all-result}@<Sndr, Rcvr> @\exposidnc{inner-ops}@;                   // \expos

    @\exposidnc{basic-operation}@(Sndr&& sndr, Rcvr&& rcvr) noexcept(@\seebelownc@)               // \expos
      : @\exposid{basic-state}@<Sndr, Rcvr>(std::forward<Sndr>(sndr), std::move(rcvr)),
        @\exposid{inner-ops}@(@\exposid{connect-all}@(this, std::forward<Sndr>(sndr), @\exposid{indices-for}@<Sndr>()))
    {}

    void start() & noexcept {
      auto& [...ops] = @\exposid{inner-ops}@;
      @\exposid{impls-for}@<tag-t>::@\exposid{start}@(this->@\exposid{state}@, this->@\exposid{rcvr}@, ops...);
    }
  };
}
\end{codeblock}

\pnum
The expression in the \tcode{noexcept} clause of
the constructor of \exposid{basic-operation} is:
\begin{codeblock}
is_nothrow_constructible_v<@\exposid{basic-state}@<Self, Rcvr>, Self, Rcvr> &&
noexcept(@\exposid{connect-all}@(this, std::forward<Sndr>(sndr), @\exposid{indices-for}@<Sndr>()))
\end{codeblock}

\pnum
\begin{codeblock}
namespace std::execution {
  struct @\exposidnc{default-impls}@ {                                        // \expos
    static constexpr auto @\exposidnc{get-attrs}@ = @\seebelownc@;                // \expos
    static constexpr auto @\exposidnc{get-env}@ = @\seebelownc@;                  // \expos
    static constexpr auto @\exposidnc{get-state}@ = @\seebelownc@;                // \expos
    static constexpr auto @\exposidnc{start}@ = @\seebelownc@;                    // \expos
    static constexpr auto @\exposidnc{complete}@ = @\seebelownc@;                 // \expos

    template<class Sndr, class... Env>
      static consteval void @\exposidnc{check-types}@();                      // \expos
  };

  template<class Tag>
  struct @\exposidnc{impls-for}@ : @\exposidnc{default-impls}@ {};                          // \expos
}
\end{codeblock}

\pnum
The member \tcode{\exposid{default-impls}::\exposid{get-attrs}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](const auto&, const auto&... child) noexcept -> decltype(auto) {
  if constexpr (sizeof...(child) == 1)
    return (@\exposid{FWD-ENV}@(get_env(child)), ...);
  else
    return env<>();
}
\end{codeblock}

\pnum
The member \tcode{\exposid{default-impls}::\exposid{get-env}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](auto, auto&, const auto& rcvr) noexcept -> decltype(auto) {
  return @\exposid{FWD-ENV}@(get_env(rcvr));
}
\end{codeblock}

\pnum
The member \tcode{\exposid{default-impls}::\exposid{get-state}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) noexcept -> decltype(auto) {
  auto& [_, data, ...child] = sndr;
  return @\exposid{allocator-aware-forward}@(std::forward_like<Sndr>(data), rcvr);
}
\end{codeblock}

\pnum
The member \tcode{\exposid{default-impls}::\exposid{start}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](auto&, auto&, auto&... ops) noexcept -> void {
  (execution::start(ops), ...);
}
\end{codeblock}

\pnum
The member \tcode{\exposid{default-impls}::\exposid{complete}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Index, class Rcvr, class Tag, class... Args>(
  Index, auto& state, Rcvr& rcvr, Tag, Args&&... args) noexcept
    -> void requires @\exposconcept{callable}@<Tag, Rcvr, Args...> {
  static_assert(Index::value == 0);
  Tag()(std::move(rcvr), std::forward<Args>(args)...);
}
\end{codeblock}

\indexlibrarymember{\exposid{check-types}}{\exposid{default-impls}}%
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{default-impls}@::@\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{Is} be the pack of integral template arguments of
the \tcode{integer_sequence} specialization denoted by
\tcode{\exposid{indices-for}<Sndr>}.

\pnum
\effects
Equivalent to:
\begin{codeblock}
(get_completion_signatures<@\exposid{child-type}@<Sndr, Is>, @\exposid{FWD-ENV-T}@(Env)...>(), ...);
\end{codeblock}

\pnum
\begin{note}
For any types \tcode{T} and \tcode{S}, and pack \tcode{E},
let \tcode{e} be the expression
\tcode{\exposid{impls-for}<T>::\exposid{check-types}<S, E...>()}.
Then exactly one of the following is \tcode{true}:
\begin{itemize}
\item \tcode{e} is ill-formed, or
\item the evaluation of \tcode{e} exits with an exception, or
\item \tcode{e} is a core constant expression.
\end{itemize}
When \tcode{e} is a core constant expression,
the pack \tcode{S, E...} uniquely determines a set of completion signatures.
\end{note}
\end{itemdescr}

\pnum
\begin{codeblock}
namespace std::execution {
  template<class Tag, class Data, class... Child>
  struct @\exposidnc{basic-sender}@ : @\exposidnc{product-type}@<Tag, Data, Child...> {     // \expos
    using sender_concept = sender_t;
    using @\exposidnc{indices-for}@ = index_sequence_for<Child...>;           // \expos

    decltype(auto) get_env() const noexcept {
      auto& [_, data, ...child] = *this;
      return @\exposid{impls-for}@<Tag>::@\exposid{get-attrs}@(data, child...);
    }

    template<@\exposconcept{decays-to}@<@\exposid{basic-sender}@> Self, @\libconcept{receiver}@ Rcvr>
    auto connect(this Self&& self, Rcvr rcvr) noexcept(@\seebelow@)
      -> @\exposid{basic-operation}@<Self, Rcvr> {
      return {std::forward<Self>(self), std::move(rcvr)};
    }

    template<@\exposconcept{decays-to}@<@\exposid{basic-sender}@> Self, class... Env>
    static constexpr auto get_completion_signatures();
  };
}
\end{codeblock}

\pnum
It is unspecified whether a specialization of \exposid{basic-sender}
is an aggregate.

\pnum
An expression of type \exposid{basic-sender} is usable as
the initializer of a structured binding declaration\iref{dcl.struct.bind}.

\pnum
The expression in the \tcode{noexcept} clause of
the \tcode{connect} member function of \exposid{basic-sender} is:
\begin{codeblock}
is_nothrow_constructible_v<@\exposid{basic-operation}@<Self, Rcvr>, Self, Rcvr>
\end{codeblock}

\indexlibrarymember{get_completion_signatures}{\exposid{basic-sender}}%
\begin{itemdecl}
template<class Tag, class Data, class... Child>
  template<class Sndr, class... Env>
    constexpr auto @\exposid{basic-sender}@<Tag, Data, Child...>::get_completion_signatures();
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{Rcvr} be the type of a receiver whose
environment has type \tcode{E}, where
\tcode{E} is the first type in the list \tcode{Env..., env<>}.
Let \tcode{\placeholder{CHECK-TYPES}()} be the expression
\tcode{\exposid{impls-for}<Tag>::template \exposid{check-types}<\linebreak{}Sndr, E>()}, and
let \tcode{CS} be a type determined as follows:

\begin{itemize}
\item%
If \tcode{\exposid{CHECK-TYPES}()} is a core constant expression,
let \tcode{op} be an lvalue subexpression
whose type is \tcode{connect_result_t<Sndr, Rcvr>}.
Then \tcode{CS} is the specialization of \tcode{completion_signatures}
the set of whose template arguments
correspond to the set of completion operations
that are potentially evaluated\iref{basic.def.odr}
as a result of evaluating \tcode{op.start()}.

\item%
Otherwise, \tcode{CS} is \tcode{completion_signatures<>}.
\end{itemize}

\pnum
\constraints
\tcode{\exposid{CHECK-TYPES}()} is a well-formed expression.

\pnum
\effects
Equivalent to:
\begin{codeblock}
@\exposid{CHECK-TYPES}@();
return CS();
\end{codeblock}
\end{itemdescr}

\pnum
\indexlibraryglobal{\exposid{overload-set}}
%%FIXME: Should this be in a namespace?
\begin{codeblock}
template<class... Fns>
struct @\exposid{overload-set}@ : Fns... {
  using Fns::operator()...;
};
\end{codeblock}

\pnum
\indexlibraryglobal{\exposid{not-a-sender}}
\indexlibrarymember{get_completion_signatures}{\exposid{not-a-sender}}
%%FIXME: Should this be in a namespace?
\begin{codeblock}
struct @\exposid{not-a-sender}@ {
  using sender_concept = sender_t;

  template<class Sndr>
    static consteval auto get_completion_signatures() -> completion_signatures<> {
      throw @\placeholder{unspecified-exception}@();
  }
};
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.

\pnum
\indexlibraryglobal{\exposid{decay-copyable-result-datums}}
%%FIXME: Should this be in a namespace?
\begin{codeblock}
constexpr void @\exposid{decay-copyable-result-datums}@(auto cs) {
  cs.@\exposid{for-each}@([]<class Tag, class... Ts>(Tag(*)(Ts...)) {
    if constexpr (!(is_constructible_v<decay_t<Ts>, Ts> &&...))
      throw @\placeholder{unspecified-exception}@();
  });
}
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.

\begin{itemdecl}
template<class T, class Context>
  decltype(auto) @\exposid{allocator-aware-forward}@(T&& obj, Context&& context);       // \expos
\end{itemdecl}

\begin{itemdescr}
\pnum
\exposid{allocator-aware-forward} is an exposition-only function template
used to either
create a new object of type \tcode{remove_cvref_t<T>} from \tcode{obj}
or forward \tcode{obj} depending on whether an allocator is available.
If the environment associated with \tcode{context} provides an allocator
(i.e., the expression \tcode{get_allocator(get_env(context))} is valid),
let \exposid{alloc} be the result of this expression
and let \tcode{P} be \tcode{remove_cvref_t<T>}.

\pnum
\returns
\begin{itemize}
\item
If \exposid{alloc} is not defined, returns \tcode{std::forward<T>(obj)},
\item
otherwise if \tcode{P} is a specialization of \exposid{product-type},
returns an object of type \tcode{P} whose elements are initialized using
\begin{codeblock}
make_obj_using_allocator<decltype(e)>(std::forward_like<T>(e), @\exposid{alloc}@)
\end{codeblock}
where \tcode{e} is the corresponding element of \tcode{obj},
\item
otherwise, returns \tcode{make_obj_using_allocator<P>(std::forward<T>(obj), \exposid{alloc})}.
\end{itemize}
\end{itemdescr}

\rSec2[exec.snd.concepts]{Sender concepts}

\pnum
The \libconcept{sender} concept defines
the requirements for a sender type\iref{exec.async.ops}.
The \libconcept{sender_in} concept defines
the requirements for a sender type
that can create asynchronous operations given an associated environment type.
The \libconcept{sender_to} concept defines
the requirements for a sender type
that can connect with a specific receiver type.
The \tcode{get_env} customization point object is used to access
a sender's associated attributes.
The connect customization point object is used to connect\iref{exec.async.ops}
a sender and a receiver to produce an operation state.

\indexlibraryglobal{\exposid{is-dependent-sender-helper}}%
\begin{codeblock}
namespace std::execution {
  template<auto>
    concept @\defexposconcept{is-constant}@ = true;                                 // \expos

  template<class Sndr>
    concept @\defexposconcept{is-sender}@ =                                         // \expos
      @\libconcept{derived_from}@<typename Sndr::sender_concept, sender_t>;

  template<class Sndr>
    concept @\defexposconcept{enable-sender}@ =                                     // \expos
      @\exposconcept{is-sender}@<Sndr> ||
      @\exposconcept{is-awaitable}@<Sndr, @\exposid{env-promise}@<env<>>>;                 // \ref{exec.awaitable}

  template<class Sndr>
    inline constexpr bool enable_sender = @\exposconcept{enable-sender}@<Sndr>;

  template<class Sndr>
    consteval bool @\exposidnc{is-dependent-sender-helper}@() try {           // \expos
      get_completion_signatures<Sndr>();
      return false;
    } catch (dependent_sender_error&) {
      return true;
    }

  template<class Sndr>
    concept @\deflibconcept{sender}@ =
      enable_sender<remove_cvref_t<Sndr>> &&
      requires (const remove_cvref_t<Sndr>& sndr) {
        { get_env(sndr) } -> @\exposconcept{queryable}@;
      } &&
      @\libconcept{move_constructible}@<remove_cvref_t<Sndr>> &&
      @\libconcept{constructible_from}@<remove_cvref_t<Sndr>, Sndr>;

  template<class Sndr, class... Env>
    concept @\deflibconcept{sender_in}@ =
      @\libconcept{sender}@<Sndr> &&
      (sizeof...(Env) <= 1) &&
      (@\exposconcept{queryable}@<Env> &&...) &&
      @\exposconcept{is-constant}@<get_completion_signatures<Sndr, Env...>()>;

  template<class Sndr>
    concept @\deflibconcept{dependent_sender}@ =
      @\libconcept{sender}@<Sndr> && bool_constant<@\exposid{is-dependent-sender-helper}@<Sndr>()>::value;

  template<class Sndr, class Rcvr>
    concept @\deflibconcept{sender_to}@ =
      @\libconcept{sender_in}@<Sndr, env_of_t<Rcvr>> &&
      @\libconcept{receiver_of}@<Rcvr, completion_signatures_of_t<Sndr, env_of_t<Rcvr>>> &&
      requires (Sndr&& sndr, Rcvr&& rcvr) {
        connect(std::forward<Sndr>(sndr), std::forward<Rcvr>(rcvr));
      };
}
\end{codeblock}

\pnum
For a type \tcode{Sndr}, if
\tcode{\libconcept{sender}<Sndr>} is \tcode{true} and
\tcode{\libconcept{dependent_sender}<Sndr>} is \tcode{false},
then \tcode{Sndr} is a non-dependent sender\iref{exec.async.ops}.

\pnum
Given a subexpression \tcode{sndr},
let \tcode{Sndr} be \tcode{decltype((sndr))} and
let \tcode{rcvr} be a receiver
with an associated environment whose type is \tcode{Env}.
A completion operation is a \defnadj{permissible}{completion}
for \tcode{Sndr} and \tcode{Env}
if its completion signature appears in the argument list of the specialization of \tcode{completion_signatures} denoted by
\tcode{completion_signatures_of_t<Sndr, Env>}.
\tcode{Sndr} and \tcode{Env} model \tcode{\libconcept{sender_in}<Sndr, Env>}
if all the completion operations
that are potentially evaluated by connecting \tcode{sndr} to \tcode{rcvr} and
starting the resulting operation state
are permissible completions for \tcode{Sndr} and \tcode{Env}.

\pnum
\remarks
Pursuant to \ref{namespace.std},
users may specialize \tcode{enable_sender} to
\tcode{true} for cv-unqualified program-defined types that
model \libconcept{sender}, and
\tcode{false} for types that do not.
Such specializations shall
be usable in constant expressions\iref{expr.const} and
have type \tcode{const bool}.

\pnum
The exposition-only concepts
\exposconcept{sender-of} and \exposconcept{sender-in-of}
define the requirements for a sender type
that completes with a given unique set of value result types.
\begin{codeblock}
namespace std::execution {
  template<class... As>
    using @\exposid{value-signature}@ = set_value_t(As...);             // \expos

  template<class Sndr, class SetValue, class... Env>
    concept @\defexposconcept{sender-in-of-impl}@ =                             // \expos
      @\libconcept{sender_in}@<Sndr, Env...> &&
      @\exposid{MATCHING-SIG}@(SetValue,                                // see \ref{exec.general}
                   @\exposid{gather-signatures}@<set_value_t,           // see \ref{exec.cmplsig}
                                     completion_signatures_of_t<Sndr, Env...>,
                                     @\exposid{value-signature}@,
                                     type_identity_t>);

  template<class Sndr, class Env, class... Values>
    concept @\defexposconcept{sender-in-of}@ =                                  // \expos
      @\exposconcept{sender-in-of-impl}@<Sndr, set_value_t(Values...), Env>;

  template<class Sndr, class... Values>
    concept @\defexposconcept{sender-of}@ =                                     // \expos
      @\exposconcept{sender-in-of-impl}@<Sndr, set_value_t(Values...)>;
}
\end{codeblock}

\pnum
Let \tcode{sndr} be an expression
such that \tcode{decltype((sndr))} is \tcode{Sndr}.
The type \tcode{tag_of_t<Sndr>} is as follows:
\begin{itemize}
\item
If the declaration
\begin{codeblock}
auto&& [tag, data, ...children] = sndr;
\end{codeblock}
would be well-formed, \tcode{tag_of_t<Sndr>} is
an alias for \tcode{decltype(auto(tag))}.
\item
Otherwise, \tcode{tag_of_t<Sndr>} is ill-formed.
\end{itemize}

\pnum
Let \exposconcept{sender-for} be an exposition-only concept defined as follows:
\begin{codeblock}
namespace std::execution {
  template<class Sndr, class Tag>
  concept @\defexposconcept{sender-for}@ =
    @\libconcept{sender}@<Sndr> &&
    @\libconcept{same_as}@<tag_of_t<Sndr>, Tag>;
}
\end{codeblock}

\pnum
For a type \tcode{T},
\tcode{\exposid{SET-VALUE-SIG}(T)} denotes the type \tcode{set_value_t()}
if \tcode{T} is \cv{} \tcode{void};
otherwise, it denotes the type \tcode{set_value_t(T)}.

\pnum
Library-provided sender types
\begin{itemize}
\item
always expose an overload of a member \tcode{connect}
that accepts an rvalue sender and
\item
only expose an overload of a member \tcode{connect}
that accepts an lvalue sender if they model \libconcept{copy_constructible}.
\end{itemize}

\rSec2[exec.awaitable]{Awaitable helpers}

\pnum
The sender concepts recognize awaitables as senders.
For \ref{exec}, an \defn{awaitable} is an expression
that would be well-formed as the operand of a \tcode{co_await} expression
within a given context.

\pnum
For a subexpression \tcode{c},
let \tcode{\exposid{GET-AWAITER}(c, p)} be expression-equivalent to
the series of transformations and conversions applied to \tcode{c}
as the operand of an \grammarterm{await-expression} in a coroutine,
resulting in lvalue \tcode{e} as described by \ref{expr.await},
where \tcode{p} is an lvalue referring to the coroutine's promise,
which has type \tcode{Promise}.
\begin{note}
This includes the invocation of
the promise type's \tcode{await_transform} member if any,
the invocation of the \tcode{operator co_await}
picked by overload resolution if any, and
any necessary implicit conversions and materializations.
\end{note}

Let \tcode{\exposid{GET-AWAITER}(c)} be
expression-equivalent to \tcode{\exposid{GET-AWAITER}(c, q)}
where \tcode{q} is an lvalue of
an unspecified empty class type \tcode{\placeholder{none-such}} that
lacks an \tcode{await_transform} member, and
where \tcode{coroutine_handle<\placeholder{none-such}>} behaves as
\tcode{coroutine_handle<void>}.

\pnum
Let \exposconcept{is-awaitable} be the following exposition-only concept:
\begin{codeblock}
namespace std {
  template<class T>
  concept @\exposconcept{await-suspend-result}@ = @\seebelow@;                     // \expos

  template<class A, class... Promise>
  concept @\defexposconcept{is-awaiter}@ =                                          // \expos
    requires (A& a, coroutine_handle<Promise...> h) {
      a.await_ready() ? 1 : 0;
      { a.await_suspend(h) } -> @\exposconcept{await-suspend-result}@;
      a.await_resume();
    };

  template<class C, class... Promise>
  concept @\defexposconcept{is-awaitable}@ =                                        // \expos
    requires (C (*fc)() noexcept, Promise&... p) {
      { @\exposid{GET-AWAITER}@(fc(), p...) } -> @\exposconcept{is-awaiter}@<Promise...>;
    };
}
\end{codeblock}

\tcode{\defexposconcept{await-suspend-result}<T>} is \tcode{true}
if and only if one of the following is \tcode{true}:
\begin{itemize}
\item \tcode{T} is \tcode{void}, or
\item \tcode{T} is \tcode{bool}, or
\item \tcode{T} is a specialization of \tcode{coroutine_handle}.
\end{itemize}

\pnum
For a subexpression \tcode{c}
such that \tcode{decltype((c))} is type \tcode{C}, and
an lvalue \tcode{p} of type \tcode{Promise},
\tcode{\exposid{await-result-\newline type}<C, Promise>} denotes
the type \tcode{decltype(\exposid{GET-AWAITER}(c, p).await_resume())} and
\tcode{\exposid{await-re\-sult-type}<C>} denotes
the type \tcode{decltype(\exposid{GET-AWAITER}(c).await_resume())}.

\pnum
Let \exposid{with-await-transform} be the exposition-only class template:
\begin{codeblock}
namespace std::execution {
  template<class T, class Promise>
    concept @\defexposconcept{has-as-awaitable}@ =                                  // \expos
      requires (T&& t, Promise& p) {
        { std::forward<T>(t).as_awaitable(p) } -> @\exposconcept{is-awaitable}@<Promise&>;
      };

  template<class Derived>
    struct @\exposid{with-await-transform}@ {                               // \expos
      template<class T>
        T&& await_transform(T&& value) noexcept {
          return std::forward<T>(value);
        }

      template<@\exposconcept{has-as-awaitable}@<Derived> T>
        auto await_transform(T&& value)
          noexcept(noexcept(std::forward<T>(value).as_awaitable(declval<Derived&>())))
          -> decltype(std::forward<T>(value).as_awaitable(declval<Derived&>())) {
          return std::forward<T>(value).as_awaitable(static_cast<Derived&>(*this));
        }
    };
}
\end{codeblock}

\pnum
Let \exposid{env-promise} be the exposition-only class template:
\begin{codeblock}
namespace std::execution {
  template<class Env>
  struct @\exposid{env-promise}@ : @\exposid{with-await-transform}@<@\exposid{env-promise}@<Env>> { // \expos
    @\unspec@ get_return_object() noexcept;
    @\unspec@ initial_suspend() noexcept;
    @\unspec@ final_suspend() noexcept;
    void unhandled_exception() noexcept;
    void return_void() noexcept;
    coroutine_handle<> unhandled_stopped() noexcept;

    const Env& get_env() const noexcept;
  };
}
\end{codeblock}
\begin{note}
Specializations of \exposid{env-promise} are used only for the purpose of type computation;
its members need not be defined.
\end{note}

\rSec2[exec.domain.default]{\tcode{execution::default_domain}}

\pnum
\begin{codeblock}
namespace std::execution {
  struct @\libglobal{default_domain}@ {
    template<@\libconcept{sender}@ Sndr, @\exposconcept{queryable}@... Env>
        requires (sizeof...(Env) <= 1)
      static constexpr @\libconcept{sender}@ decltype(auto) transform_sender(Sndr&& sndr, const Env&... env)
        noexcept(@\seebelow@);

    template<@\libconcept{sender}@ Sndr, @\exposconcept{queryable}@ Env>
      static constexpr @\exposconcept{queryable}@ decltype(auto) transform_env(Sndr&& sndr, Env&& env) noexcept;

    template<class Tag, @\libconcept{sender}@ Sndr, class... Args>
      static constexpr decltype(auto) apply_sender(Tag, Sndr&& sndr, Args&&... args)
        noexcept(@\seebelow@);
  };
}
\end{codeblock}

\indexlibrarymember{transform_sender}{default_domain}%
\begin{itemdecl}
template<@\libconcept{sender}@ Sndr, @\exposconcept{queryable}@... Env>
  requires (sizeof...(Env) <= 1)
constexpr @\libconcept{sender}@ decltype(auto) transform_sender(Sndr&& sndr, const Env&... env)
  noexcept(@\seebelow@);
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{e} be the expression
\begin{codeblock}
tag_of_t<Sndr>().transform_sender(std::forward<Sndr>(sndr), env...)
\end{codeblock}
if that expression is well-formed;
otherwise, \tcode{std::forward<Sndr>(sndr)}.

\pnum
\returns
\tcode{e}.

\pnum
\remarks
The exception specification is equivalent to \tcode{noexcept(e)}.
\end{itemdescr}

\indexlibrarymember{transform_env}{default_domain}%
\begin{itemdecl}
template<@\libconcept{sender}@ Sndr, @\exposconcept{queryable}@ Env>
  constexpr @\exposconcept{queryable}@ decltype(auto) transform_env(Sndr&& sndr, Env&& env) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{e} be the expression
\begin{codeblock}
tag_of_t<Sndr>().transform_env(std::forward<Sndr>(sndr), std::forward<Env>(env))
\end{codeblock}
if that expression is well-formed;
otherwise, \tcode{\exposid{FWD-ENV}(std::forward<Env>(env))}.

\pnum
\mandates
\tcode{noexcept(e)} is \tcode{true}.

\pnum
\returns
\tcode{e}.
\end{itemdescr}

\indexlibrarymember{apply_sender}{default_domain}%
\begin{itemdecl}
template<class Tag, @\libconcept{sender}@ Sndr, class... Args>
constexpr decltype(auto) apply_sender(Tag, Sndr&& sndr, Args&&... args)
  noexcept(@\seebelow@);
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{e} be the expression
\begin{codeblock}
  Tag().apply_sender(std::forward<Sndr>(sndr), std::forward<Args>(args)...)
\end{codeblock}

\pnum
\constraints
\tcode{e} is a well-formed expression.

\pnum
\returns
\tcode{e}.

\pnum
\remarks
The exception specification is equivalent to \tcode{noexcept(e)}.
\end{itemdescr}

\rSec2[exec.snd.transform]{\tcode{execution::transform_sender}}

\indexlibraryglobal{transform_sender}%
\begin{itemdecl}
namespace std::execution {
  template<class Domain, @\libconcept{sender}@ Sndr, @\exposconcept{queryable}@... Env>
      requires (sizeof...(Env) <= 1)
    constexpr @\libconcept{sender}@ decltype(auto) transform_sender(Domain dom, Sndr&& sndr, const Env&... env)
      noexcept(@\seebelow@);
}
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \exposid{transformed-sndr} be the expression
\begin{codeblock}
dom.transform_sender(std::forward<Sndr>(sndr), env...)
\end{codeblock}
if that expression is well-formed; otherwise,
\begin{codeblock}
default_domain().transform_sender(std::forward<Sndr>(sndr), env...)
\end{codeblock}
Let \exposid{final-sndr} be the expression \exposid{transformed-sndr}
if \exposid{transformed-sndr} and \exposid{sndr}
have the same type ignoring cv-qualifiers;
otherwise, it is
the expression \tcode{transform_sender(dom, \exposid{transformed-sndr}, env...)}.

\pnum
\returns
\exposid{final-sndr}.

\pnum
\remarks
The exception specification is equivalent to
\tcode{noexcept(\exposid{final-sndr})}.
\end{itemdescr}

\rSec2[exec.snd.transform.env]{\tcode{execution::transform_env}}

\indexlibraryglobal{transform_env}%
\begin{itemdecl}
namespace std::execution {
  template<class Domain, @\libconcept{sender}@ Sndr, @\exposconcept{queryable}@ Env>
    constexpr @\exposconcept{queryable}@ decltype(auto) transform_env(Domain dom, Sndr&& sndr, Env&& env) noexcept;
}
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{e} be the expression
\begin{codeblock}
dom.transform_env(std::forward<Sndr>(sndr), std::forward<Env>(env))
\end{codeblock}
if that expression is well-formed; otherwise,
\begin{codeblock}
default_domain().transform_env(std::forward<Sndr>(sndr), std::forward<Env>(env))
\end{codeblock}

\pnum
\mandates
\tcode{noexcept(e)} is \tcode{true}.

\pnum
\returns
\tcode{e}.
\end{itemdescr}

\rSec2[exec.snd.apply]{\tcode{execution::apply_sender}}

\indexlibraryglobal{apply_sender}%
\begin{itemdecl}
namespace std::execution {
  template<class Domain, class Tag, @\libconcept{sender}@ Sndr, class... Args>
    constexpr decltype(auto) apply_sender(Domain dom, Tag, Sndr&& sndr, Args&&... args)
      noexcept(@\seebelow@);
}
\end{itemdecl}

\begin{itemdescr}
\pnum
Let $e$ be the expression
\begin{codeblock}
dom.apply_sender(Tag(), std::forward<Sndr>(sndr), std::forward<Args>(args)...)
\end{codeblock}
if that expression is well-formed; otherwise,
\begin{codeblock}
default_domain().apply_sender(Tag(), std::forward<Sndr>(sndr), std::forward<Args>(args)...)
\end{codeblock}

\pnum
\constraints
The expression $e$ is well-formed.

\pnum
\returns
$e$.

\pnum
\remarks
The exception specification is equivalent to \tcode{noexcept($e$)}.
\end{itemdescr}

\rSec2[exec.getcomplsigs]{\tcode{execution::get_completion_signatures}}

\indexlibraryglobal{get_completion_signatures}%
%%FIXME: Should this be in namespace std::execution?
\begin{itemdecl}
template<class Sndr, class... Env>
  consteval auto get_completion_signatures() -> @\exposconcept{valid-completion-signatures}@ auto;
\end{itemdecl}

\begin{itemdescr}
\pnum
Let $except$ be an rvalue subexpression of
an unspecified class type $Except$ such that
\tcode{\libconceptx{move_construc\-tible}{move_constructible}<$Except$> \&\& \libconcept{derived_from}<$Except$, exception>}
is \tcode{true}.
Let \tcode{\placeholder{CHECKED-COMPLSIGS}($e$)} be $e$
if $e$ is a core constant expression whose
type satisfies \exposconcept{valid-completion-signatures};
otherwise, it is the following expression:
\begin{codeblock}
(@$e$@, throw @$except$@, completion_signatures())
\end{codeblock}
Let \tcode{\placeholder{get-complsigs}<Sndr, Env...>()}
be expression-equivalent to
\tcode{remove_reference_t<Sndr>::tem\-plate get_completion_signatures<Sndr, Env...>()}.
Let \tcode{NewSndr} be \tcode{Sndr}
if \tcode{sizeof...(Env) == 0} is \tcode{true};
otherwise, \tcode{decltype($s$)}
where $s$ is the following expression:
\begin{codeblock}
transform_sender(
  @\exposid{get-domain-late}@(declval<Sndr>(), declval<Env>()...),
  declval<Sndr>(),
  declval<Env>()...)
\end{codeblock}

\pnum
\constraints
\tcode{sizeof...(Env) <= 1} is \tcode{true}.

\pnum
\effects
Equivalent to: \tcode{return $e$;}
where $e$ is expression-equivalent to the following:
\begin{itemize}
\item
\tcode{\placeholder{CHECKED-COMPLSIGS}(\placeholder{get-complsigs}<NewSndr, Env...>())}
if \tcode{\placeholder{get-complsigs}<NewSndr, Env\linebreak{}...>()}
is a well-formed expression.

\item
Otherwise,
\tcode{\placeholder{CHECKED-COMPLSIGS}(\placeholder{get-complsigs}<NewSndr>())}
if \tcode{\placeholder{get-complsigs}<NewSndr>()}
is a well-formed expression.

\item
Otherwise,
\begin{codeblock}
completion_signatures<
  @\exposid{SET-VALUE-SIG}@(@\exposid{await-result-type}@<NewSndr, @\exposid{env-promise}@<Env>...>),   // \ref{exec.snd.concepts}
  set_error_t(exception_ptr),
  set_stopped_t()>
\end{codeblock}
if \tcode{\exposconcept{is-awaitable}<NewSndr, \exposid{env-promise}<Env>...>}
is \tcode{true}.

\item
Otherwise,
\tcode{(throw \placeholder{dependent-sender-error}(), completion_signatures())}
if \tcode{sizeof...(\linebreak{}Env) == 0} is \tcode{true},
where \tcode{\placeholder{dependent-sender-error}} is
\tcode{dependent_sender_error} or
an unspecified type derived publicly and unambiguously from
\tcode{dependent_sender_error}.

\item
Otherwise,
\tcode{(throw $except$, completion_signatures())}.
\end{itemize}
\end{itemdescr}

\pnum
Given a type \tcode{Env}, if
\tcode{completion_signatures_of_t<Sndr>} and
\tcode{completion_signatures_of_t<Sndr, Env>}
are both well-formed,
they shall denote the same type.

\pnum
Let \tcode{rcvr} be an rvalue
whose type \tcode{Rcvr} models \libconcept{receiver}, and
let \tcode{Sndr} be the type of a sender
such that \tcode{\libconcept{sender_in}<Sndr, env_of_t<Rcvr>>} is \tcode{true}.
Let \tcode{Sigs...} be the template arguments of
the \tcode{completion_signatures} specialization
named by \tcode{completion_signatures_of_t<Sndr, env_of_t<Rcvr>>}.
Let \tcode{CSO} be a completion function.
If sender \tcode{Sndr} or its operation state cause
the expression \tcode{CSO(rcvr, args...)}
to be potentially evaluated\iref{basic.def.odr}
then there shall be a signature \tcode{Sig} in \tcode{Sigs...}
such that
\begin{codeblock}
@\exposid{MATCHING-SIG}@(@\exposid{decayed-typeof}@<CSO>(decltype(args)...), Sig)
\end{codeblock}
is \tcode{true}\iref{exec.general}.

\rSec2[exec.connect]{\tcode{execution::connect}}

\pnum
\tcode{connect} connects\iref{exec.async.ops} a sender with a receiver.

\pnum
The name \tcode{connect} denotes a customization point object.
For subexpressions \tcode{sndr} and \tcode{rcvr},
let \tcode{Sndr} be \tcode{decltype((sndr))} and
\tcode{Rcvr} be \tcode{decltype((rcvr))},
let \tcode{new_sndr} be the expression
\begin{codeblock}
transform_sender(decltype(@\exposid{get-domain-late}@(sndr, get_env(rcvr))){}, sndr, get_env(rcvr))
\end{codeblock}
and let \tcode{DS} and \tcode{DR} be
\tcode{decay_t<decltype((new_sndr))>} and \tcode{decay_t<Rcvr>}, respectively.

\pnum
Let \exposid{connect-awaitable-promise} be the following exposition-only class:

\begin{codeblock}
namespace std::execution {
  struct @\exposid{connect-awaitable-promise}@ : @\exposid{with-await-transform}@<@\exposid{connect-awaitable-promise}@> {

    @\exposid{connect-awaitable-promise}@(DS&, DR& rcvr) noexcept : @\exposid{rcvr}@(rcvr) {}

    suspend_always initial_suspend() noexcept { return {}; }
    [[noreturn]] suspend_always final_suspend() noexcept { terminate(); }
    [[noreturn]] void unhandled_exception() noexcept { terminate(); }
    [[noreturn]] void return_void() noexcept { terminate(); }

    coroutine_handle<> unhandled_stopped() noexcept {
      set_stopped(std::move(@\exposid{rcvr}@));
      return noop_coroutine();
    }

    @\exposid{operation-state-task}@ get_return_object() noexcept {
      return @\exposid{operation-state-task}@{
        coroutine_handle<@\exposid{connect-awaitable-promise}@>::from_promise(*this)};
    }

    env_of_t<DR> get_env() const noexcept {
      return execution::get_env(@\exposid{rcvr}@);
    }

  private:
    DR& @\exposid{rcvr}@;                           // \expos
  };
}
\end{codeblock}

\pnum
Let \exposid{operation-state-task} be the following exposition-only class:
\begin{codeblock}
namespace std::execution {
  struct @\exposid{operation-state-task}@ {                              // \expos
    using operation_state_concept = operation_state_t;
    using promise_type = @\exposid{connect-awaitable-promise}@;

    explicit @\exposid{operation-state-task}@(coroutine_handle<> h) noexcept : coro(h) {}
    @\exposid{operation-state-task}@(@\exposid{operation-state-task}@&&) = delete;
    ~@\exposid{operation-state-task}@() { @\exposid{coro}@.destroy(); }

    void start() & noexcept {
      @\exposid{coro}@.resume();
    }

  private:
    coroutine_handle<> @\exposid{coro}@;                                    // \expos
  };
}
\end{codeblock}

\pnum
Let \tcode{V} name the type
\tcode{\exposid{await-result-type}<DS, \exposid{connect-awaitable-promise}>},
let \tcode{Sigs} name the type
\begin{codeblock}
completion_signatures<
  @\exposid{SET-VALUE-SIG}@(V),         // see~\ref{exec.snd.concepts}
  set_error_t(exception_ptr),
  set_stopped_t()>
\end{codeblock}
and let \exposid{connect-awaitable} be an exposition-only coroutine
defined as follows:
\begin{codeblock}
namespace std::execution {
  template<class Fun, class... Ts>
  auto @\exposid{suspend-complete}@(Fun fun, Ts&&... as) noexcept {    // \expos
    auto fn = [&, fun]() noexcept { fun(std::forward<Ts>(as)...); };

    struct awaiter {
      decltype(fn) @\exposid{fn}@;                                     // \expos

      static constexpr bool await_ready() noexcept { return false; }
      void await_suspend(coroutine_handle<>) noexcept { @\exposid{fn}@(); }
      [[noreturn]] void await_resume() noexcept { unreachable(); }
    };
    return awaiter{fn};
  }

  @\exposid{operation-state-task}@ @\exposid{connect-awaitable}@(DS sndr, DR rcvr) requires @\libconcept{receiver_of}@<DR, Sigs> {
    exception_ptr ep;
    try {
      if constexpr (@\libconcept{same_as}@<V, void>) {
        co_await std::move(sndr);
        co_await @\exposid{suspend-complete}@(set_value, std::move(rcvr));
      } else {
        co_await @\exposid{suspend-complete}@(set_value, std::move(rcvr), co_await std::move(sndr));
      }
    } catch(...) {
      ep = current_exception();
    }
    co_await @\exposid{suspend-complete}@(set_error, std::move(rcvr), std::move(ep));
  }
}
\end{codeblock}

\pnum
The expression \tcode{connect(sndr, rcvr)} is expression-equivalent to:
\begin{itemize}
\item
\tcode{new_sndr.connect(rcvr)} if that expression is well-formed.

\mandates
The type of the expression above satisfies \libconcept{operation_state}.

\item
Otherwise, \tcode{\exposid{connect-awaitable}(new_sndr, rcvr)}.
\end{itemize}
Except that \tcode{rcvr} is evaluated only once.

\mandates
The following are \tcode{true}:
\begin{itemize}
\item
\tcode{\libconcept{sender_in}<Sndr, env_of_t<Rcvr>>}
\item
\tcode{\libconcept{receiver_of}<Rcvr, completion_signatures_of_t<Sndr, env_of_t<Rcvr>>>}
\end{itemize}

\rSec2[exec.factories]{Sender factories}

\rSec3[exec.schedule]{\tcode{execution::schedule}}

\pnum
\tcode{schedule} obtains a schedule sender\iref{exec.async.ops}
from a scheduler.

\pnum
The name \tcode{schedule} denotes a customization point object.
For a subexpression \tcode{sch},
the expression \tcode{schedule(sch)} is expression-equivalent to
\tcode{sch.schedule()}.

\pnum
\mandates
The type of \tcode{sch.schedule()} satisfies \libconcept{sender}.

\pnum
If the expression
\begin{codeblock}
get_completion_scheduler<set_value_t>(get_env(sch.schedule())) == sch
\end{codeblock}
is ill-formed or evaluates to \tcode{false},
the behavior of calling \tcode{schedule(sch)} is undefined.

\rSec3[exec.just]{\tcode{execution::just}, \tcode{execution::just_error}, \tcode{execution::just_stopped}}

\pnum
\tcode{just}, \tcode{just_error}, and \tcode{just_stopped} are sender factories
whose asynchronous operations complete synchronously in their start operation
with a value completion operation,
an error completion operation, or
a stopped completion operation, respectively.

\pnum
The names \tcode{just}, \tcode{just_error}, and \tcode{just_stopped} denote
customization point objects.
Let \exposid{just-cpo} be one of
\tcode{just}, \tcode{just_error}, or \tcode{just_stopped}.
For a pack of subexpressions \tcode{ts},
let \tcode{Ts} be the pack of types \tcode{decltype((ts))}.
The expression \tcode{\exposid{just-cpo}(ts...)} is ill-formed if
\begin{itemize}
\item
\tcode{(\exposconcept{movable-value}<Ts> \&\&...)} is \tcode{false}, or
\item
\exposid{just-cpo} is \tcode{just_error} and
\tcode{sizeof...(ts) == 1} is \tcode{false}, or
\item
\exposid{just-cpo} is \tcode{just_stopped} and
\tcode{sizeof...(ts) == 0} is \tcode{false}.
\end{itemize}

Otherwise, it is expression-equivalent to
\tcode{\exposid{make-sender}(\exposid{just-cpo}, \exposid{product-type}\{ts...\})}.

For \tcode{just}, \tcode{just_error}, and \tcode{just_stopped},
let \exposid{set-cpo} be
\tcode{set_value}, \tcode{set_error}, and \tcode{set_stopped}, respectively.
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \exposid{just-cpo} as follows:
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<@\exposid{decayed-typeof}@<@\exposid{just-cpo}@>> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{start}@ =
      [](auto& state, auto& rcvr) noexcept -> void {
        auto& [...ts] = state;
        @\exposid{set-cpo}@(std::move(rcvr), std::move(ts)...);
      };
  };
}
\end{codeblock}

\rSec3[exec.read.env]{\tcode{execution::read_env}}

\pnum
\tcode{read_env} is a sender factory for a sender
whose asynchronous operation completes synchronously in its start operation
with a value completion result equal to
a value read from the receiver's associated environment.

\pnum
\tcode{read_env} is a customization point object.
For some query object \tcode{q},
the expression \tcode{read_env(q)} is expression-equivalent to
\tcode{\exposid{make-sender}(read_env, q)}.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{read_env} as follows:
\indexlibraryglobal{\exposid{impls-for}<\exposid{decayed-typeof}<read_env>>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<@\exposid{decayed-typeof}@<read_env>> : @\exposid{default-impls}@ {
    static constexpr auto start =
      [](auto query, auto& rcvr) noexcept -> void {
        @\exposid{TRY-SET-VALUE}@(rcvr, query(get_env(rcvr)));
      };
  };

  template<class Sndr, class Env>
    static consteval void @\exposid{check-types}@();
}
\end{codeblock}

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<\exposid{decayed-typeof}<read_env>>}
\begin{itemdecl}
template<class Sndr, class Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{Q} be \tcode{decay_t<\exposid{data-type}<Sndr>>}.

\pnum
\throws
An exception of an unspecified type derived from \tcode{exception} if
the expression \tcode{Q()(env)} is ill-formed or has type \tcode{void}, where
\tcode{env} is an lvalue subexpression whose type is \tcode{Env}.
\end{itemdescr}

\rSec2[exec.adapt]{Sender adaptors}

\rSec3[exec.adapt.general]{General}

\pnum
Subclause \ref{exec.adapt} specifies a set of sender adaptors.

\pnum
The bitwise inclusive \logop{or} operator is overloaded
for the purpose of creating sender chains.
The adaptors also support function call syntax with equivalent semantics.

\pnum
Unless otherwise specified:
\begin{itemize}
\item
A sender adaptor is prohibited from causing observable effects,
apart from moving and copying its arguments,
before the returned sender is connected with a receiver using \tcode{connect},
and \tcode{start} is called on the resulting operation state.
\item
A parent sender\iref{exec.async.ops} with a single child sender \tcode{sndr} has
an associated attribute object equal to
\tcode{\exposid{FWD-ENV}(get_env(sndr))}\iref{exec.fwd.env}.
\item
A parent sender with more than one child sender has
an associated attributes object equal to \tcode{env<>\{\}}.
\item
When a parent sender is connected to a receiver \tcode{rcvr},
any receiver used to connect a child sender has
an associated environment equal to \tcode{\exposid{FWD-ENV}(get_env(rcvr))}.
\item
An adaptor whose child senders are all non-dependent\iref{exec.async.ops}
is itself non-dependent.
\item
These requirements apply to any function
that is selected by the implementation of the sender adaptor.
\item
 \recommended
Implementations should use
the completion signatures of the adaptors
to communicate type errors to users and
to propagate any such type errors from child senders.
\end{itemize}

\pnum
If a sender returned from a sender adaptor specified in \ref{exec.adapt}
is specified to include \tcode{set_error_t(Err)}
among its set of completion signatures
where \tcode{decay_t<Err>} denotes the type \tcode{exception_ptr},
but the implementation does not potentially evaluate
an error completion operation with an \tcode{exception_ptr} argument,
the implementation is allowed to omit
the \tcode{exception_ptr} error completion signature from the set.

\rSec3[exec.adapt.obj]{Closure objects}

\pnum
A \defnadj{pipeable}{sender adaptor closure object} is a function object
that accepts one or more \libconcept{sender} arguments and returns a \libconcept{sender}.
For a pipeable sender adaptor closure object \tcode{c} and
an expression \tcode{sndr}
such that \tcode{decltype((sndr))} models \libconcept{sender},
the following expressions are equivalent and yield a \libconcept{sender}:
\begin{codeblock}
c(sndr)
sndr | c
\end{codeblock}
Given an additional pipeable sender adaptor closure object \tcode{d},
the expression \tcode{c | d} produces
another pipeable sender adaptor closure object \tcode{e}:

\tcode{e} is a perfect forwarding call wrapper\iref{func.require}
with the following properties:
\begin{itemize}
\item
Its target object is an object \tcode{d2} of type \tcode{decltype(auto(d))}
direct-non-list-initialized with \tcode{d}.
\item
It has one bound argument entity,
an object \tcode{c2} of type \tcode{decltype(auto(c))}
direct-non-list-initialized with \tcode{c}.
\item
Its call pattern is \tcode{d2(c2(arg))},
where arg is the argument used in a function call expression of \tcode{e}.
\end{itemize}
The expression \tcode{c | d} is well-formed if and only if
the initializations of the state entities\iref{func.def} of \tcode{e}
are all well-formed.

\pnum
An object \tcode{t} of type \tcode{T} is
a pipeable sender adaptor closure object
if \tcode{T} models \tcode{\libconcept{derived_from}<sender_adaptor_closure<T>>},
\tcode{T} has no other base classes
of type \tcode{sender_adaptor_closure<U>} for any other type \tcode{U}, and
\tcode{T} does not satisfy \libconcept{sender}.

\pnum
The template parameter \tcode{D} for \tcode{sender_adaptor_closure} can be
an incomplete type.
Before any expression of type \cv{} \tcode{D} appears as
an operand to the \tcode{|} operator,
\tcode{D} shall be complete and
model \tcode{\libconcept{derived_from}<sender_adaptor_closure<D>>}.
The behavior of an expression involving an object of type \cv{} \tcode{D}
as an operand to the \tcode{|} operator is undefined
if overload resolution selects a program-defined \tcode{operator|} function.

\pnum
A \defnadj{pipeable}{sender adaptor object} is a customization point object
that accepts a \libconcept{sender} as its first argument and
returns a \libconcept{sender}.
If a pipeable sender adaptor object accepts only one argument,
then it is a pipeable sender adaptor closure object.

\pnum
If a pipeable sender adaptor object adaptor accepts more than one argument,
then let \tcode{sndr} be an expression
such that \tcode{decltype((sndr))} models \libconcept{sender},
let \tcode{args...} be arguments
such that \tcode{adaptor(sndr, args...)} is a well-formed expression
as specified below, and
let \tcode{BoundArgs} be a pack that denotes \tcode{decltype(auto(args))...}.
The expression \tcode{adaptor(args...)} produces
a pipeable sender adaptor closure object \tcode{f}
that is a perfect forwarding call wrapper with the following properties:
\begin{itemize}
\item
Its target object is a copy of adaptor.
\item
Its bound argument entities \tcode{bound_args} consist of
objects of types \tcode{BoundArgs...} direct-non-list-initialized with
\tcode{std::forward<decltype((args))>(args)...}, respectively.
\item
Its call pattern is \tcode{adaptor(rcvr, bound_args...)},
where \tcode{rcvr} is
the argument used in a function call expression of \tcode{f}.
\end{itemize}
The expression \tcode{adaptor(args...)} is well-formed if and only if
the initializations of the bound argument entities of the result,
as specified above, are all well-formed.

\rSec3[exec.write.env]{\tcode{execution::write_env}}

\pnum
\tcode{write_env} is a sender adaptor
that accepts a sender and a queryable object, and
that returns a sender that,
when connected with a receiver \tcode{rcvr},
connects the adapted sender with a receiver
whose execution environment is the result of
joining the \exposconcept{queryable} object
to the result of \tcode{get_env(rcvr)}.

\pnum
\tcode{write_env} is a customization point object.
For some subexpressions \tcode{sndr} and \tcode{env},
if \tcode{decltype((sndr))} does not satisfy \libconcept{sender} or
if \tcode{decltype((env))} does not satisfy \exposconcept{queryable},
the expression \tcode{write_env(sndr, env)} is ill-formed.
Otherwise, it is expression-equivalent to
\tcode{\exposid{make-sender}(write_env, env, sndr)}.

\pnum
Let \exposid{write-env-t} denote the type \tcode{decltype(auto(write_env))}.
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \exposid{write-env-t} as follows:
\indexlibraryglobal{\exposid{impls-for}<\exposid{write-env-t}>}
\begin{codeblock}
template<>
struct @\exposid{impls-for}@<@\exposid{write-env-t}@> : @\exposid{default-impls}@ {
  static constexpr auto @\exposid{join-env}@(const auto& state, const auto& env) noexcept {
    return @\seebelow@;
  }

  static constexpr auto @\exposid{get-env}@ =
    [](auto, const auto& state, const auto& rcvr) noexcept {
      return @\exposid{join-env}@(state, @\exposid{FWD-ENV}@(get_env(rcvr)));
    };

  template<class Sndr, class... Env>
    static consteval void @\exposid{check-types}@();
};
\end{codeblock}

\pnum
Invocation of
\tcode{\exposid{impls-for}<\exposid{write-env-t}>::\exposid{join-env}}
returns an object \tcode{e} such that
\begin{itemize}
\item
\tcode{decltype(e)} models \exposconcept{queryable} and
\item
given a query object \tcode{q},
the expression \tcode{e.query(q)} is expression-equivalent
to \tcode{state.query(q)} if that expression is valid,
otherwise, \tcode{e.query(q)} is expression-equivalent
to \tcode{env.query(q)}.
\end{itemize}

\pnum
For a type \tcode{Sndr} and a pack of types \tcode{Env},
let \tcode{State} be \tcode{\exposid{data-type}<Sndr>} and
let \tcode{JoinEnv} be the pack
\tcode{decltype(\exposid{join-env}(declval<State>(), \exposid{FWD-ENV}(declval<Env>())))}.
Then \tcode{\exposid{impls-for}<\exposid{write-env-\brk{}t}>::\exposid{check-types}<Sndr, Env...>()}
is expression-equivalent to
\tcode{get_completion_signatures<\exposid{child-\linebreak{}type}<Sndr>, JoinEnv...>()}.

\rSec3[exec.unstoppable]{\tcode{execution::unstoppable}}

\pnum
\tcode{unstoppable} is a sender adaptor
that connects its inner sender
with a receiver that has the execution environment of the outer receiver
but with an object of type \tcode{never_stop_token}
as the result of the \tcode{get_stop_token query}.

\pnum
For a subexpression \tcode{sndr},
\tcode{unstoppable(sndr)} is expression-equivalent to
\tcode{write_env(sndr, prop(get_stop_token, never_stop_token\{\}))}.

\rSec3[exec.starts.on]{\tcode{execution::starts_on}}

\pnum
\tcode{starts_on} adapts an input sender into a sender
that will start on an execution agent belonging to
a particular scheduler's associated execution resource.

\pnum
The name \tcode{starts_on} denotes a customization point object.
For subexpressions \tcode{sch} and \tcode{sndr},
if \tcode{decltype((\newline sch))} does not satisfy \libconcept{scheduler}, or
\tcode{decltype((sndr))} does not satisfy \libconcept{sender},
\tcode{starts_on(sch, sndr)} is ill-formed.

\pnum
Otherwise,
the expression \tcode{starts_on(sch, sndr)} is expression-equivalent to:
\begin{codeblock}
transform_sender(
  @\exposid{query-with-default}@(get_domain, sch, default_domain()),
  @\exposid{make-sender}@(starts_on, sch, sndr))
\end{codeblock}
except that \tcode{sch} is evaluated only once.

\pnum
Let \tcode{out_sndr} and \tcode{env} be subexpressions
such that \tcode{OutSndr} is \tcode{decltype((out_sndr))}.
If \tcode{\exposconcept{sender-for}<Out\-Sndr, starts_on_t>} is \tcode{false},
then the expressions \tcode{starts_on.transform_env(out_sndr, env)} and\linebreak
\tcode{starts_on.transform_sender(out_sndr, env)} are ill-formed; otherwise
\begin{itemize}
\item
\tcode{starts_on.transform_env(out_sndr, env)} is equivalent to:
\begin{codeblock}
auto&& [_, sch, _] = out_sndr;
return @\exposid{JOIN-ENV}@(@\exposid{SCHED-ENV}@(sch), @\exposid{FWD-ENV}@(env));
\end{codeblock}
\item
\tcode{starts_on.transform_sender(out_sndr, env)} is equivalent to:
\begin{codeblock}
auto&& [_, sch, sndr] = out_sndr;
return let_value(
  schedule(sch),
  [sndr = std::forward_like<OutSndr>(sndr)]() mutable
    noexcept(is_nothrow_move_constructible_v<decay_t<OutSndr>>) {
    return std::move(sndr);
  });
\end{codeblock}
\end{itemize}

\pnum
Let \tcode{out_sndr} be a subexpression denoting
a sender returned from \tcode{starts_on(sch, sndr)} or one equal to such, and
let \tcode{OutSndr} be the type \tcode{decltype((out_sndr))}.
Let \tcode{out_rcvr} be a subexpression denoting a receiver
that has an environment of type \tcode{Env}
such that \tcode{\libconcept{sender_in}<OutSndr, Env>} is \tcode{true}.
Let \tcode{op} be an lvalue referring to the operation state
that results from connecting \tcode{out_sndr} with \tcode{out_rcvr}.
Calling \tcode{start(op)} shall start \tcode{sndr}
on an execution agent of the associated execution resource of \tcode{sch}.
If scheduling onto \tcode{sch} fails,
an error completion on \tcode{out_rcvr} shall be executed
on an unspecified execution agent.

\rSec3[exec.continues.on]{\tcode{execution::continues_on}}

\pnum
\tcode{continues_on} adapts a sender into one
that completes on the specified scheduler.

\pnum
The name \tcode{continues_on} denotes a pipeable sender adaptor object.
For subexpressions \tcode{sch} and \tcode{sndr},
if \tcode{decltype((sch))} does not satisfy \libconcept{scheduler}, or
\tcode{decltype((sndr))} does not satisfy \libconcept{sender},
\tcode{continues_on(sndr, sch)} is ill-formed.

\pnum
Otherwise,
the expression \tcode{continues_on(sndr, sch)} is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(continues_on, sch, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{continues_on_t} as follows:
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<continues_on_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-attrs}@ =
      [](const auto& data, const auto& child) noexcept -> decltype(auto) {
        return @\exposid{JOIN-ENV}@(@\exposid{SCHED-ATTRS}@(data), @\exposid{FWD-ENV}@(get_env(child)));
      };
  };
}
\end{codeblock}

\pnum
Let \tcode{sndr} and \tcode{env} be subexpressions
such that \tcode{Sndr} is \tcode{decltype((sndr))}.
If \tcode{\exposconcept{sender-for}<Sndr, continues\-_on_t>} is \tcode{false},
then
the expression \tcode{continues_on.transform_sender(sndr, env)} is ill-formed;
otherwise, it is equal to:
\begin{codeblock}
auto [_, data, child] = sndr;
return schedule_from(std::move(data), std::move(child));
\end{codeblock}
\begin{note}
This causes the \tcode{continues_on(sndr, sch)} sender to become
\tcode{schedule_from(sch, sndr)} when it is connected with a receiver
whose execution domain does not customize \tcode{continues_on}.
\end{note}

\pnum
Let \tcode{out_sndr} be a subexpression denoting
a sender returned from \tcode{continues_on(sndr, sch)} or one equal to such, and
let \tcode{OutSndr} be the type \tcode{decltype((out_sndr))}.
Let \tcode{out_rcvr} be a subexpression denoting a receiver
that has an environment of type \tcode{Env}
such that \tcode{\libconcept{sender_in}<OutSndr, Env>} is \tcode{true}.
Let \tcode{op} be an lvalue referring to the operation state
that results from connecting \tcode{out_sndr} with \tcode{out_rcvr}.
Calling \tcode{start(op)} shall
start \tcode{sndr} on the current execution agent and
execute completion operations on \tcode{out_rcvr}
on an execution agent of the execution resource associated with \tcode{sch}.
If scheduling onto \tcode{sch} fails,
an error completion on \tcode{out_rcvr} shall be executed
on an unspecified execution agent.

\rSec3[exec.schedule.from]{\tcode{execution::schedule_from}}

\pnum
\tcode{schedule_from} schedules work dependent on the completion of a sender
onto a scheduler's associated execution resource.
\begin{note}
\tcode{schedule_from} is not meant to be used in user code;
it is used in the implementation of \tcode{continues_on}.
\end{note}

\pnum
The name \tcode{schedule_from} denotes a customization point object.
For some subexpressions \tcode{sch} and \tcode{sndr},
let \tcode{Sch} be \tcode{decltype((sch))} and
\tcode{Sndr} be \tcode{decltype((sndr))}.
If \tcode{Sch} does not satisfy \libconcept{scheduler}, or
\tcode{Sndr} does not satisfy \libconcept{sender},
\tcode{schedule_from(sch, sndr)} is ill-formed.

\pnum
Otherwise,
the expression \tcode{schedule_from(sch, sndr)} is expression-equivalent to:
\begin{codeblock}
transform_sender(
  @\exposid{query-with-default}@(get_domain, sch, default_domain()),
  @\exposid{make-sender}@(schedule_from, sch, sndr))
\end{codeblock}
except that \tcode{sch} is evaluated only once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{schedule_from_t} as follows:
\indexlibraryglobal{\exposid{impls-for}<schedule_from_t>}%
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<schedule_from_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-attrs}@ = @\seebelow@;
    static constexpr auto @\exposid{get-state}@ = @\seebelow@;
    static constexpr auto @\exposid{complete}@ = @\seebelow@;

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@();
  };
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<schedule_from_t>::\exposid{get-attrs}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](const auto& data, const auto& child) noexcept -> decltype(auto) {
  return @\exposid{JOIN-ENV}@(@\exposid{SCHED-ATTRS}@(data), @\exposid{FWD-ENV}@(get_env(child)));
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<schedule_from_t>::\exposid{get-state}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) noexcept(@\seebelow@)
    requires @\libconcept{sender_in}@<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(env_of_t<Rcvr>)> {

  auto& [_, sch, child] = sndr;

  using sched_t = decltype(auto(sch));
  using variant_t = @\seebelow@;
  using receiver_t = @\seebelow@;
  using operation_t = connect_result_t<schedule_result_t<sched_t>, receiver_t>;
  constexpr bool nothrow = noexcept(connect(schedule(sch), receiver_t{nullptr}));

  struct @\exposid{state-type}@ {
    Rcvr& @\exposid{rcvr}@;                 // \expos
    variant_t @\exposid{async-result}@;     // \expos
    operation_t @\exposid{op-state}@;       // \expos

    explicit @\exposid{state-type}@(sched_t sch, Rcvr& rcvr) noexcept(nothrow)
      : @\exposid{rcvr}@(rcvr), @\exposid{op-state}@(connect(schedule(sch), receiver_t{this})) {}
  };

  return @\exposid{state-type}@{sch, rcvr};
}
\end{codeblock}

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<schedule_from_t>}
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
get_completion_signatures<schedule_result_t<@\exposid{data-type}@<Sndr>>, @\exposid{FWD-ENV-T}@(Env)...>();
auto cs = get_completion_signatures<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)...>();
@\exposid{decay-copyable-result-datums}@(cs);   // see \ref{exec.snd.expos}
\end{codeblock}
\end{itemdescr}

\pnum
Objects of the local class \exposid{state-type} can be used
to initialize a structured binding.

\pnum
Let \tcode{Sigs} be
a pack of the arguments to the \tcode{completion_signatures} specialization
named by \tcode{completion_signatures_of_t<\exposid{child-type}<Sndr>, \exposid{FWD-ENV-T}(env_of_t<Rcvr>)>}.
Let \exposid{as-tuple} be an alias template such that
\tcode{\exposid{as-tuple}<Tag(Args...)>} denotes
the type \tcode{\exposid{decayed-tuple}<Tag, Args...>}, and
let \exposid{is-no\-throw-decay-copy-sig} be a variable template such that
\tcode{auto(\exposid{is-nothrow-decay-copy-sig}<Tag(Args...\linebreak{})>)} is
a constant expression of type \tcode{bool} and
equal to \tcode{(is_nothrow_constructible_v<decay_t<Args>, Args> \&\& ...)}.
Let \exposid{error-completion} be a pack consisting of
the type \tcode{set_error_t(exception_ptr)}
if \tcode{(\exposid{is-nothrow-decay-copy-sig}<Sigs> \&\&...)} is \tcode{false},
and an empty pack otherwise.
Then \tcode{variant_t} denotes
the type \tcode{variant<monostate, \exposid{as-tuple}<Sigs>..., \exposid{error-completion}...>},
except with duplicate types removed.

\pnum
\tcode{receiver_t} is an alias for the following exposition-only class:
\begin{codeblock}
namespace std::execution {
  struct @\exposid{receiver-type}@ {
    using receiver_concept = receiver_t;
    @\exposid{state-type}@* @\exposid{state}@;          // \expos

    void set_value() && noexcept {
      visit(
        [this]<class Tuple>(Tuple& result) noexcept -> void {
          if constexpr (!@\libconcept{same_as}@<monostate, Tuple>) {
            auto& [tag, ...args] = result;
            tag(std::move(@\exposid{state}@->@\exposid{rcvr}@), std::move(args)...);
          }
        },
        @\exposid{state}@->@\exposid{async-result}@);
    }

    template<class Error>
    void set_error(Error&& err) && noexcept {
      execution::set_error(std::move(@\exposid{state}@->@\exposid{rcvr}@), std::forward<Error>(err));
    }

    void set_stopped() && noexcept {
      execution::set_stopped(std::move(@\exposid{state}@->@\exposid{rcvr}@));
    }

    decltype(auto) get_env() const noexcept {
      return @\exposid{FWD-ENV}@(execution::get_env(@\exposid{state}@->@\exposid{rcvr}@));
    }
  };
}
\end{codeblock}

\pnum
The expression in the \tcode{noexcept} clause of the lambda is \tcode{true}
if the construction of the returned \exposid{state-type} object
is not potentially throwing;
otherwise, \tcode{false}.

\pnum
The member \tcode{\exposid{impls-for}<schedule_from_t>::\exposid{complete}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Tag, class... Args>(auto, auto& state, auto& rcvr, Tag, Args&&... args) noexcept
    -> void {
  using result_t = @\exposid{decayed-tuple}@<Tag, Args...>;
  constexpr bool nothrow = (is_nothrow_constructible_v<decay_t<Args>, Args> && ...);

  try {
    state.@\exposid{async-result}@.template emplace<result_t>(Tag(), std::forward<Args>(args)...);
  } catch (...) {
    if constexpr (!nothrow)
      state.@\exposid{async-result}@.template emplace<tuple<set_error_t,
                                                exception_ptr>>(set_error, current_exception());
  }
  start(state.@\exposid{op-state}@);
};
\end{codeblock}

\pnum
Let \tcode{out_sndr} be a subexpression denoting
a sender returned from \tcode{schedule_from(sch, sndr)} or one equal to such,
and let \tcode{OutSndr} be the type \tcode{decltype((out_sndr))}.
Let \tcode{out_rcvr} be a subexpression denoting a receiver
that has an environment of type \tcode{Env}
such that \tcode{\libconcept{sender_in}<OutSndr, Env>} is \tcode{true}.
Let \tcode{op} be an lvalue referring to the operation state
that results from connecting \tcode{out_sndr} with \tcode{out_rcvr}.
Calling \tcode{start(op)} shall
start \tcode{sndr} on the current execution agent and
execute completion operations on \tcode{out_rcvr}
on an execution agent of the execution resource associated with \tcode{sch}.
If scheduling onto \tcode{sch} fails,
an error completion on \tcode{out_rcvr} shall be executed
on an unspecified execution agent.

\rSec3[exec.on]{\tcode{execution::on}}

\pnum
The \tcode{on} sender adaptor has two forms:
\begin{itemize}
\item
\tcode{on(sch, sndr)},
which starts a sender \tcode{sndr} on an execution agent
belonging to a scheduler \tcode{sch}'s associated execution resource and
that, upon \tcode{sndr}'s completion,
transfers execution back to the execution resource
on which the \tcode{on} sender was started.
\item
\tcode{on(sndr, sch, closure)},
which upon completion of a sender \tcode{sndr},
transfers execution to an execution agent
belonging to a scheduler \tcode{sch}'s associated execution resource,
then executes a sender adaptor closure \tcode{closure}
with the async results of the sender, and
that then transfers execution back to the execution resource
on which \tcode{sndr} completed.
\end{itemize}

\pnum
The name \tcode{on} denotes a pipeable sender adaptor object.
For subexpressions \tcode{sch} and \tcode{sndr},
\tcode{on(sch, sndr)} is ill-formed if any of the following is \tcode{true}:
\begin{itemize}
\item
\tcode{decltype((sch))} does not satisfy \libconcept{scheduler}, or
\item
\tcode{decltype((sndr))} does not satisfy \libconcept{sender} and
\tcode{sndr} is not
a pipeable sender adaptor closure object\iref{exec.adapt.obj}, or
\item
\tcode{decltype((sndr))} satisfies \libconcept{sender} and
\tcode{sndr }is also a pipeable sender adaptor closure object.
\end{itemize}

\pnum
Otherwise, if \tcode{decltype((sndr))} satisfies \libconcept{sender},
the expression \tcode{on(sch, sndr)} is expression-equivalent to:
\begin{codeblock}
transform_sender(
  @\exposid{query-with-default}@(get_domain, sch, default_domain()),
  @\exposid{make-sender}@(on, sch, sndr))
\end{codeblock}
except that \tcode{sch} is evaluated only once.

\pnum
For subexpressions \tcode{sndr}, \tcode{sch}, and \tcode{closure}, if
\begin{itemize}
\item
\tcode{decltype((sch))} does not satisfy \libconcept{scheduler}, or
\item
\tcode{decltype((sndr))} does not satisfy \libconcept{sender}, or
\item
\tcode{closure} is not a pipeable sender adaptor closure object\iref{exec.adapt.obj},
\end{itemize}
the expression \tcode{on(sndr, sch, closure)} is ill-formed;
otherwise, it is expression-equivalent to:
\begin{codeblock}
transform_sender(
  @\exposid{get-domain-early}@(sndr),
  @\exposid{make-sender}@(on, @\exposid{product-type}@{sch, closure}, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.

\pnum
Let \tcode{out_sndr} and \tcode{env} be subexpressions,
let \tcode{OutSndr} be \tcode{decltype((out_sndr))}, and
let \tcode{Env} be \tcode{decltype((\linebreak env))}.
If \tcode{\exposconcept{sender-for}<OutSndr, on_t>} is \tcode{false},
then the expressions \tcode{on.transform_env(out_sndr, env)} and
\tcode{on.transform_sender(out_sndr, env)} are ill-formed.

\pnum
Otherwise:
Let \exposid{not-a-scheduler} be an unspecified empty class type.

\pnum
The expression \tcode{on.transform_env(out_sndr, env)}
has effects equivalent to:
\begin{codeblock}
auto&& [_, data, _] = out_sndr;
if constexpr (@\libconcept{scheduler}@<decltype(data)>) {
  return @\exposid{JOIN-ENV}@(@\exposid{SCHED-ENV}@(std::forward_like<OutSndr>(data)), @\exposid{FWD-ENV}@(std::forward<Env>(env)));
} else {
  return std::forward<Env>(env);
}
\end{codeblock}

\pnum
The expression \tcode{on.transform_sender(out_sndr, env)}
has effects equivalent to:
\begin{codeblock}
auto&& [_, data, child] = out_sndr;
if constexpr (@\libconcept{scheduler}@<decltype(data)>) {
  auto orig_sch =
    @\exposid{query-with-default}@(get_scheduler, env, @\exposid{not-a-scheduler}@());

  if constexpr (@\libconcept{same_as}@<decltype(orig_sch), @\exposid{not-a-scheduler}@>) {
    return @\exposid{not-a-sender}@{};
  } else {
    return continues_on(
      starts_on(std::forward_like<OutSndr>(data), std::forward_like<OutSndr>(child)),
      std::move(orig_sch));
  }
} else {
  auto& [sch, closure] = data;
  auto orig_sch = @\exposid{query-with-default}@(
    get_completion_scheduler<set_value_t>,
    get_env(child),
    @\exposid{query-with-default}@(get_scheduler, env, @\exposid{not-a-scheduler}@()));

  if constexpr (@\libconcept{same_as}@<decltype(orig_sch), @\exposid{not-a-scheduler}@>) {
    return @\exposid{not-a-sender}@{};
  } else {
    return write_env(
      continues_on(
        std::forward_like<OutSndr>(closure)(
          continues_on(
            write_env(std::forward_like<OutSndr>(child), @\exposid{SCHED-ENV}@(orig_sch)),
            sch)),
        orig_sch),
      @\exposid{SCHED-ENV}@(sch));
  }
}
\end{codeblock}

\pnum
Let \tcode{out_sndr} be a subexpression denoting
a sender returned from \tcode{on(sch, sndr)} or one equal to such, and
let \tcode{OutSndr} be the type \tcode{decltype((out_sndr))}.
Let \tcode{out_rcvr} be a subexpression denoting a receiver
that has an environment of type \tcode{Env}
such that \tcode{\libconcept{sender_in}<OutSndr, Env>} is \tcode{true}.
Let \tcode{op} be an lvalue referring to the operation state
that results from connecting \tcode{out_sndr} with \tcode{out_rcvr}.
Calling \tcode{start(op)} shall
\begin{itemize}
\item
remember the current scheduler, \tcode{get_scheduler(get_env(rcvr))};
\item
start \tcode{sndr} on an execution agent belonging to
\tcode{sch}'s associated execution resource;
\item
upon \tcode{sndr}'s completion,
transfer execution back to the execution resource
associated with the scheduler remembered in step 1; and
\item
forward \tcode{sndr}'s async result to \tcode{out_rcvr}.
\end{itemize}
If any scheduling operation fails,
an error completion on \tcode{out_rcvr} shall be executed
on an unspecified execution agent.

\pnum
Let \tcode{out_sndr} be a subexpression denoting
a sender returned from \tcode{on(sndr, sch, closure)} or one equal to such, and
let \tcode{OutSndr} be the type \tcode{decltype((out_sndr))}.
Let \tcode{out_rcvr} be a subexpression denoting a receiver
that has an environment of type \tcode{Env}
such that \tcode{\libconcept{sender_in}<OutSndr, Env>} is \tcode{true}.
Let \tcode{op} be an lvalue referring to the operation state
that results from connecting \tcode{out_sndr} with \tcode{out_rcvr}.
Calling \tcode{start(op)} shall
\begin{itemize}
\item
remember the current scheduler,
which is the first of the following expressions that is well-formed:
\begin{itemize}
\item \tcode{get_completion_scheduler<set_value_t>(get_env(sndr))}
\item \tcode{get_scheduler(get_env(rcvr))};
\end{itemize}
\item
start \tcode{sndr} on the current execution agent;
\item
upon \tcode{sndr}'s completion,
transfer execution to an agent
owned by \tcode{sch}'s associated execution resource;
\item
forward \tcode{sndr}'s async result as if by
connecting and starting a sender \tcode{closure(S)},
where \tcode{S} is a sender
that completes synchronously with \tcode{sndr}'s async result; and
\item
upon completion of the operation started in the previous step,
transfer execution back to the execution resource
associated with the scheduler remembered in step 1 and
forward the operation's async result to \tcode{out_rcvr}.
\end{itemize}
If any scheduling operation fails,
an error completion on \tcode{out_rcvr} shall be executed on
an unspecified execution agent.

\rSec3[exec.then]{\tcode{execution::then}, \tcode{execution::upon_error}, \tcode{execution::upon_stopped}}

\pnum
\tcode{then} attaches an invocable as a continuation
for an input sender's value completion operation.
\tcode{upon_error} and \tcode{upon_stopped} do the same
for the error and stopped completion operations, respectively,
sending the result of the invocable as a value completion.

\pnum
The names \tcode{then}, \tcode{upon_error}, and \tcode{upon_stopped}
denote pipeable sender adaptor objects.
Let the expression \exposid{then-cpo} be one of
\tcode{then}, \tcode{upon_error}, or \tcode{upon_stopped}.
For subexpressions \tcode{sndr} and \tcode{f},
if \tcode{decltype((sndr))} does not satisfy \libconcept{sender}, or
\tcode{decltype((f))} does not satisfy \exposconcept{movable-value},
\tcode{\exposid{then-cpo}(\linebreak sndr, f) }is ill-formed.

\pnum
Otherwise,
the expression \tcode{\exposid{then-cpo}(sndr, f)} is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(@\exposid{then-cpo}@, f, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.

\pnum
For \tcode{then}, \tcode{upon_error}, and \tcode{upon_stopped},
let \exposid{set-cpo} be
\tcode{set_value}, \tcode{set_error}, and \tcode{set_stopped}, respectively.
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \exposid{then-cpo} as follows:
\indexlibraryglobal{\exposid{impls-for}<\exposid{decayed-typeof}<\exposid{then-cpo}>>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<@\exposid{decayed-typeof}@<@\exposid{then-cpo}@>> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{complete}@ =
      []<class Tag, class... Args>
        (auto, auto& fn, auto& rcvr, Tag, Args&&... args) noexcept -> void {
          if constexpr (@\libconcept{same_as}@<Tag, @\exposid{decayed-typeof}@<set-cpo>>) {
            @\exposid{TRY-SET-VALUE}@(rcvr,
                          invoke(std::move(fn), std::forward<Args>(args)...));
          } else {
            Tag()(std::move(rcvr), std::forward<Args>(args)...);
          }
        };

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@();
  };
}
\end{codeblock}

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<\exposid{decayed-typeof}<\exposid{then-cpo}>>}
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto cs = get_completion_signatures<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)...>();
auto fn = []<class... Ts>(set_value_t(*)(Ts...)) {
  if constexpr (!@\libconcept{invocable}@<remove_cvref_t<@\exposid{data-type}@<Sndr>>, Ts...>)
    throw @\placeholder{unspecified-exception}@();
};
cs.@\exposid{for-each}@(@\exposid{overload-set}@{fn, [](auto){}});
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.
\end{itemdescr}

\pnum
The expression \tcode{\exposid{then-cpo}(sndr, f)} has undefined behavior
unless it returns a sender \tcode{out_sndr} that
\begin{itemize}
\item
invokes \tcode{f} or a copy of such
with the value, error, or stopped result datums of \tcode{sndr}
for \tcode{then}, \tcode{upon_error}, and \tcode{upon_stopped}, respectively,
using the result value of \tcode{f} as \tcode{out_sndr}'s value completion, and
\item
forwards all other completion operations unchanged.
\end{itemize}

\rSec3[exec.let]{\tcode{execution::let_value}, \tcode{execution::let_error}, \tcode{execution::let_stopped}}

\pnum
\tcode{let_value}, \tcode{let_error}, and \tcode{let_stopped} transform
a sender's value, error, and stopped completions, respectively,
into a new child asynchronous operation
by passing the sender's result datums to a user-specified callable,
which returns a new sender that is connected and started.

\pnum
For \tcode{let_value}, \tcode{let_error}, and \tcode{let_stopped},
let \exposid{set-cpo} be
\tcode{set_value}, \tcode{set_error}, and \tcode{set_stopped}, respectively.
Let the expression \exposid{let-cpo} be one of
\tcode{let_value}, \tcode{let_error}, or \tcode{let_stopped}.
For a subexpression \tcode{sndr},
let \tcode{\exposid{let-env}(sndr)} be expression-equivalent to
the first well-formed expression below:
\begin{itemize}
\item
\tcode{\exposid{SCHED-ENV}(get_completion_scheduler<\exposid{decayed-typeof}<\exposid{set-cpo}>>(get_env(sndr)))}
\item
\tcode{\exposid{MAKE-ENV}(get_domain, get_domain(get_env(sndr)))}
\item
\tcode{(void(sndr), env<>\{\})}
\end{itemize}

\pnum
The names \tcode{let_value}, \tcode{let_error}, and \tcode{let_stopped} denote
pipeable sender adaptor objects.
For subexpressions \tcode{sndr} and \tcode{f},
let \tcode{F} be the decayed type of \tcode{f}.
If \tcode{decltype((sndr))} does not satisfy \libconcept{sender} or
if \tcode{decltype((f))} does not satisfy \exposconcept{movable-value},
the expression \tcode{\exposid{let-cpo}(sndr, f)} is ill-formed.
If \tcode{F} does not satisfy \libconcept{invocable},
the expression \tcode{let_stopped(sndr, f)} is ill-formed.

\pnum
Otherwise,
the expression \tcode{\exposid{let-cpo}(sndr, f)} is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(@\exposid{let-cpo}@, f, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \exposid{let-cpo} as follows:
\indexlibraryglobal{\exposid{impls-for}<\exposid{decayed-typeof}<\exposid{let-cpo}>>}
\begin{codeblock}
namespace std::execution {
  template<class State, class Rcvr, class... Args>
  void @\exposid{let-bind}@(State& state, Rcvr& rcvr, Args&&... args);      // \expos

  template<>
  struct @\exposid{impls-for}@<@\exposid{decayed-typeof}@<@\exposid{let-cpo}@>> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-state}@ = @\seebelow@;
    static constexpr auto @\exposid{complete}@ = @\seebelow@;

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@();
  };
}
\end{codeblock}

\pnum
Let \exposid{receiver2} denote the following exposition-only class template:
\begin{codeblock}
namespace std::execution {
  template<class Rcvr, class Env>
  struct @\exposid{receiver2}@ {
    using receiver_concept = receiver_t;

    template<class... Args>
    void set_value(Args&&... args) && noexcept {
      execution::set_value(std::move(@\exposid{rcvr}@), std::forward<Args>(args)...);
    }

    template<class Error>
    void set_error(Error&& err) && noexcept {
      execution::set_error(std::move(@\exposid{rcvr}@), std::forward<Error>(err));
    }

    void set_stopped() && noexcept {
      execution::set_stopped(std::move(@\exposid{rcvr}@));
    }

    decltype(auto) get_env() const noexcept {
      return @\seebelow@;
    }

    Rcvr& @\exposid{rcvr}@;                 // \expos
    Env @\exposid{env}@;                    // \expos
  };
}
\end{codeblock}
Invocation of the function \tcode{\exposid{receiver2}::get_env}
returns an object \tcode{e} such that
\begin{itemize}
\item
\tcode{decltype(e)} models \exposconcept{queryable} and
\item
given a query object \tcode{q},
the expression \tcode{e.query(q)} is expression-equivalent
to \tcode{\exposid{env}.query(q)} if that expression is valid;
otherwise,
if the type of \tcode{q} satisfies \exposconcept{forwarding-query},
\tcode{e.query(q)} is expression-equivalent
to \tcode{get_env(\exposid{rcvr}).query(q)};
otherwise,
\tcode{e.query(q)} is ill-formed.
\end{itemize}

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<\exposid{decayed-typeof}<\exposid{let-cpo}>>}
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
using LetFn = remove_cvref_t<@\exposid{data-type}@<Sndr>>;
auto cs = get_completion_signatures<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)...>();
auto fn = []<class... Ts>(@\exposid{decayed-typeof}@<@\exposid{set-cpo}@>(*)(Ts...)) {
  if constexpr (!@\placeholder{is-valid-let-sender}@)   // \seebelow
    throw @\placeholder{unspecified-exception}@();
};
cs.@\exposid{for-each}@(@\exposid{overload-set}@(fn, [](auto){}));
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}, and
where \tcode{\placeholder{is-valid-let-sender}} is \tcode{true} if and only if
all of the following are \tcode{true}:
\begin{itemize}
\item \tcode{(\libconcept{constructible_from}<decay_t<Ts>, Ts> \&\&...)}
\item \tcode{\libconcept{invocable}<LetFn, decay_t<Ts>\&...>}
\item \tcode{\libconcept{sender}<invoke_result_t<LetFn, decay_t<Ts>\&...>>}
\item%
\tcode{sizeof...(Env) == 0 || \libconcept{sender_in}<invoke_result_t<LetFn, decay_t<Ts>\&...>, \placeholder{env-t}\linebreak{}...>}
\end{itemize}
where \tcode{\placeholder{env-t}} is the pack
\tcode{decltype(\exposid{let-cpo}.transform_env(declval<Sndr>(), declval<Env>()))}.
\end{itemdescr}

\pnum
\tcode{\exposid{impls-for}<\exposid{decayed-typeof}<\exposid{let-cpo}>>::\exposid{get-state}}
is initialized with a callable object equivalent to the following:
\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) requires @\seebelow@ {
  auto& [_, fn, child] = sndr;
  using fn_t = decay_t<decltype(fn)>;
  using env_t = decltype(@\exposid{let-env}@(child));
  using args_variant_t = @\seebelow@;
  using ops2_variant_t = @\seebelow@;

  struct @\exposid{state-type}@ {
    fn_t @\exposid{fn}@;                    // \expos
    env_t @\exposid{env}@;                  // \expos
    args_variant_t @\exposid{args}@;        // \expos
    ops2_variant_t @\exposid{ops2}@;        // \expos
  };
  return @\exposid{state-type}@{@\exposid{allocator-aware-forward}@(std::forward_like<Sndr>(fn), rcvr),
                    @\exposid{let-env}@(child), {}, {}};
}
\end{codeblock}

\pnum
Let \tcode{Sigs} be a pack of the arguments
to the \tcode{completion_signatures} specialization named by
\tcode{completion_signatures_of_t<\exposid{child-type}<Sndr>, \exposid{FWD-ENV-T}(env_of_t<Rcvr>)>}.
Let \tcode{LetSigs} be a pack of those types in \tcode{Sigs}
with a return type of \tcode{\exposid{decayed-typeof}<\exposid{set-cpo}>}.
Let \exposid{as-tuple} be an alias template
such that \tcode{\exposid{as-tuple}<Tag(Args...)>} denotes
the type \tcode{\exposid{decayed-tuple}<Args...>}.
Then \tcode{args_variant_t} denotes
the type \tcode{variant<monostate, \exposid{as-tuple}<LetSigs>...>}
except with duplicate types removed.

\pnum
Given a type \tcode{Tag} and a pack \tcode{Args},
let \exposid{as-sndr2} be an alias template
such that \tcode{\exposid{as-sndr2}<Tag(Args...)>} denotes
the type \tcode{\exposid{call-result-t}<F, decay_t<Args>\&...>}.
Then \tcode{ops2_variant_t} denotes
the type
\begin{codeblock}
variant<monostate, connect_result_t<@\exposid{as-sndr2}@<LetSigs>, @\exposid{receiver2}@<Rcvr, env_t>>...>
\end{codeblock}
except with duplicate types removed.

\pnum
The \grammarterm{requires-clause} constraining the above lambda is satisfied
if and only if
the types \tcode{args_variant_t} and \tcode{ops2_variant_t} are well-formed.

\pnum
The exposition-only function template \exposid{let-bind}
has effects equivalent to:
\begin{codeblock}
using args_t = @\exposid{decayed-tuple}@<Args...>;
auto mkop2 = [&] {
  return connect(
    apply(std::move(state.fn),
          state.args.template emplace<args_t>(std::forward<Args>(args)...)),
    @\exposid{receiver2}@{rcvr, std::move(state.env)});
};
start(state.ops2.template emplace<decltype(mkop2())>(@\exposid{emplace-from}@{mkop2}));
\end{codeblock}

\pnum
\tcode{\exposid{impls-for}<\exposid{decayed-typeof}<let-cpo>>::\exposid{complete}}
is initialized with a callable object equivalent to the following:
\begin{codeblock}
[]<class Tag, class... Args>
  (auto, auto& state, auto& rcvr, Tag, Args&&... args) noexcept -> void {
    if constexpr (@\libconcept{same_as}@<Tag, @\exposid{decayed-typeof}@<@\exposid{set-cpo}@>>) {
      @\exposid{TRY-EVAL}@(rcvr, @\exposid{let-bind}@(state, rcvr, std::forward<Args>(args)...));
    } else {
      Tag()(std::move(rcvr), std::forward<Args>(args)...);
    }
  }
\end{codeblock}

\pnum
Let \tcode{sndr} and \tcode{env} be subexpressions, and
let \tcode{Sndr} be \tcode{decltype((sndr))}.
If
\tcode{\exposconcept{sender-for}<Sndr, \exposid{decayed-\linebreak typeof}<\exposid{let-cpo}>>}
is \tcode{false},
then the expression \tcode{\exposid{let-cpo}.transform_env(sndr, env)}
is ill-formed.
Otherwise, it is equal to:
\begin{codeblock}
auto& [_, _, child] = sndr;
return @\exposid{JOIN-ENV}@(@\exposid{let-env}@(child), @\exposid{FWD-ENV}@(env));
\end{codeblock}

\pnum
Let the subexpression \tcode{out_sndr} denote
the result of the invocation \tcode{\exposid{let-cpo}(sndr, f)} or
an object equal to such, and
let the subexpression \tcode{rcvr} denote a receiver
such that the expression \tcode{connect(out_sndr, rcvr)} is well-formed.
The expression \tcode{connect(out_sndr, rcvr)} has undefined behavior
unless it creates an asynchronous operation\iref{exec.async.ops} that,
when started:
\begin{itemize}
\item
invokes \tcode{f} when \exposid{set-cpo} is called
with \tcode{sndr}'s result datums,
\item
makes its completion dependent on
the completion of a sender returned by \tcode{f}, and
\item
propagates the other completion operations sent by \tcode{sndr}.
\end{itemize}

\rSec3[exec.bulk]{\tcode{execution::bulk}, \tcode{execution::bulk_chunked}, and \tcode{execution::bulk_unchunked}}

\pnum
\tcode{bulk}, \tcode{bulk_chunked}, and \tcode{bulk_unchunked}
run a task repeatedly for every index in an index space.

\pnum
The names \tcode{bulk}, \tcode{bulk_chunked}, and \tcode{bulk_unchunked}
denote pipeable sender adaptor objects.
Let \tcode{\placeholder{bulk-algo}} be either
\tcode{bulk}, \tcode{bulk_chunked}, or \tcode{bulk_unchunked}.
For subexpressions \tcode{sndr}, \tcode{policy}, \tcode{shape}, and \tcode{f},
let
\tcode{Policy} be \tcode{remove_cvref_t<decltype(policy)>},
\tcode{Shape} be \tcode{decltype(auto(shape))}, and
\tcode{Func} be \tcode{decay_t<decltype((f))>}.
If
\begin{itemize}
\item
\tcode{decltype((sndr))} does not satisfy \libconcept{sender}, or
\item
\tcode{is_execution_policy_v<Policy>} is \tcode{false}, or
\item
\tcode{Shape} does not satisfy \libconcept{integral}, or
\item
\tcode{Func} does not model \libconcept{copy_constructible},
\end{itemize}
\tcode{\placeholder{bulk-algo}(sndr, policy, shape, f)} is ill-formed.

\pnum
Otherwise,
the expression \tcode{\placeholder{bulk-algo}(sndr, policy, shape, f)}
is expression-equivalent to:

\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(
    @\placeholder{bulk-algo}@, @\exposid{product-type}@<@\seebelow@, Shape, Func>{policy, shape, f}, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.
The first template argument of \exposid{product-type} is \tcode{Policy}
if \tcode{Policy} models \libconcept{copy_constructible}, and
\tcode{const Policy\&} otherwise.

\pnum
Let \tcode{sndr} and \tcode{env} be subexpressions such that
\tcode{Sndr} is \tcode{decltype((sndr))}.
If \tcode{\exposconcept{sender-for}<Sndr, bulk_t>} is \tcode{false}, then
the expression \tcode{bulk.transform_sender(sndr, env)} is ill-formed;
otherwise, it is equivalent to:
\begin{codeblock}
auto [_, data, child] = sndr;
auto& [policy, shape, f] = data;
auto new_f = [func = std::move(f)](Shape begin, Shape end, auto&&... vs)
    noexcept(noexcept(f(begin, vs...))) {
  while (begin != end) func(begin++, vs...);
}
return bulk_chunked(std::move(child), policy, shape, std::move(new_f));
\end{codeblock}
\begin{note}
This causes the \tcode{bulk(sndr, policy, shape, f)} sender to be
expressed in terms of \tcode{bulk_chunked(sndr, policy, shape, f)} when
it is connected to a receiver whose
execution domain does not customize \tcode{bulk}.
\end{note}

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{bulk_chunked_t} as follows:
\indexlibraryglobal{\exposid{impls-for}<bulk_chunked_t>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<bulk_chunked_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{complete}@ = @\seebelow@;

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@();
  };
}
\end{codeblock}
The member \tcode{\exposid{impls-for}<bulk_chunked_t>::\exposid{complete}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Index, class State, class Rcvr, class Tag, class... Args>
  (Index, State& state, Rcvr& rcvr, Tag, Args&&... args) noexcept
  -> void requires @\seebelow@ {
    if constexpr (@\libconcept{same_as}@<Tag, set_value_t>) {
      auto& [policy, shape, f] = state;
      constexpr bool nothrow = noexcept(f(auto(shape), auto(shape), args...));
      @\exposid{TRY-EVAL}@(rcvr, [&]() noexcept(nothrow) {
        f(static_cast<decltype(auto(shape))>(0), auto(shape), args...);
        Tag()(std::move(rcvr), std::forward<Args>(args)...);
      }());
    } else {
      Tag()(std::move(rcvr), std::forward<Args>(args)...);
    }
  }
\end{codeblock}
The expression in the \grammarterm{requires-clause} of the lambda above is
\tcode{true} if and only
if \tcode{Tag} denotes a type other than \tcode{set_value_t} or
if the expression \tcode{f(auto(shape), auto(shape), args...)} is well-formed.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{bulk_unchunked_t} as follows:
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<bulk_unchunked_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{complete}@ = @\seebelow@;
  };
}
\end{codeblock}
The member \tcode{\exposid{impls-for}<bulk_unchunked_t>::\exposid{complete}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Index, class State, class Rcvr, class Tag, class... Args>
  (Index, State& state, Rcvr& rcvr, Tag, Args&&... args) noexcept
  -> void requires @\seebelow@ {
    if constexpr (@\libconcept{same_as}@<Tag, set_value_t>) {
      auto& [shape, f] = state;
      constexpr bool nothrow = noexcept(f(auto(shape), args...));
      @\exposid{TRY-EVAL}@(rcvr, [&]() noexcept(nothrow) {
        for (decltype(auto(shape)) i = 0; i < shape; ++i) {
          f(auto(i), args...);
        }
        Tag()(std::move(rcvr), std::forward<Args>(args)...);
      }());
    } else {
      Tag()(std::move(rcvr), std::forward<Args>(args)...);
    }
  }
\end{codeblock}
The expression in the \grammarterm{requires-clause} of the lambda above
is \tcode{true} if and only
if \tcode{Tag} denotes a type other than \tcode{set_value_t} or
if the expression \tcode{f(auto(shape), args...)} is well-formed.

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<bulk_t>}
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto cs = get_completion_signatures<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)...>();
auto fn = []<class... Ts>(set_value_t(*)(Ts...)) {
  if constexpr (!@\libconcept{invocable}@<remove_cvref_t<@\exposid{data-type}@<Sndr>>, Ts&...>)
    throw @\placeholder{unspecified-exception}@();
};
cs.@\exposid{for-each}@(@\exposid{overload-set}@(fn, [](auto){}));
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.
\end{itemdescr}

\pnum
Let the subexpression \tcode{out_sndr} denote
the result of the invocation
\tcode{\placeholder{bulk-algo}(sndr, policy, shape, f)} or
an object equal to such, and
let the subexpression \tcode{rcvr} denote a receiver
such that the expression \tcode{connect(out_sndr, rcvr)} is well-formed.
The expression \tcode{connect(out_sndr, rcvr)} has undefined behavior
unless it creates an asynchronous operation\iref{exec.async.ops} that,
when started:

\begin{itemize}
\item
If \tcode{sndr} has a successful completion, where
\tcode{args} is a pack of lvalue subexpressions
referring to the value completion result datums of \tcode{sndr}, or
decayed copies of those values if they model \libconcept{copy_constructible},
then:

  \begin{itemize}
  \item
  If \tcode{out_sndr} also completes successfully, then:

    \begin{itemize}
    \item
    for \tcode{bulk},
    invokes \tcode{f($i$, args...)} for every $i$ of type \tcode{Shape}
    from \tcode{0} to \tcode{shape};

    \item
    for \tcode{bulk_unchunked},
    invokes \tcode{f($i$, args...)} for every $i$ of type \tcode{Shape}
    from \tcode{0} to \tcode{shape};

    \recommended
    The underlying scheduler should execute each iteration
    on a distinct execution agent.

    \item
    for \tcode{bulk_chunked},
    invokes \tcode{f($b$, $e$, args...)} zero or more times
    with pairs of $b$ and $e$ of type \tcode{Shape}
    in range \crange{\tcode{0}}{\tcode{shape}},
    such that $b < e$ and
    for every $i$ of type \tcode{Shape} from \tcode{0} to \tcode{shape},
    there is exactly one invocation with a pair $b$ and $e$,
    such that $i$ is in the range \range{$b$}{$e$}.
    \end{itemize}

  \item
  If \tcode{out_sndr} completes with \tcode{set_error(rcvr, eptr)}, then
  the asynchronous operation may invoke a subset of
  the invocations of \tcode{f}
  before the error completion handler is called, and
  \tcode{eptr} is an \tcode{exception_ptr} containing either:
    \begin{itemize}
    \item
    an exception thrown by an invocation of \tcode{f}, or
    \item
    a \tcode{bad_alloc} exception if
    the implementation fails to allocate required resources, or
    \item
    an exception derived from \tcode{runtime_error}.
    \end{itemize}

  \item
  If \tcode{out_sndr} completes with \tcode{set_stopped(rcvr)}, then
  the asynchronous operation may invoke a subset of
  the invocations of \tcode{f}
  before the stopped completion handler.
  \end{itemize}

\item
If \tcode{sndr} does not complete with \tcode{set_value}, then
the completion is forwarded to \tcode{recv}.

\item
For \tcode{\placeholder{bulk-algo}},
the parameter \tcode{policy} describes
the manner in which
the execution of the asynchronous operations corresponding to these algorithms
may be parallelized and
the manner in which
%%FIXME: Should this be "apply to f"?
they apply \tcode{f}.
Permissions and requirements
on parallel algorithm element access functions\iref{algorithms.parallel.exec}
apply to \tcode{f}.
\end{itemize}

\pnum
\begin{note}
The asynchronous operation corresponding to
\tcode{\placeholder{bulk-algo}(sndr, policy, shape, f)}
can complete with \tcode{set_stopped} if cancellation is requested or
ignore cancellation requests.
\end{note}

\rSec3[exec.when.all]{\tcode{execution::when_all}}

\pnum
\tcode{when_all} and \tcode{when_all_with_variant}
both adapt multiple input senders into a sender
that completes when all input senders have completed.
\tcode{when_all} only accepts senders
with a single value completion signature and
on success concatenates all the input senders' value result datums
into its own value completion operation.
\tcode{when_all_with_variant(sndrs...)} is semantically equivalent to
w\tcode{hen_all(into_variant(sndrs)...)},
where \tcode{sndrs} is a pack of subexpressions
whose types model \libconcept{sender}.

\pnum
The names \tcode{when_all} and \tcode{when_all_with_variant} denote
customization point objects.
Let \tcode{sndrs} be a pack of subexpressions,
let \tcode{Sndrs} be a pack of the types \tcode{decltype((sndrs))...}, and
let \tcode{CD} be
the type \tcode{common_type_t<decltype(\exposid{get-domain-early}(sndrs))...>}.
Let \tcode{CD2} be \tcode{CD} if \tcode{CD} is well-formed, and
\tcode{default_domain} otherwise.
The expressions \tcode{when_all(sndrs...)} and
\tcode{when_all_with_variant(sndrs...)} are ill-formed
if any of the following is \tcode{true}:
\begin{itemize}
\item
\tcode{sizeof...(sndrs)} is \tcode{0}, or
\item
\tcode{(\libconcept{sender}<Sndrs> \&\& ...)} is \tcode{false}.
\end{itemize}

\pnum
The expression \tcode{when_all(sndrs...)} is expression-equivalent to:
\begin{codeblock}
transform_sender(CD2(), @\exposid{make-sender}@(when_all, {}, sndrs...))
\end{codeblock}

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{when_all_t} as follows:
\indexlibraryglobal{\exposid{impls-for}<when_all_t>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<when_all_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-attrs}@ = @\seebelow@;
    static constexpr auto @\exposid{get-env}@ = @\seebelow@;
    static constexpr auto @\exposid{get-state}@ = @\seebelow@;
    static constexpr auto @\exposid{start}@ = @\seebelow@;
    static constexpr auto @\exposid{complete}@ = @\seebelow@;

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@();
  };
}
\end{codeblock}

\pnum
Let \exposid{make-when-all-env} be
the following exposition-only function template:
\indexlibraryglobal{\exposid{make-when-all-env}}
%%FIXME: Should this be in namespace std::execution?
\begin{codeblock}
template<class Env>
  constexpr auto @\exposid{make-when-all-env}@(inplace_stop_source& stop_src,               // \expos
                                   Env&& env) noexcept {
  return @\seebelow@;
}
\end{codeblock}
Returns an object \tcode{e} such that
\begin{itemize}
\item
\tcode{decltype(e)} models \exposconcept{queryable}, and
\item
\tcode{e.query(get_stop_token)} is expression-equivalent to
\tcode{state.\exposid{stop-src}.get_token()}, and
\item
given a query object \tcode{q}
with type other than \cv{} \tcode{stop_token_t} and
whose type satisfies \exposconceptx{forwarding-que\-ry}{forwarding-query},
\tcode{e.query(q)} is expression-equivalent to \tcode{get_env(rcvr).query(q)}.
\end{itemize}

\pnum
Let \tcode{\placeholder{when-all-env}} be an alias template such that
\tcode{\placeholder{when-all-env}<Env>} denotes the type
\tcode{decltype(\exposid{make-\linebreak{}when-all-env}(declval<inplace_stop_source\&>(), declval<Env>()))}.

\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<when_all_t>}
\begin{itemdecl}
template<class Sndr, class... Env>
  static consteval void @\exposid{check-types}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \tcode{Is} be the pack of integral template arguments of
the \tcode{integer_sequence} specialization denoted by
\tcode{\exposid{indices-for}<Sndr>}.

\pnum
\effects
Equivalent to:
\begin{codeblock}
auto fn = []<class Child>() {
  auto cs = get_completion_signatures<Child, @\placeholder{when-all-env}@<Env>...>();
  if constexpr (cs.@\exposid{count-of}@(set_value) >= 2)
    throw @\placeholder{unspecified-exception}@();
  @\exposid{decay-copyable-result-datums}@(cs); // see \ref{exec.snd.expos}
};
(fn.template operator()<@\exposid{child-type}@<Sndr, Is>>(), ...);
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.

\pnum
\throws
Any exception thrown as a result of evaluating the \Fundescx{Effects}, or
an exception of an unspecified type
derived from \tcode{exception} when \tcode{CD} is ill-formed.
\end{itemdescr}

\pnum
The member \tcode{\exposid{impls-for}<when_all_t>::\exposid{get-attrs}}
is initialized with a callable object
equivalent to the following lambda expression:
\begin{codeblock}
[](auto&&, auto&&... child) noexcept {
  if constexpr (@\libconcept{same_as}@<CD, default_domain>) {
    return env<>();
  } else {
    return @\exposid{MAKE-ENV}@(get_domain, CD());
  }
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<when_all_t>::\exposid{get-env}}
is initialized with a callable object
equivalent to the following lambda expression:
\begin{codeblock}
[]<class State, class Rcvr>(auto&&, State& state, const Receiver& rcvr) noexcept {
  return @\exposid{make-when-all-env}@(state.@\exposid{stop-src}@, get_env(rcvr));
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<when_all_t>::\exposid{get-state}}
is initialized with a callable object
equivalent to the following lambda expression:
\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) noexcept(noexcept(@$e$@)) -> decltype(@$e$@) {
  return @$e$@;
}
\end{codeblock}
where $e$ is the expression
\begin{codeblock}
std::forward<Sndr>(sndr).@\exposid{apply}@(@\exposid{make-state}@<Rcvr>())
\end{codeblock}
and where \exposid{make-state} is the following exposition-only class template:
\begin{codeblock}
enum class @\exposid{disposition}@ { @\exposid{started}@, @\exposid{error}@, @\exposid{stopped}@ };             // \expos

template<class Rcvr>
struct @\exposid{make-state}@ {
  template<class... Sndrs>
  auto operator()(auto, auto, Sndrs&&... sndrs) const {
    using values_tuple = @\seebelow@;
    using errors_variant = @\seebelow@;
    using stop_callback = stop_callback_for_t<stop_token_of_t<env_of_t<Rcvr>>, @\exposid{on-stop-request}@>;

    struct @\exposid{state-type}@ {
      void @\exposid{arrive}@(Rcvr& rcvr) noexcept {                        // \expos
        if (0 == --count) {
          @\exposid{complete}@(rcvr);
        }
      }

      void @\exposid{complete}@(Rcvr& rcvr) noexcept;                       // \expos

      atomic<size_t> @\exposid{count}@{sizeof...(sndrs)};                   // \expos
      inplace_stop_source @\exposid{stop_src}@{};                           // \expos
      atomic<@\exposid{disposition}@> disp{@\exposidnc{disposition}@::@\exposidnc{started}@};           // \expos
      errors_variant @\exposid{errors}@{};                                  // \expos
      values_tuple @\exposid{values}@{};                                    // \expos
      optional<stop_callback> @\exposid{on_stop}@{nullopt};                 // \expos
    };

    return @\exposid{state-type}@{};
  }
};
\end{codeblock}

\pnum
Let \exposid{copy-fail} be \tcode{exception_ptr}
if decay-copying any of the child senders' result datums can potentially throw;
otherwise, \tcode{\placeholder{none-such}},
where \tcode{\placeholder{none-such}} is an unspecified empty class type.

\pnum
The alias \tcode{values_tuple} denotes the type
\begin{codeblock}
tuple<value_types_of_t<Sndrs, @\exposid{FWD-ENV-T}@(env_of_t<Rcvr>), @\exposid{decayed-tuple}@, optional>...>
\end{codeblock}
if that type is well-formed; otherwise, \tcode{tuple<>}.

\pnum
The alias \tcode{errors_variant} denotes
the type \tcode{variant<\placeholder{none-such}, \exposid{copy-fail}, Es...>}
with duplicate types removed,
where \tcode{Es} is the pack of the decayed types
of all the child senders' possible error result datums.

\pnum
The member
\tcode{void \exposid{state-type}::\exposid{complete}(Rcvr\& rcvr) noexcept}
behaves as follows:
\begin{itemize}
\item
If \tcode{disp} is equal to \tcode{\exposid{disposition}::\exposid{started}},
evaluates:
\begin{codeblock}
auto tie = []<class... T>(tuple<T...>& t) noexcept { return tuple<T&...>(t); };
auto set = [&](auto&... t) noexcept { set_value(std::move(rcvr), std::move(t)...); };

@\exposid{on_stop}@.reset();
apply(
  [&](auto&... opts) noexcept {
    apply(set, tuple_cat(tie(*opts)...));
  },
  values);
\end{codeblock}
\item
Otherwise,
if \tcode{disp} is equal to \tcode{\exposid{disposition}::\exposid{error}},
evaluates:
\begin{codeblock}
@\exposid{on_stop}@.reset();
visit(
  [&]<class Error>(Error& error) noexcept {
    if constexpr (!@\libconcept{same_as}@<Error, @\placeholder{none-such}@>) {
      set_error(std::move(rcvr), std::move(error));
    }
  },
  errors);
\end{codeblock}
\item
Otherwise, evaluates:
\begin{codeblock}
@\exposid{on_stop}@.reset();
set_stopped(std::move(rcvr));
\end{codeblock}
\end{itemize}

\pnum
The member \tcode{\exposid{impls-for}<when_all_t>::\exposid{start}}
is initialized with a callable object
equivalent to the following lambda expression:
\begin{codeblock}
[]<class State, class Rcvr, class... Ops>(
    State& state, Rcvr& rcvr, Ops&... ops) noexcept -> void {
  state.@\exposid{on_stop}@.emplace(
    get_stop_token(get_env(rcvr)),
    @\exposid{on-stop-request}@{state.@\exposid{stop_src}@});
  if (state.@\exposid{stop_src}@.stop_requested()) {
    state.@\exposid{on_stop.}@reset();
    set_stopped(std::move(rcvr));
  } else {
    (start(ops), ...);
  }
}
\end{codeblock}

\pnum
The member \exposid{\tcode{impls-for}<when_all_t>::\exposid{complete}}
is initialized with a callable object
equivalent to the following lambda expression:
\begin{codeblock}
[]<class Index, class State, class Rcvr, class Set, class... Args>(
    this auto& complete, Index, State& state, Rcvr& rcvr, Set, Args&&... args) noexcept -> void {
  if constexpr (@\libconcept{same_as}@<Set, set_error_t>) {
    if (@\exposid{disposition}@::@\exposid{error}@ != state.disp.exchange(@\exposid{disposition}@::@\exposid{error}@)) {
      state.@\exposid{stop_src}@.request_stop();
      @\exposid{TRY-EMPLACE-ERROR}@(state.errors, std::forward<Args>(args)...);
    }
  } else if constexpr (@\libconcept{same_as}@<Set, set_stopped_t>) {
    auto expected = @\exposid{disposition}@::@\exposid{started}@;
    if (state.disp.compare_exchange_strong(expected, @\exposid{disposition}@::@\exposid{stopped}@)) {
      state.@\exposid{stop_src}@.request_stop();
    }
  } else if constexpr (!@\libconcept{same_as}@<decltype(State::values), tuple<>>) {
    if (state.disp == @\exposid{disposition}@::@\exposid{started}@) {
      auto& opt = get<Index::value>(state.values);
      @\exposid{TRY-EMPLACE-VALUE}@(complete, opt, std::forward<Args>(args)...);
    }
  }
  state.@\exposid{arrive}@(rcvr);
}
\end{codeblock}
where \tcode{\exposid{TRY-EMPLACE-ERROR}(v, e)},
for subexpressions \tcode{v} and \tcode{e}, is equivalent to:
\begin{codeblock}
try {
  v.template emplace<decltype(auto(e))>(e);
} catch (...) {
  v.template emplace<exception_ptr>(current_exception());
}
\end{codeblock}
if the expression \tcode{decltype(auto(e))(e)} is potentially throwing;
otherwise, \tcode{v.template emplace<decl\-type(auto(e))>(e)};
and where \tcode{\exposid{TRY-EMPLACE-VALUE}(c, o, as...)},
for subexpressions \tcode{c}, \tcode{o}, and pack of subexpressions \tcode{as},
is equivalent to:
\begin{codeblock}
try {
  o.emplace(as...);
} catch (...) {
  c(Index(), state, rcvr, set_error, current_exception());
  return;
}
\end{codeblock}
if the expression \tcode{\exposid{decayed-tuple}<decltype(as)...>\{as...\}}
is potentially throwing;
otherwise, \tcode{o.emplace(\linebreak as...)}.

\pnum
The expression \tcode{when_all_with_variant(sndrs...)}
is expression-equivalent to:
\begin{codeblock}
transform_sender(CD2(), @\exposid{make-sender}@(when_all_with_variant, {}, sndrs...));
\end{codeblock}

\pnum
Given subexpressions \tcode{sndr} and \tcode{env},
if
\tcode{\exposconcept{sender-for}<decltype((sndr)), when_all_with_variant_t>}
is \tcode{false},
then the expression \tcode{when_all_with_variant.transform_sender(sndr, env)}
is ill-formed;
otherwise, it is equivalent to:
\begin{codeblock}
auto&& [_, _, ...child] = sndr;
return when_all(into_variant(std::forward_like<decltype((sndr))>(child))...);
\end{codeblock}
\begin{note}
This causes the \tcode{when_all_with_variant(sndrs...)} sender
to become \tcode{when_all(into_variant(sndrs)...)}
when it is connected with a receiver
whose execution domain does not customize \tcode{when_all_with_variant}.
\end{note}

\rSec3[exec.into.variant]{\tcode{execution::into_variant}}

\pnum
\tcode{into_variant} adapts a sender with multiple value completion signatures
into a sender with just one value completion signature
consisting of a \tcode{variant} of \tcode{tuple}s.

\pnum
The name \tcode{into_variant} denotes a pipeable sender adaptor object.
For a subexpression \tcode{sndr}, let \tcode{Sndr} be \tcode{decltype((sndr))}.
If \tcode{Sndr} does not satisfy \libconcept{sender},
\tcode{into_variant(sndr)} is ill-formed.

\pnum
Otherwise, the expression \tcode{into_variant(sndr)}
is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(into_variant, {}, sndr))
\end{codeblock}
except that \tcode{sndr} is only evaluated once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{into_variant} as follows:
\indexlibraryglobal{\exposid{impls-for}<into_variant_t>}
\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<into_variant_t>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<into_variant_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-state}@ = @\seebelow@;
    static constexpr auto @\exposid{complete}@ = @\seebelow@;

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@() {
        auto cs = get_completion_signatures<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)...>();
        @\exposid{decay-copyable-result-datums}@(cs);   // see \ref{exec.snd.expos}
      }
  };
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<into_variant_t>::\exposid{get-state}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) noexcept
  -> type_identity<value_types_of_t<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(env_of_t<Rcvr>)>> {
  return {};
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<into_variant_t>::\exposid{complete}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[]<class State, class Rcvr, class Tag, class... Args>(
    auto, State, Rcvr& rcvr, Tag, Args&&... args) noexcept -> void {
  if constexpr (@\libconcept{same_as}@<Tag, set_value_t>) {
    using variant_type = typename State::type;
    @\exposid{TRY-SET-VALUE}@(rcvr, variant_type(@\exposid{decayed-tuple}@<Args...>{std::forward<Args>(args)...}));
  } else {
    Tag()(std::move(rcvr), std::forward<Args>(args)...);
  }
}
\end{codeblock}

\rSec3[exec.stopped.opt]{\tcode{execution::stopped_as_optional}}

\pnum
\tcode{stopped_as_optional} maps a sender's stopped completion operation
into a value completion operation as a disengaged \tcode{optional}.
The sender's value completion operation
is also converted into an \tcode{optional}.
The result is a sender that never completes with stopped,
reporting cancellation by completing with a disengaged \tcode{optional}.

\pnum
The name \tcode{stopped_as_optional} denotes a pipeable sender adaptor object.
For a subexpression \tcode{sndr}, let \tcode{Sndr} be \tcode{decltype((sndr))}.
The expression \tcode{stopped_as_optional(sndr)} is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(stopped_as_optional, {}, sndr))
\end{codeblock}
except that \tcode{sndr} is only evaluated once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{stopped_as_optional_t} as follows:
\indexlibraryglobal{\exposid{impls-for}<stopped_as_optional_t>}
\indexlibrarymember{\exposid{check-types}}{\exposid{impls-for}<stopped_as_optional_t>}
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<stopped_as_optional_t> : @\exposid{default-impls}@ {
    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@() {
        @\exposid{default-impls}@::@\exposid{check-types}@<Sndr, Env...>();
        if constexpr (!requires {
          requires (!@\libconcept{same_as}@<void, @\exposid{single-sender-value-type}@<@\exposid{child-type}@<Sndr>,
                                                            @\exposid{FWD-ENV-T}@(Env)...>>); })
          throw @\placeholder{unspecified-exception}@();
      }
  };
}
\end{codeblock}
where \tcode{\placeholder{unspecified-exception}} is
a type derived from \tcode{exception}.

\pnum
Let \tcode{sndr} and \tcode{env} be subexpressions
such that \tcode{Sndr} is \tcode{decltype((sndr))} and
\tcode{Env} is \tcode{decltype((env))}.
If \tcode{\exposconcept{sender-for}<Sndr, stopped_as_optional_t>}
is \tcode{false}
then the expression \tcode{stopped_as_optional.trans\-form_sender(sndr, env)}
is ill-formed;
otherwise,
if \tcode{\libconcept{sender_in}<\exposid{child-type}<Sndr>, \exposid{FWD-ENV-T}(Env)>}
is \tcode{false},
the expression \tcode{stopped_as_optional.transform_sender(sndr, env)}
is equivalent to \tcode{\exposid{not-a-sen\-der}()};
otherwise, it is equivalent to:
\begin{codeblock}
auto&& [_, _, child] = sndr;
using V = @\exposid{single-sender-value-type}@<@\exposid{child-type}@<Sndr>, @\exposid{FWD-ENV-T}@(Env)>;
return let_stopped(
  then(std::forward_like<Sndr>(child),
       []<class... Ts>(Ts&&... ts) noexcept(is_nothrow_constructible_v<V, Ts...>) {
         return optional<V>(in_place, std::forward<Ts>(ts)...);
       }),
  []() noexcept { return just(optional<V>()); });
\end{codeblock}

\rSec3[exec.stopped.err]{\tcode{execution::stopped_as_error}}

\pnum
\tcode{stopped_as_error} maps an input sender's stopped completion operation
into an error completion operation as a custom error type.
The result is a sender that never completes with stopped,
reporting cancellation by completing with an error.

\pnum
The name \tcode{stopped_as_error} denotes a pipeable sender adaptor object.
For some subexpressions \tcode{sndr} and \tcode{err},
let \tcode{Sndr} be \tcode{decltype((sndr))} and
let \tcode{Err} be \tcode{decltype((err))}.
If the type \tcode{Sndr} does not satisfy \libconcept{sender} or
if the type \tcode{Err} does not satisfy \exposconcept{movable-value},
\tcode{stopped_as_error(sndr, err)} is ill-formed.
Otherwise, the expression \tcode{stopped_as_error(sndr, err)}
is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(stopped_as_error, err, sndr))
\end{codeblock}
except that \tcode{sndr} is only evaluated once.

\pnum
Let \tcode{sndr} and \tcode{env} be subexpressions
such that \tcode{Sndr} is \tcode{decltype((sndr))} and
\tcode{Env} is \tcode{decltype((env))}.
If \tcode{\exposconcept{sender-for}<Sndr, stopped_as_error_t>} is \tcode{false},
then the expression \tcode{stopped_as_error.transform_sender(sndr, env)}
is ill-formed;
otherwise, it is equivalent to:
\begin{codeblock}
auto&& [_, err, child] = sndr;
using E = decltype(auto(err));
return let_stopped(
  std::forward_like<Sndr>(child),
  [err = std::forward_like<Sndr>(err)]() mutable noexcept(is_nothrow_move_constructible_v<E>) {
    return just_error(std::move(err));
  });
\end{codeblock}

\rSec3[exec.associate]{\tcode{execution::associate}}

\pnum
\tcode{associate} tries to associate
a sender with an async scope such that
the scope can track the lifetime of any asynchronous operations
created with the sender.

\pnum
Let \exposid{associate-data} be the following exposition-only class template:

\indexlibraryglobal{execution::\exposid{associate-data}}%
\begin{codeblock}
namespace std::execution {
  template<@\libconcept{scope_token}@ Token, @\libconcept{sender}@ Sender>
  struct @\exposid{associate-data}@ {                                       // \expos
    using @\exposid{wrap-sender}@ =                                         // \expos
      remove_cvref_t<decltype(declval<Token&>().wrap(declval<Sender>()))>;

    explicit @\exposid{associate-data}@(Token t, Sender&& s)
      : @\exposid{sndr}@(t.wrap(std::forward<Sender>(s))),
        @\exposid{token}@(t) {
      if (!@\exposid{token}@.try_associate())
        @\exposid{sndr}@.reset();
    }

    @\exposid{associate-data}@(const @\exposid{associate-data}@& other)
      noexcept(is_nothrow_copy_constructible_v<@\exposid{wrap-sender}@> &&
               noexcept(other.@\exposid{token}@.try_associate()));

    @\exposid{associate-data}@(@\exposid{associate-data}@&& other)
      noexcept(is_nothrow_move_constructible_v<@\exposid{wrap-sender}@>);

    ~@\exposid{associate-data}@();

    optional<pair<Token, @\exposid{wrap-sender}@>>
      release() && noexcept(is_nothrow_move_constructible_v<@\exposid{wrap-sender}@>);

  private:
    optional<@\exposid{wrap-sender}@> @\exposid{sndr}@;  // \expos
    Token @\exposid{token}@;                 // \expos
  };

  template<@\libconcept{scope_token}@ Token, @\libconcept{sender}@ Sender>
    @\exposid{associate-data}@(Token, Sender&&) -> @\exposid{associate-data}@<Token, Sender>;
}
\end{codeblock}

\pnum
For an \exposid{associate-data} object \tcode{a},
\tcode{a.\exposid{sndr}.has_value()} is \tcode{true}
if and only if
an association was successfully made and is owned by \tcode{a}.

\indexlibraryctor{execution::\exposid{associate-data}}%
\begin{itemdecl}
@\exposid{associate-data}@(const @\exposid{associate-data}@& other)
  noexcept(is_nothrow_copy_constructible_v<@\exposid{wrap-sender}@> &&
           noexcept(other.@\exposid{token}@.try_associate()));
\end{itemdecl}

\begin{itemdescr}
\pnum
\constraints
\tcode{\libconcept{copy_constructible}<\exposid{wrap-sender}>} is \tcode{true}.

\pnum
\effects
Value-initializes \exposid{sndr} and
initializes \exposid{token} with \tcode{other.\exposid{token}}.
If \tcode{other.\exposid{sndr}.has_value()} is \tcode{false},
no further effects;
otherwise,
calls \tcode{\exposid{token}.try_associate()} and,
if that returns \tcode{true},
calls \tcode{\exposid{sndr}.emplace(*other.\exposid{sndr})} and,
if that exits with an exception,
calls \tcode{\exposid{token}.disassociate()} before propagating the exception.
\end{itemdescr}

\indexlibraryctor{execution::\exposid{associate-data}}%
\begin{itemdecl}
@\exposid{associate-data}@(@\exposid{associate-data}@&& other)
  noexcept(is_nothrow_move_constructible_v<@\exposid{wrap-sender}@>);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Initializes \exposid{sndr} with \tcode{std::move(other.\exposid{sndr})} and
initializes \exposid{token} with \tcode{std::move(other.\brk{}\exposid{token})} and
then calls \tcode{other.\exposid{sndr}.reset()}.
\end{itemdescr}

\indexlibrarydtor{execution::\exposid{associate-data}}%
\begin{itemdecl}
~@\exposid{associate-data}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \tcode{\exposid{sndr}.has_value()} returns \tcode{false} then no effect;
otherwise, invokes \tcode{\exposid{sndr}.reset()}
before invoking \tcode{\exposid{token}.disassociate()}.
\end{itemdescr}

\indexlibrarymember{release}{execution::\exposid{associate-data}}%
\begin{itemdecl}
optional<pair<Token, @\exposid{wrap-sender}@>>
  release() && noexcept(is_nothrow_move_constructible_v<@\exposid{wrap-sender}@>);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \tcode{\exposid{sndr}.has_value()} returns \tcode{false} then
returns an \tcode{optional} that does not contain a value;
otherwise returns an \tcode{optional}
containing a value of type \tcode{pair<Token, \exposid{wrap-sender}>}
as if by:
\begin{codeblock}
return optional(pair(@\exposid{token}@, std::move(*@\exposid{sndr}@)));
\end{codeblock}

\pnum
\ensures
\exposid{sndr} does not contain a value.
\end{itemdescr}

\pnum
The name \tcode{associate} denotes a pipeable sender adaptor object.
For subexpressions \tcode{sndr} and \tcode{token}:
\begin{itemize}
\item
If \tcode{decltype((sndr))} does not satisfy \libconcept{sender}, or
\tcode{remove_cvref_t<decltype((token))>}
does not satisfy \libconcept{scope_token}, then
\tcode{associate(sndr, token)} is ill-formed.
\item
Otherwise,
the expression \tcode{associate(sndr, token)}
is expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr),
                 @\exposid{make-sender}@(associate, @\exposid{associate-data}@(token, sndr)))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.
\end{itemize}

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{associate_t} as follows:
\indexlibraryglobal{execution::\exposid{impls-for}<associate_t>}%
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<associate_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-state}@ = @\seebelow@;                // \expos
    static constexpr auto @\exposid{start}@ = @\seebelow@;                    // \expos

    template<class Sndr, class... Env>
      static consteval void @\exposid{check-types}@() {                     // \expos
        using associate_data_t = remove_cvref_t<@\exposid{data-type}@<Sndr>>;
        using child_type_t = typename associate_data_t::@\exposid{wrap-sender}@;
        (void)get_completion_signatures<child_type_t, @\exposid{FWD-ENV-T}@(Env)...>();
    }
  };
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<associate_t>::\exposid{get-state}}
is initialized with a callable object equivalent to the following lambda:

\begin{codeblock}
[]<class Sndr, class Rcvr>(Sndr&& sndr, Rcvr& rcvr) noexcept(@\seebelow@) {
  auto [_, data] = std::forward<Sndr>(sndr);
  auto dataParts = std::move(data).release();

  using scope_tkn = decltype(dataParts->first);
  using wrap_sender = decltype(dataParts->second);
  using op_t = connect_result_t<wrap_sender, Rcvr>;

  struct op_state {
    bool @\exposid{associated}@ = false;    // \expos
    union {
      Rcvr* @\exposid{rcvr}@;               // \expos
      struct {
        scope_tkn @\exposid{token}@;        // \expos
        op_t @\exposid{op}@;                // \expos
      } @\exposid{assoc}@;                  // \expos
    };

    explicit op_state(Rcvr& r) noexcept
      : @\exposid{rcvr}@(addressof(r)) {}

    explicit op_state(scope_tkn tkn, wrap_sender&& sndr, Rcvr& r) try
      : @\exposid{associated}@(true),
        @\exposid{assoc}@(tkn, connect(std::move(sndr), std::move(r))) {
    }
    catch (...) {
      tkn.disassociate();
      throw;
    }

    op_state(op_state&&) = delete;

    ~op_state() {
      if (@\exposid{associated}@) {
        @\exposid{assoc}@.@\exposid{op}@.~op_t();
        @\exposid{assoc}@.@\exposid{token}@.disassociate();
        @\exposid{assoc}@.@\exposid{token}@.~scope_tkn();
      }
    }

    void @\exposid{run}@() noexcept {       // \expos
      if (@\exposid{associated}@)
        start(@\exposid{assoc}@.@\exposid{op}@);
      else
        set_stopped(std::move(*@\exposid{rcvr}@));
    }
  };

  if (dataParts)
    return op_state{std::move(dataParts->first), std::move(dataParts->second), rcvr};
  else
    return op_state{rcvr};
}
\end{codeblock}

\pnum
The expression in the \tcode{noexcept} clause of
\tcode{\exposid{impls-for}<associate_t>::\exposid{get-state}} is
\begin{codeblock}
is_nothrow_constructible_v<remove_cvref_t<Sndr>, Sndr> &&
is_nothrow_move_constructible_v<@\exposid{wrap-sender}@> &&
@\exposconcept{nothrow-callable}@<connect_t, @\exposid{wrap-sender}@, Rcvr>
\end{codeblock}
where \exposid{wrap-sender} is the type
\tcode{remove_cvref_t<\exposid{data-type}<Sndr>>::\exposid{wrap-sender}}.

\pnum
The member \tcode{\exposid{impls-for}<associate_t>::\exposid{start}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](auto& state, auto&) noexcept -> void {
  state.@\exposid{run}@();
}
\end{codeblock}

\pnum
%%FIXME: What are "sndr" and "token" referring to here?
The evaluation of \tcode{associate(sndr, token)}
may cause side effects observable
via \tcode{token}{'s} associated async scope object.

\rSec3[exec.stop.when]{Exposition-only \tcode{execution::\exposid{stop-when}}}

\pnum
%%FIXME: Should stop-when be declared somewhere as \expos?
\exposid{stop-when} fuses an additional stop token \tcode{t}
into a sender so that, upon connecting to a receiver \tcode{r},
the resulting operation state receives stop requests from both
\tcode{t} and the token returned from \tcode{get_stop_token(get_env(r))}.

\pnum
The name \exposid{stop-when} denotes an exposition-only sender adaptor.
For subexpressions \tcode{sndr} and \tcode{token}:
\begin{itemize}
\item
If \tcode{decltype((sndr))} does not satisfy \libconcept{sender}, or
\tcode{remove_cvref_t<decltype((token))>}
does not satisfy \libconcept{stoppable_token},
then \tcode{\exposid{stop-when}(sndr, token)} is ill-formed.

\item
Otherwise,
if \tcode{remove_cvref_t<decltype((token))>} models
\libconcept{unstoppable_token} then
\tcode{\exposid{stop-when}(\brk{}sndr, token)} is expression-equivalent to
\tcode{sndr}.

\item
Otherwise,
\tcode{\exposid{stop-when}(sndr, token)} returns a sender \tcode{osndr}.
%%FIXME: What is rtoken if osndr is not connected to a receiver?
If \tcode{osndr} is connected to a receiver \tcode{r},
let \tcode{rtoken} be the result of \tcode{get_stop_token(get_env(r))}.

\begin{itemize}
\item
If the type of \tcode{rtoken} models \libconcept{unstoppable_token} then
the effects of connecting \tcode{osndr} to \tcode{r}
are equivalent to
\tcode{connect(write_env(sndr, prop(get_stop_token, token)), r)}.

\item
Otherwise,
the effects of connecting \tcode{osndr} to \tcode{r}
are equivalent to
\tcode{connect(write_env(sndr, prop(get_stop_token, stoken)), r)}
where \tcode{stoken} is an object of
an exposition-only type \exposid{stoken-t} such that:
  \begin{itemize}
  \item
  \exposid{stoken-t} models \libconcept{stoppable_token};
  \item
  \tcode{stoken.stop_requested()} returns
  \tcode{token.stop_requested() || rtoken.stop_reques-\linebreak{}ted()};
  \item
  \tcode{stoken.stop_possible()} returns
  \tcode{token.stop_possible() || rtoken.stop_possible()}; and
  \item
  for types \tcode{Fn} and \tcode{Init} such that both
  \tcode{\libconcept{invocable}<Fn>} and
  \tcode{\libconcept{constructible_from}<Fn, Init>}
  are modeled,
  \tcode{\exposid{stoken-t}::callback_type<Fn>} models
  \tcode{\exposconcept{stoppable-callback-for}<Fn, \exposid{sto\-ken-t}, Init>}.
  \begin{tailnote}
  For an object \tcode{fn} of type \tcode{Fn}
  constructed from a value, \tcode{init}, of type \tcode{Init},
  registering \tcode{fn} using
  \tcode{\exposid{stoken-t}::callback_type<Fn>(stoken, init)}
  results in an invocation of \tcode{fn} when
  a callback registered with \tcode{token} or \tcode{rtoken} would be invoked.
  \tcode{fn} is invoked at most once.
  \end{tailnote}
  \end{itemize}
\end{itemize}
\end{itemize}

\rSec3[exec.spawn.future]{\tcode{execution::spawn_future}}

\pnum
\tcode{spawn_future} attempts to associate the given input sender
with the given token's async scope and, on success,
eagerly starts the input sender;
the return value is a sender that, when connected and started,
completes with either
the result of the eagerly-started input sender or with
\tcode{set_stopped} if the input sender was not started.

\pnum
The name \tcode{spawn_future} denotes a customization point object.
For subexpressions \tcode{sndr}, \tcode{token}, and \tcode{env},
\begin{itemize}
\item let \tcode{Sndr} be \tcode{decltype((sndr))},
\item let \tcode{Token} be \tcode{remove_cvref_t<decltype((token))>}, and
\item let \tcode{Env} be \tcode{remove_cvref_t<decltype((env))>}.
\end{itemize}
If any of
\tcode{\libconcept{sender}<Sndr>},
\tcode{\libconcept{scope_token}<Token>}, or
\tcode{\exposconcept{queryable}<Env>}
are not satisfied,
the expression \tcode{spawn_future(sndr, token, env)} is ill-formed.

\pnum
Let \exposid{spawn-future-state-base} be the exposition-only class template:

\indexlibraryglobal{execution::\exposid{spawn-future-state-base}}%
\begin{codeblock}
namespace std::execution {
  template<class Completions>
  struct @\exposid{spawn-future-state-base}@;                                   // \expos

  template<class... Sigs>
  struct @\exposid{spawn-future-state-base}@<completion_signatures<Sigs...>> {  // \expos
    using @\exposid{variant-t}@ = @\seebelow@;                                    // \expos
    @\exposid{variant-t}@ @\exposid{result}@;                                               // \expos
    virtual void @\exposid{complete}@() noexcept = 0;                           // \expos
  };
}
\end{codeblock}

\pnum
Let \tcode{Sigs} be the pack of arguments to
the \tcode{completion_signatures} specialization provided as
a parameter to the \exposid{spawn-future-state-base} class template.
Let \exposid{as-tuple} be an alias template that
transforms a completion signature \tcode{Tag(Args...)}
into the tuple specialization \tcode{\exposid{decayed-tuple}<Tag, Args...>}.

\begin{itemize}
\item
If \tcode{is_nothrow_constructible_v<decay_t<Arg>, Arg>} is \tcode{true}
for every type \tcode{Arg}
in every parameter pack \tcode{Args}
in every completion signature \tcode{Tag(Args...)}
in \tcode{Sigs} then
\exposid{variant-t} denotes the type
\tcode{variant<monostate, tuple<set_stopped_t>, \placeholder{as-tuple}<Sigs>...>},
except with duplicate types removed.

\item
Otherwise
\exposid{variant-t} denotes the type
\tcode{variant<monostate, tuple<set_stopped_t>, tuple<set_error_t, exception_ptr>, \placeholder{as-tuple}<Sigs>...>},
except with duplicate types removed.
\end{itemize}

\pnum
Let \exposid{spawn-future-receiver} be the exposition-only class template:

\indexlibraryglobal{execution::\exposid{spawn-future-receiver}}%
\begin{codeblock}
namespace std::execution {
  template<class Completions>
  struct @\exposid{spawn-future-receiver}@ {                                // \expos
    using receiver_concept = receiver_t;

    @\exposid{spawn-future-state-base}@<Completions>* @\exposid{state}@;                // \expos

    template<class... T>
      void set_value(T&&... t) && noexcept {
        @\exposid{set-complete}@<set_value_t>(std::forward<T>(t)...);
      }

    template<class E>
      void set_error(E&& e) && noexcept {
        @\exposid{set-complete}@<set_error_t>(std::forward<E>(e));
      }

    void set_stopped() && noexcept {
      @\exposid{set-complete}@<set_stopped_t>();
    }

  private:
    template<class CPO, class... T>
      void @\exposid{set-complete}@(T&&... t) noexcept {                    // \expos
        constexpr bool nothrow = (is_nothrow_constructible_v<decay_t<T>, T> && ...);
        try {
          @\exposid{state}@->@\exposid{result}@.template emplace<@\exposid{decayed-tuple}@<CPO, T...>>(CPO{},
                                                                   std::forward<T>(t)...);
        }
        catch (...) {
          if constexpr (!nothrow) {
            using tuple_t = @\exposid{decayed-tuple}@<set_error_t, exception_ptr>;
            @\exposid{state}@->@\exposid{result}@.template emplace<tuple_t>(set_error_t{}, current_exception());
          }
        }
        @\exposid{state}@->@\exposid{complete}@();
      }
  };
}
\end{codeblock}

\pnum
Let \placeholder{ssource-t} be an unspecified type
that models \exposconcept{stoppable-source} and
let \tcode{ssource} be an lvalue of type \placeholder{ssource-t}.
Let \tcode{\placeholder{stoken-t}} be \tcode{decltype(ssource.get_token())}.
Let \exposid{future-spawned-sender} be the alias template:

\begin{codeblock}
template<@\libconcept{sender}@ Sender, class Env>
using @\exposid{future-spawned-sender}@ =                                   // \expos
  decltype(write_env(@\exposid{stop-when}@(declval<Sender>(), declval<@\placeholder{stoken-t}@>()), declval<Env>()));
\end{codeblock}

\pnum
Let \exposid{spawn-future-state} be the exposition-only class template:

\indexlibraryglobal{execution::\exposid{spawn-future-state}}%
\begin{codeblock}
namespace std::execution {
  template<class Alloc, @\libconcept{scope_token}@ Token, @\libconcept{sender}@ Sender, class Env>
  struct @\exposid{spawn-future-state}@                                                 // \expos
    : @\exposid{spawn-future-state-base}@<completion_signatures_of_t<@\exposid{future-spawned-sender}@<Sender, Env>>> {
    using @\exposid{sigs-t}@ =                                                          // \expos
      completion_signatures_of_t<@\exposid{future-spawned-sender}@<Sender, Env>>;
    using @\exposid{receiver-t}@ =                                                      // \expos
      @\exposid{spawn-future-receiver}@<@\exposid{sigs-t}@>;
    using @\exposid{op-t}@ =                                                            // \expos
      connect_result_t<@\exposid{future-spawned-sender}@<Sender, Env>, @\exposid{receiver-t}@>;

    @\exposid{spawn-future-state}@(Alloc alloc, Sender&& sndr, Token token, Env env)    // \expos
      : @\exposid{alloc}@(std::move(alloc)),
        @\exposid{op}@(connect(
          write_env(@\exposid{stop-when}@(std::forward<Sender>(sndr), @\exposid{ssource}@.get_token()), std::move(env)),
          @\exposid{receiver-t}@(this))),
        @\exposid{token}@(std::move(token)),
        @\exposid{associated}@(token.try_associate()) {
          if (associated)
            start(@\exposid{op}@);
          else
            set_stopped(@\exposid{receiver-t}@(this));
        }

    void @\exposid{complete}@() noexcept override;                                      // \expos
    void @\exposid{consume}@(@\libconcept{receiver}@ auto& rcvr) noexcept;                             // \expos
    void @\exposid{abandon}@() noexcept;                                                // \expos

  private:
    using @\exposid{alloc-t}@ =                                                         // \expos
      typename allocator_traits<Alloc>::template rebind_alloc<@\exposid{spawn-future-state}@>;

    @\exposid{alloc-t}@ @\exposid{alloc}@;                                                          // \expos
    @\exposid{ssource-t}@ @\exposid{ssource}@;                                                      // \expos
    @\exposid{op-t}@ @\exposid{op}@;                                                                // \expos
    Token @\exposid{token}@;                                                            // \expos
    bool @\exposid{associated}@;                                                        // \expos

    void @\exposid{destroy}@() noexcept;                                                // \expos
  };
}
\end{codeblock}

\pnum
For purposes of determining the existence of a data race,
\exposid{complete}, \exposid{consume}, and \exposid{abandon}
behave as atomic operations\iref{intro.multithread}.
These operations on a single object of a type
that is a specialization of \exposid{spawn-future-state}
appear to occur in a single total order.

\indexlibrarymember{\exposid{complete}}{execution::\exposid{spawn-future-state}}%
\begin{itemdecl}
void @\exposid{complete}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
\begin{itemize}
\item
No effects if this invocation of \exposid{complete} happens before
an invocation of \exposid{consume} or \exposid{abandon} on \tcode{*this};
\item
otherwise,
if an invocation of \exposid{consume} on \tcode{*this} happens before
this invocation of \exposid{complete} then
there is a receiver, \tcode{rcvr}, registered and
that receiver is completed as if by \tcode{\exposid{consume}(rcvr)};
\item
otherwise,
\exposid{destroy} is invoked.
\end{itemize}
\end{itemdescr}

\indexlibrarymember{\exposid{consume}}{execution::\exposid{spawn-future-state}}%
\begin{itemdecl}
void @\exposid{consume}@(@\libconcept{receiver}@ auto& rcvr) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
\begin{itemize}
\item
If this invocation of \exposid{consume} happens before
an invocation of \exposid{complete} on \tcode{*this} then
\tcode{rcvr} is registered to be completed when
\exposid{complete} is subsequently invoked on \tcode{*this};

\item
otherwise,
\tcode{rcvr} is completed as if by:
\begin{codeblock}
std::move(this->@\exposid{result}@).visit(
  [&rcvr](auto&& tuple) noexcept {
    if constexpr (!@\libconcept{same_as}@<remove_reference_t<decltype(tuple)>, monostate>) {
      apply([&rcvr](auto cpo, auto&&... vals) {
        cpo(std::move(rcvr), std::move(vals)...);
      }, std::move(tuple));
    }
  });
\end{codeblock}
\end{itemize}
\end{itemdescr}

\indexlibrarymember{\exposid{abandon}}{execution::\exposid{spawn-future-state}}%
\begin{itemdecl}
void @\exposid{abandon}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
\begin{itemize}
\item
If this invocation of \exposid{abandon} happens before
an invocation of \exposid{complete} on \tcode{*this} then
equivalent to:
\begin{codeblock}
@\exposid{ssource}@.request_stop();
\end{codeblock}
\item
otherwise,
\exposid{destroy} is invoked.
\end{itemize}
\end{itemdescr}

\indexlibrarymember{\exposid{destroy}}{execution::\exposid{spawn-future-state}}%
\begin{itemdecl}
void @\exposid{destroy}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto token = std::move(this->@\exposid{token}@);
bool associated = this->@\exposid{associated}@;

{
  auto alloc = std::move(this->@\exposid{alloc}@);

  allocator_traits<@\exposid{alloc-t}@>::destroy(alloc, this);
  allocator_traits<@\exposid{alloc-t}@>::deallocate(alloc, this, 1);
}

if (associated)
  token.disassociate();
\end{codeblock}
\end{itemdescr}

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{spawn_future_t} as follows:

\indexlibraryglobal{execution::\exposid{impls-for}<spawn_future_t>}%
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<spawn_future_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{start}@ = @\seebelow@;                    // \expos
  };
}
\end{codeblock}

\pnum
The member \tcode{\exposid{impls-for}<spawn_future_t>::\exposid{start}}
is initialized with a callable object equivalent to the following lambda:
\begin{codeblock}
[](auto& state, auto& rcvr) noexcept -> void {
  state->@\exposid{consume}@(rcvr);
}
\end{codeblock}

\pnum
For the expression \tcode{spawn_future(sndr, token, env)}
let \tcode{new_sender} be the expression \tcode{token.wrap(sndr)} and
let \tcode{alloc} and \tcode{senv} be defined as follows:
\begin{itemize}
\item
if the expression \tcode{get_allocator(env)} is well-formed, then
\tcode{alloc} is the result of \tcode{get_allocator(env)} and
\tcode{senv} is the expression \tcode{env};
\item
otherwise,
if the expression \tcode{get_allocator(get_env(new_sender))} is well-formed, then
\tcode{alloc} is the result of \tcode{get_allocator(get_env(new_sender))} and
\tcode{senv} is the expression
\tcode{\exposid{JOIN-ENV}(prop(get_allocator, alloc), env)};
\item
otherwise,
\tcode{alloc} is \tcode{allocator<void>()} and
\tcode{senv} is the expression \tcode{env}.
\end{itemize}

\pnum
The expression \tcode{spawn_future(sndr, token, env)}
has the following effects:

\begin{itemize}
\item
Uses \tcode{alloc} to allocate and construct an object \tcode{s} of
a type that is a specialization of \exposid{spawn-future-\brk{}state}
from \tcode{alloc}, \tcode{token.wrap(sndr)}, \tcode{token}, and \tcode{senv}.
If an exception is thrown then
any constructed objects are destroyed and
any allocated memory is deallocated.

\item
Constructs an object \tcode{u} of
a type that is a specialization of \tcode{unique_ptr} such that:
  \begin{itemize}
  \item
  \tcode{u.get()} is equal to the address of \tcode{s}, and
  \item
  \tcode{u.get_deleter()(u.release())} is equivalent to
  \tcode{u.release()->\exposid{abandon}()}.
  \end{itemize}

\item
Returns \tcode{\exposid{make-sender}(spawn_future, std::move(u))}.
\end{itemize}

\pnum
The expression \tcode{spawn_future(sndr, token)} is expression-equivalent to
\tcode{spawn_future(sndr, token, ex\-ecution::env<>())}.

\rSec2[exec.consumers]{Sender consumers}

\rSec3[exec.sync.wait]{\tcode{this_thread::sync_wait}}

\pnum
\tcode{this_thread::sync_wait} and \tcode{this_thread::sync_wait_with_variant}
are used
to block the current thread of execution
until the specified sender completes and
to return its async result.
\tcode{sync_wait} mandates
that the input sender has exactly one value completion signature.

\pnum
Let \exposid{sync-wait-env} be the following exposition-only class type:
\begin{codeblock}
namespace std::this_thread {
  struct @\exposid{sync-wait-env}@ {
    execution::run_loop* @\exposid{loop}@;                                  // \expos

    auto query(execution::get_scheduler_t) const noexcept {
      return @\exposid{loop}@->get_scheduler();
    }

    auto query(execution::get_delegation_scheduler_t) const noexcept {
      return @\exposid{loop}@->get_scheduler();
    }
  };
}
\end{codeblock}

\pnum
Let \exposid{sync-wait-result-type} and
\exposid{sync-wait-with-variant-result-type}
be exposition-only alias templates defined as follows:
\begin{codeblock}
namespace std::this_thread {
  template<execution::@\libconcept{sender_in}@<@\exposid{sync-wait-env}@> Sndr>
    using @\exposid{sync-wait-result-type}@ =
      optional<execution::value_types_of_t<Sndr, @\exposid{sync-wait-env}@, @\exposid{decayed-tuple}@,
               type_identity_t>>;

  template<execution::@\libconcept{sender_in}@<@\exposid{sync-wait-env}@> Sndr>
    using @\exposid{sync-wait-with-variant-result-type}@ =
      optional<execution::value_types_of_t<Sndr, @\exposid{sync-wait-env}@>>;
}
\end{codeblock}

\pnum
The name \tcode{this_thread::sync_wait} denotes a customization point object.
For a subexpression \tcode{sndr}, let \tcode{Sndr} be \tcode{decltype((sndr))}.
The expression \tcode{this_thread::sync_wait(sndr)}
is expression-equivalent to the following,
except that \tcode{sndr} is evaluated only once:
\begin{codeblock}
apply_sender(@\exposid{get-domain-early}@(sndr), sync_wait, sndr)
\end{codeblock}
\mandates
\begin{itemize}
\item
\tcode{\libconcept{sender_in}<Sndr, \exposid{sync-wait-env}>} is \tcode{true}.
\item
The type \tcode{\exposid{sync-wait-result-type}<Sndr>} is well-formed.
\item
\tcode{\libconcept{same_as}<decltype($e$), \exposid{sync-wait-result-type}<Sndr>>}
is \tcode{true}, where $e$ is the \tcode{apply_sender} expression above.
\end{itemize}

\pnum
Let \exposid{sync-wait-state} and \exposid{sync-wait-receiver}
be the following exposition-only class templates:
\begin{codeblock}
namespace std::this_thread {
  template<class Sndr>
  struct @\exposid{sync-wait-state}@ {                                      // \expos
    execution::run_loop @\exposid{loop}@;                                   // \expos
    exception_ptr @\exposid{error}@;                                        // \expos
    @\exposid{sync-wait-result-type}@<Sndr> @\exposidnc{result}@;                         // \expos
  };

  template<class Sndr>
  struct @\exposid{sync-wait-receiver}@ {                                   // \expos
    using receiver_concept = execution::receiver_t;
    @\exposidnc{sync-wait-state}@<Sndr>* @\exposid{state}@;                               // \expos

    template<class... Args>
    void set_value(Args&&... args) && noexcept;

    template<class Error>
    void set_error(Error&& err) && noexcept;

    void set_stopped() && noexcept;

    @\exposid{sync-wait-env}@ get_env() const noexcept { return {&@\exposid{state}@->@\exposid{loop}@}; }
  };
}
\end{codeblock}

\begin{itemdecl}
template<class... Args>
void set_value(Args&&... args) && noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
try {
  @\exposid{state}@->@\exposid{result}@.emplace(std::forward<Args>(args)...);
} catch (...) {
  @\exposid{state}@->@\exposid{error}@ = current_exception();
}
@\exposid{state}@->@\exposid{loop}@.finish();
\end{codeblock}
\end{itemdescr}

\begin{itemdecl}
template<class Error>
void set_error(Error&& err) && noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
@\exposid{state}@->@\exposid{error}@ = @\exposid{AS-EXCEPT-PTR}@(std::forward<Error>(err));    // see \ref{exec.general}
@\exposid{state}@->@\exposid{loop}@.finish();
\end{codeblock}
\end{itemdescr}

\begin{itemdecl}
void set_stopped() && noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to \tcode{\exposid{state}->\exposid{loop}.finish()}.
\end{itemdescr}

\pnum
For a subexpression \tcode{sndr}, let \tcode{Sndr} be \tcode{decltype((sndr))}.
If \tcode{\libconcept{sender_to}<Sndr, \exposid{sync-wait-receiver}<\linebreak Sndr>>}
is \tcode{false},
the expression \tcode{sync_wait.apply_sender(sndr)} is ill-formed;
otherwise, it is equivalent to:
\begin{codeblock}
@\exposid{sync-wait-state}@<Sndr> state;
auto op = connect(sndr, @\exposid{sync-wait-receiver}@<Sndr>{&state});
start(op);

state.@\exposid{loop}@.run();
if (state.@\exposid{error}@) {
  rethrow_exception(std::move(state.@\exposid{error}@));
}
return std::move(state.@\exposid{result}@);
\end{codeblock}

\pnum
The behavior of \tcode{this_thread::sync_wait(sndr)} is undefined unless:
\begin{itemize}
\item
It blocks the current thread of execution\iref{defns.block}
with forward progress guarantee delegation\iref{intro.progress}
until the specified sender completes.
\begin{note}
The default implementation of \tcode{sync_wait} achieves
forward progress guarantee delegation by providing a \tcode{run_loop} scheduler
via the \tcode{get_delegation_scheduler} query
on the \exposid{sync-wait-receiver}'s environment.
The \tcode{run_loop} is driven by the current thread of execution.
\end{note}
\item
It returns the specified sender's async results as follows:
\begin{itemize}
\item
For a value completion,
the result datums are returned in
a \tcode{tuple} in an engaged \tcode{optional} object.
\item
For an error completion, an exception is thrown.
\item
For a stopped completion, a disengaged \tcode{optional} object is returned.
\end{itemize}
\end{itemize}

\rSec3[exec.sync.wait.var]{\tcode{this_thread::sync_wait_with_variant}}

\pnum
The name \tcode{this_thread::sync_wait_with_variant} denotes
a customization point object.
For a subexpression \tcode{sndr},
let \tcode{Sndr} be \tcode{decltype(into_variant(sndr))}.
The expression \tcode{this_thread::sync_wait_with_variant(sndr)}
is expression-equivalent to the following,
except \tcode{sndr} is evaluated only once:
\begin{codeblock}
apply_sender(@\exposid{get-domain-early}@(sndr), sync_wait_with_variant, sndr)
\end{codeblock}
\mandates
\begin{itemize}
\item
\tcode{\libconcept{sender_in}<Sndr, \exposid{sync-wait-env}>} is \tcode{true}.
\item
The type \tcode{\exposid{sync-wait-with-variant-result-type}<Sndr>}
is well-formed.
\item
\tcode{\libconcept{same_as}<decltype($e$), \exposid{sync-wait-with-variant-result-type}<Sndr>>}
is \tcode{true}, where $e$ is the \tcode{ap\-ply_sender} expression above.
\end{itemize}

\pnum
The expression \tcode{sync_wait_with_variant.apply_sender(sndr)} is equivalent to:
\begin{codeblock}
using result_type = @\exposid{sync-wait-with-variant-result-type}@<Sndr>;
if (auto opt_value = sync_wait(into_variant(sndr))) {
  return result_type(std::move(get<0>(*opt_value)));
}
return result_type(nullopt);
\end{codeblock}

\pnum
The behavior of \tcode{this_thread::sync_wait_with_variant(sndr)}
is undefined unless:
\begin{itemize}
\item
It blocks the current thread of execution\iref{defns.block}
with forward progress guarantee delegation\iref{intro.progress}
until the specified sender completes.
\begin{note}
The default implementation of \tcode{sync_wait_with_variant} achieves
forward progress guarantee delegation by relying on
the forward progress guarantee delegation provided by \tcode{sync_wait}.
\end{note}
\item
It returns the specified sender's async results as follows:
\begin{itemize}
\item
For a value completion,
the result datums are returned in an engaged \tcode{optional} object
that contains a \tcode{variant} of \tcode{tuple}s.
\item
For an error completion, an exception is thrown.
\item
For a stopped completion, a disengaged \tcode{optional} object is returned.
\end{itemize}
\end{itemize}

\rSec3[exec.spawn]{\tcode{execution::spawn}}

\pnum
\tcode{spawn} attempts to associate the given input sender with
the given token's async scope and, on success,
eagerly starts the input sender.

\pnum
The name \tcode{spawn} denotes a customization point object.
For subexpressions \tcode{sndr}, \tcode{token}, and \tcode{env},
\begin{itemize}
\item let \tcode{Sndr} be \tcode{decltype((sndr))},
\item let \tcode{Token} be \tcode{remove_cvref_t<decltype((token))>}, and
\item let \tcode{Env} be \tcode{remove_cvref_t<decltype((env))>}.
\end{itemize}
If any of
\tcode{\libconcept{sender}<Sndr>},
\tcode{\libconcept{scope_token}<Token>}, or
\tcode{\exposconcept{queryable}<Env>}
are not satisfied,
the expression \tcode{spawn(\brk{}sndr, token, env)} is ill-formed.

\pnum
Let \exposid{spawn-state-base} be the exposition-only class:

\indexlibraryglobal{execution::\exposid{spawn-state-base}}%
\begin{codeblock}
namespace std::execution {
  struct @\exposid{spawn-state-base}@ {                                 // \expos
    virtual void @\exposid{complete}@() noexcept = 0;                   // \expos
  };
}
\end{codeblock}

\pnum
Let \exposid{spawn-receiver} be the exposition-only class:

\indexlibraryglobal{execution::\exposid{spawn-receiver}}%
\begin{codeblock}
namespace std::execution {
  struct @\exposid{spawn-receiver}@ {                                   // \expos
    using receiver_concept = receiver_t;

    @\exposid{spawn-state-base}@* @\exposid{state}@;                                // \expos
    void set_value() && noexcept { @\exposid{state}@->@\exposid{complete}@(); }
    void set_stopped() && noexcept { @\exposid{state}@->@\exposid{complete}@(); }
  };
}
\end{codeblock}

\pnum
Let \exposid{spawn-state} be the exposition-only class template:

\indexlibraryglobal{execution::\exposid{spawn-state}}%
\begin{codeblock}
namespace std::execution {
  template<class Alloc, @\libconcept{scope_token}@ Token, @\libconcept{sender}@ Sender>
  struct @\exposid{spawn-state}@ : @\exposid{spawn-state-base}@ {                   // \expos
    using @\exposid{op-t}@ = connect_result_t<Sender, @\exposid{spawn-receiver}@>;  // \expos

    @\exposid{spawn-state}@(Alloc alloc, Sender&& sndr, Token token);   // \expos
    void @\exposid{complete}@() noexcept override;                      // \expos
    void @\exposid{run}@();                                             // \expos

  private:
    using @\exposid{alloc-t}@ =                                         // \expos
      typename allocator_traits<Alloc>::template rebind_alloc<@\exposid{spawn-state}@>;

    @\exposid{alloc-t}@ @\exposid{alloc}@;                                          // \expos
    @\exposid{op-t}@ @\exposid{op}@;                                                // \expos
    Token @\exposid{token}@;                                            // \expos

    void @\exposid{destroy}@() noexcept;                                // \expos
  };
}
\end{codeblock}

\indexlibraryctor{execution::\exposid{spawn-state}}%
\begin{itemdecl}
@\exposid{spawn-state}@(Alloc alloc, Sender&& sndr, Token token);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Initializes
\exposid{alloc} with \tcode{alloc},
\exposid{token} with \tcode{token}, and
\exposid{op} with:
\begin{codeblock}
connect(std::move(sndr), @\exposid{spawn-receiver}@(this))
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{\exposid{run}}{execution::\exposid{spawn-state}}%
\begin{itemdecl}
void @\exposid{run}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
if (@\exposid{token}@.try_associate())
  start(@\exposid{op}@);
else
  @\exposid{destroy}@();
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{\exposid{complete}}{execution::\exposid{spawn-state}}%
\begin{itemdecl}
void @\exposid{complete}@() noexcept override;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto token = std::move(this->@\exposid{token}@);

@\exposid{destroy}@();
token.disassociate();
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{\exposid{destroy}}{execution::\exposid{spawn-state}}%
\begin{itemdecl}
void @\exposid{destroy}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
auto alloc = std::move(this->@\exposid{alloc}@);

allocator_traits<@\exposid{alloc-t}@>::destroy(alloc, this);
allocator_traits<@\exposid{alloc-t}@>::deallocate(alloc, this, 1);
\end{codeblock}
\end{itemdescr}

\pnum
For the expression \tcode{spawn(sndr, token, env)}
let \tcode{new_sender} be the expression \tcode{token.wrap(sndr)} and
let \tcode{alloc} and \tcode{senv} be defined as follows:
\begin{itemize}
\item
if the expression \tcode{get_allocator(env)} is well-formed, then
\tcode{alloc} is the result of \tcode{get_allocator(env)} and
\tcode{senv} is the expression \tcode{env},
\item
otherwise
if the expression \tcode{get_allocator(get_env(new_sender))} is well-formed, then
\tcode{alloc} is the result of \tcode{get_allocator(get_env(new_sender))} and
\tcode{senv} is the expression \tcode{\exposid{JOIN-ENV}(prop(get_allocator, alloc), env)},
\item
otherwise
\tcode{alloc} is \tcode{allocator<void>()} and
\tcode{senv} is the expression \tcode{env}.
\end{itemize}

\pnum
The expression \tcode{spawn(sndr, token, env)} is of type \tcode{void} and
has the following effects:
%%FIXME: Was this supposed to be more than a single bullet?
\begin{itemize}
\item
Uses \tcode{alloc} to allocate and construct an object \tcode{o} of
type that is a specialization of \tcode{\exposid{spawn-state}} from
\tcode{alloc}, \tcode{write_env(token.wrap(sndr), senv)}, and \tcode{token}
and then
invokes \tcode{o.\exposid{run}()}.
If an exception is thrown then
any constructed objects are destroyed and any allocated memory is deallocated.
\end{itemize}

\pnum
The expression \tcode{spawn(sndr, token)} is expression-equivalent to
\tcode{spawn(sndr, token, execution::env<>(\brk{}))}.

\rSec1[exec.cmplsig]{Completion signatures}

\pnum
\tcode{completion_signatures} is a type
that encodes a set of completion signatures\iref{exec.async.ops}.

\pnum
\begin{example}
\begin{codeblock}
struct my_sender {
  using sender_concept = sender_t;
  using completion_signatures =
    execution::completion_signatures<
      set_value_t(),
      set_value_t(int, float),
      set_error_t(exception_ptr),
      set_error_t(error_code),
      set_stopped_t()>;
};
\end{codeblock}
Declares \tcode{my_sender} to be a sender
that can complete by calling one of the following
for a receiver expression \tcode{rcvr}:
\begin{itemize}
\item \tcode{set_value(rcvr)}
\item \tcode{set_value(rcvr, int\{...\}, float\{...\})}
\item \tcode{set_error(rcvr, exception_ptr\{...\})}
\item \tcode{set_error(rcvr, error_code\{...\})}
\item \tcode{set_stopped(rcvr)}
\end{itemize}
\end{example}

\pnum
This subclause makes use of the following exposition-only entities:
\begin{codeblock}
template<class Fn>
  concept @\defexposconcept{completion-signature}@ = @\seebelow@;
\end{codeblock}

\pnum
A type \tcode{Fn} satisfies \exposconcept{completion-signature}
if and only if it is a function type with one of the following forms:
\begin{itemize}
\item
\tcode{set_value_t(Vs...)},
where \tcode{Vs} is a pack of object or reference types.
\item
\tcode{set_error_t(Err)},
where \tcode{Err} is an object or reference type.
\item
\tcode{set_stopped_t()}
\end{itemize}

\pnum
\begin{codeblock}
template<bool>
  struct @\exposid{indirect-meta-apply}@ {
    template<template<class...> class T, class... As>
      using @\exposid{meta-apply}@ = T<As...>;                              // \expos
  };

template<class...>
  concept @\defexposconcept{always-true}@ = true;                                   // \expos

template<class Tag,
         @\exposconcept{valid-completion-signatures}@ Completions,
         template<class...> class Tuple,
         template<class...> class Variant>
  using @\exposid{gather-signatures}@ = @\seebelow@;
\end{codeblock}

\pnum
Let \tcode{Fns} be a pack of the arguments of
the \tcode{completion_signatures} specialization named by \tcode{Completions},
let \tcode{TagFns} be a pack of the function types in \tcode{Fns}
whose return types are \tcode{Tag}, and
let $\tcode{Ts}_n$ be a pack of the function argument types
in the $n$-th type in \tcode{TagFns}.
Then, given two variadic templates \tcode{Tuple} and \tcode{Variant},
the type \tcode{\exposid{gather-signatures}<Tag, Completions, Tuple, Variant>}
names the type
\begin{codeblock}
@\exposid{META-APPLY}@(Variant, @\exposid{META-APPLY}@(Tuple, Ts@$_0$@...),
                    @\itcorr[1]\exposid{META-APPLY}@(Tuple, Ts@$_1$@...),
                    @\itcorr[1]\ldots@,
                    @\itcorr[1]\exposid{META-APPLY}@(Tuple, Ts@$_{m-1}$@...))
\end{codeblock}
where $m$ is the size of the pack \tcode{TagFns} and
\tcode{META-APPLY(T, As...)} is equivalent to:
\begin{codeblock}
typename @\exposid{indirect-meta-apply}@<@\exposid{always-true}@<As...>>::template @\exposid{meta-apply}@<T, As...>
\end{codeblock}

\pnum
\begin{note}
The purpose of \exposid{META-APPLY} is to make it valid
to use non-variadic templates as \tcode{Variant} and \tcode{Tuple} arguments
to \exposid{gather-signatures}.
\end{note}

\pnum
\indexlibraryglobal{execution::completion_signatures}%
\indexlibrarymember{\exposid{for-each}}{execution::completion_signatures}%
\indexlibrarymember{\exposid{count-of}}{execution::completion_signatures}%
\begin{codeblock}
namespace std::execution {
  template<@\exposconcept{completion-signature}@... Fns>
    struct completion_signatures {
      template<class Tag>
        static constexpr size_t @\exposid{count-of}@(Tag) { return @\seebelow@; }

      template<class Fn>
        static constexpr void @\exposid{for-each}@(Fn&& fn) {               // \expos
          (std::forward<Fn>(fn)(static_cast<Fns*>(nullptr)), ...);
        }
    };

  template<class Sndr, class Env = env<>,
           template<class...> class Tuple = @\exposid{decayed-tuple}@,
           template<class...> class Variant = @\exposid{variant-or-empty}@>
      requires @\libconcept{sender_in}@<Sndr, Env>
    using value_types_of_t =
      @\exposid{gather-signatures}@<set_value_t, completion_signatures_of_t<Sndr, Env>, Tuple, Variant>;

  template<class Sndr, class Env = env<>,
           template<class...> class Variant = @\exposid{variant-or-empty}@>
      requires @\libconcept{sender_in}@<Sndr, Env>
    using error_types_of_t =
      @\exposid{gather-signatures}@<set_error_t, completion_signatures_of_t<Sndr, Env>,
                        type_identity_t, Variant>;

  template<class Sndr, class Env = env<>>
      requires @\libconcept{sender_in}@<Sndr, Env>
    constexpr bool sends_stopped =
      !@\libconcept{same_as}@<@\exposid{type-list}@<>,
               @\exposid{gather-signatures}@<set_stopped_t, completion_signatures_of_t<Sndr, Env>,
                                 @\exposid{type-list}@, @\exposid{type-list}@>>;
}
\end{codeblock}

\pnum
For a subexpression \tcode{tag},
let \tcode{Tag} be the decayed type of \tcode{tag}.
\tcode{completion_signatures<Fns...>::\exposid{count-of}(\linebreak{}tag)}
returns the count of function types in \tcode{Fns...} that
are of the form \tcode{Tag(Ts...)} where \tcode{Ts} is a pack of types.

\rSec1[exec.envs]{Queryable utilities}

\rSec2[exec.prop]{Class template \tcode{prop}}

\begin{codeblock}
namespace std::execution {
  template<class QueryTag, class ValueType>
  struct @\libglobal{prop}@ {
    QueryTag @\exposid{query_}@;            // \expos
    ValueType @\exposid{value_}@;           // \expos

    constexpr const ValueType& query(QueryTag) const noexcept {
      return @\exposid{value_}@;
    }
  };

  template<class QueryTag, class ValueType>
    prop(QueryTag, ValueType) -> prop<QueryTag, unwrap_reference_t<ValueType>>;
}
\end{codeblock}

\pnum
Class template \tcode{prop} is for building a queryable object
from a query object and a value.

\pnum
\mandates
\tcode{\exposconcept{callable}<QueryTag, \exposid{prop-like}<ValueType>>}
is modeled,
where \exposid{prop-like} is the following exposition-only class template:
\begin{codeblock}
template<class ValueType>
struct @\exposid{prop-like}@ {              // \expos
  const ValueType& query(auto) const noexcept;
};
\end{codeblock}

\pnum
\begin{example}
\begin{codeblock}
template<@\libconcept{sender}@ Sndr>
sender auto parameterize_work(Sndr sndr) {
  // Make an environment such that \tcode{get_allocator(env)} returns a reference to a copy of \tcode{my_alloc\{\}}.
  auto e = prop(get_allocator, my_alloc{});

  // Parameterize the input sender so that it will use our custom execution environment.
  return write_env(sndr, e);
}
\end{codeblock}
\end{example}

\pnum
Specializations of \tcode{prop} are not assignable.

\rSec2[exec.env]{Class template \tcode{env}}

\begin{codeblock}
namespace std::execution {
  template<@\exposconcept{queryable}@... Envs>
  struct @\libglobal{env}@ {
    Envs@$_0$@ @$\exposid{envs}_0$@;               // \expos
    Envs@$_1$@ @$\exposid{envs}_1$@;               // \expos
      @\vdots@
    Envs@$_{n-1}$@ @$\exposid{envs}_{n-1}$@;           // \expos

    template<class QueryTag>
      constexpr decltype(auto) query(QueryTag q) const noexcept(@\seebelow@);
  };

  template<class... Envs>
    env(Envs...) -> env<unwrap_reference_t<Envs>...>;
}
\end{codeblock}

\pnum
The class template \tcode{env} is used to construct a queryable object
from several queryable objects.
Query invocations on the resulting object are resolved
by attempting to query each subobject in lexical order.

\pnum
Specializations of \tcode{env} are not assignable.

\pnum
It is unspecified
whether \tcode{env} supports initialization
using a parenthesized \grammarterm{expression-list}\iref{dcl.init},
unless the \grammarterm{expression-list} consist of
a single element of type (possibly const) \tcode{env}.

\pnum
\begin{example}
\begin{codeblock}
template<@\libconcept{sender}@ Sndr>
sender auto parameterize_work(Sndr sndr) {
  // Make an environment such that:
  //   \tcode{get_allocator(env)} returns a reference to a copy of \tcode{my_alloc\{\}}
  //   \tcode{get_scheduler(env)} returns a reference to a copy of \tcode{my_sched\{\}}
  auto e = env{prop(get_allocator, my_alloc{}),
               prop(get_scheduler, my_sched{})};

  // Parameterize the input sender so that it will use our custom execution environment.
  return write_env(sndr, e);
}
\end{codeblock}
\end{example}

\indexlibrarymember{query}{env}%
\begin{itemdecl}
template<class QueryTag>
constexpr decltype(auto) query(QueryTag q) const noexcept(@\seebelow@);
\end{itemdecl}

\begin{itemdescr}
\pnum
Let \exposconcept{has-query} be the following exposition-only concept:
\begin{codeblock}
template<class Env, class QueryTag>
  concept @\defexposconcept{has-query}@ =                   // \expos
    requires (const Env& env) {
      env.query(QueryTag());
    };
\end{codeblock}

\pnum
Let \exposid{fe} be the first element of
$\exposid{envs}_0$, $\exposid{envs}_1$, $\dotsc$, $\exposid{envs}_{n-1}$
such that the expression \tcode{\exposid{fe}.query(q)} is well-formed.

\pnum
\constraints
\tcode{(\exposconcept{has-query}<Envs, QueryTag> || ...)} is \tcode{true}.

\pnum
\effects
Equivalent to: \tcode{return \exposid{fe}.query(q);}

\pnum
\remarks
The expression in the \tcode{noexcept} clause is equivalent
to \tcode{noexcept(\exposid{fe}.query(q))}.
\end{itemdescr}

\rSec1[exec.ctx]{Execution contexts}

\rSec2[exec.run.loop]{\tcode{execution::run_loop}}

\rSec3[exec.run.loop.general]{General}

\pnum
A \tcode{run_loop} is an execution resource on which work can be scheduled.
It maintains a thread-safe first-in-first-out queue of work.
Its \tcode{run} member function removes elements from the queue and
executes them in a loop on the thread of execution that calls \tcode{run}.

\pnum
A \tcode{run_loop} instance has an associated \defn{count}
that corresponds to the number of work items that are in its queue.
Additionally, a \tcode{run_loop} instance has an associated state
that can be one of
\defn{starting}, \defn{running}, \defn{finishing}, or \defn{finished}.

\pnum
Concurrent invocations of the member functions of \tcode{run_loop}
other than \tcode{run} and its destructor do not introduce data races.
The member functions
\exposid{pop-front}, \exposid{push-back}, and \tcode{finish}
execute atomically.

\pnum
\recommended
Implementations should use an intrusive queue of operation states
to hold the work units to make scheduling allocation-free.

\begin{codeblock}
namespace std::execution {
  class @\libglobal{run_loop}@ {
    // \ref{exec.run.loop.types}, associated types
    class @\exposid{run-loop-scheduler}@;                                   // \expos
    class @\exposid{run-loop-sender}@;                                      // \expos
    struct @\exposid{run-loop-opstate-base}@ {                              // \expos
      virtual void @\exposid{execute}@() = 0;                               // \expos
      run_loop* @\exposid{loop}@;                                           // \expos
      @\exposid{run-loop-opstate-base}@* @\exposid{next}@;                              // \expos
    };
    template<class Rcvr>
      using @\exposid{run-loop-opstate}@ = @\unspec@;                     // \expos

    // \ref{exec.run.loop.members}, member functions
    @\exposid{run-loop-opstate-base}@* @\exposid{pop-front}@();                         // \expos
    void @\exposid{push-back}@(@\exposid{run-loop-opstate-base}@*);                     // \expos

  public:
    // \ref{exec.run.loop.ctor}, constructor and destructor
    run_loop() noexcept;
    run_loop(run_loop&&) = delete;
    ~run_loop();

    // \ref{exec.run.loop.members}, member functions
    @\exposid{run-loop-scheduler}@ get_scheduler();
    void run();
    void finish();
  };
}
\end{codeblock}

\rSec3[exec.run.loop.types]{Associated types}

\begin{itemdecl}
class @\exposid{run-loop-scheduler}@;
\end{itemdecl}

\pnum
\exposid{run-loop-scheduler} is an unspecified type
that models \libconcept{scheduler}.

\pnum
Instances of \exposid{run-loop-scheduler} remain valid
until the end of the lifetime of the \tcode{run_loop} instance
from which they were obtained.

\pnum
Two instances of \exposid{run-loop-scheduler} compare equal
if and only if they were obtained from the same \tcode{run_loop} instance.

\pnum
Let \exposid{sch} be an expression of type \exposid{run-loop-scheduler}.
The expression \tcode{schedule(\exposid{sch})}
has type \exposid{run-loop-\newline sender} and
is not potentially-throwing if \exposid{sch} is not potentially-throwing.

\begin{itemdecl}
class @\exposid{run-loop-sender}@;
\end{itemdecl}

\pnum
\exposid{run-loop-sender} is an exposition-only type
that satisfies \libconcept{sender}.
\tcode{completion_signatures_of_t<\exposid{run-\linebreak{}loop-sender}>} is
\begin{codeblock}
completion_signatures<set_value_t(), set_error_t(exception_ptr), set_stopped_t()>
\end{codeblock}

\pnum
An instance of \exposid{run-loop-sender} remains valid
until the end of the lifetime of its associated \tcode{run_loop} instance.

\pnum
Let \exposid{sndr} be an expression of type \exposid{run-loop-sender},
let \exposid{rcvr} be an expression
such that \tcode{\libconcept{receiver_of}<decltype((\exposid{rcvr})), CS>} is \tcode{true}
where \tcode{CS} is the \tcode{completion_signatures} specialization above.
Let \tcode{C} be either \tcode{set_value_t} or \tcode{set_stopped_t}.
Then:
\begin{itemize}
\item
The expression \tcode{connect(\exposid{sndr}, \exposid{rcvr})}
has type \tcode{\exposid{run-loop-opstate}<decay_t<decltype((\exposid{rcvr}))>>}
and is potentially-throwing if and only if
\tcode{(void(\exposid{sndr}), auto(\exposid{rcvr}))} is potentially-throwing.
\item
The expression \tcode{get_completion_scheduler<C>(get_env(\exposid{sndr}))}
is potentially-throwing if and only if \exposid{sndr} is potentially-throwing,
has type \exposid{run-loop-scheduler}, and
compares equal to the \exposid{run-loop-\newline scheduler} instance
from which \exposid{sndr} was obtained.
\end{itemize}

\begin{itemdecl}
template<class Rcvr>
  struct @\exposid{run-loop-opstate}@;
\end{itemdecl}

\pnum
\tcode{\exposid{run-loop-opstate}<Rcvr>}
inherits privately and unambiguously from \exposid{run-loop-opstate-base}.

\pnum
Let $o$ be a non-const lvalue of type \tcode{\exposid{run-loop-opstate}<Rcvr>},
and let \tcode{REC($o$)} be a non-const lvalue reference to an instance of type \tcode{Rcvr}
that was initialized with the expression \exposid{rcvr}
passed to the invocation of connect that returned $o$.
Then:
\begin{itemize}
\item
The object to which \tcode{\exposid{REC}($o$)} refers
remains valid for the lifetime of the object to which $o$ refers.
\item
The type \tcode{\exposid{run-loop-opstate}<Rcvr>} overrides
\tcode{\exposid{run-loop-opstate-base}::\exposid{execute}()}
such that \tcode{$o$.\exposid{exe\-cute}()} is equivalent to:
\begin{codeblock}
if (get_stop_token(@\exposid{REC}@(@$o$@)).stop_requested()) {
  set_stopped(std::move(@\exposid{REC}@(@$o$@)));
} else {
  set_value(std::move(@\exposid{REC}@(@$o$@)));
}
\end{codeblock}
\item
The expression \tcode{start($o$)} is equivalent to:
\begin{codeblock}
try {
  @$o$@.@\exposid{loop}@->@\exposid{push-back}@(addressof(@$o$@));
} catch(...) {
  set_error(std::move(@\exposid{REC}@(@$o$@)), current_exception());
}
\end{codeblock}
\end{itemize}

\rSec3[exec.run.loop.ctor]{Constructor and destructor}

\indexlibraryctor{run_loop}%
\begin{itemdecl}
run_loop() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\ensures
\exposid{count} is \tcode{0} and \exposid{state} is \exposid{starting}.
\end{itemdescr}

\indexlibrarydtor{run_loop}%
\begin{itemdecl}
~run_loop();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \exposid{count} is not \tcode{0} or if \exposid{state} is \exposid{running},
invokes \tcode{terminate}\iref{except.terminate}.
Otherwise, has no effects.
\end{itemdescr}

\rSec3[exec.run.loop.members]{Member functions}

\begin{itemdecl}
@\exposid{run-loop-opstate-base}@* @\exposid{pop-front}@();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Blocks\iref{defns.block} until one of the following conditions is \tcode{true}:
\begin{itemize}
\item
\exposid{count} is \tcode{0} and \exposid{state} is \exposid{finishing},
in which case \exposid{pop-front} sets \exposid{state} to \exposid{finished}
and returns \tcode{nullptr}; or
\item
\exposid{count} is greater than \tcode{0},
in which case an item is removed from the front of the queue,
\exposid{count} is decremented by \tcode{1}, and
the removed item is returned.
\end{itemize}
\end{itemdescr}

\begin{itemdecl}
void @\exposid{push-back}@(@\exposid{run-loop-opstate-base}@* item);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Adds \tcode{item} to the back of the queue and
increments \exposid{count} by \tcode{1}.

\pnum
\sync
This operation synchronizes with
the \exposid{pop-front} operation that obtains \tcode{item}.
\end{itemdescr}

\indexlibrarymember{get_scheduler}{run_loop}%
\begin{itemdecl}
@\exposid{run-loop-scheduler}@ get_scheduler();
\end{itemdecl}

\begin{itemdescr}
\pnum
\returns
An instance of \exposid{run-loop-scheduler}
that can be used to schedule work onto this \tcode{run_loop} instance.
\end{itemdescr}

\indexlibrarymember{run}{run_loop}%
\begin{itemdecl}
void run();
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
\exposid{state} is either \exposid{starting} or \exposid{finishing}.

\pnum
\effects
If \exposid{state} is \exposid{starting},
sets the \exposid{state} to \exposid{running},
otherwise leaves \exposid{state} unchanged.
Then, equivalent to:
\begin{codeblock}
while (auto* op = @\exposid{pop-front}@()) {
  op->@\exposid{execute}@();
}
\end{codeblock}

\pnum
\remarks
When \exposid{state} changes, it does so without introducing data races.
\end{itemdescr}

\indexlibrarymember{finish}{run_loop}%
\begin{itemdecl}
void finish();
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
\exposid{state} is either \exposid{starting} or \exposid{running}.

\pnum
\effects
Changes \exposid{state} to \exposid{finishing}.

\pnum
\sync
\tcode{finish} synchronizes with the \exposid{pop-front} operation
that returns \tcode{nullptr}.
\end{itemdescr}

\rSec1[exec.coro.util]{Coroutine utilities}

\rSec2[exec.as.awaitable]{\tcode{execution::as_awaitable}}

\pnum
\tcode{as_awaitable} transforms an object into one
that is awaitable within a particular coroutine.
Subclause \ref{exec.coro.util} makes use of
the following exposition-only entities:
\begin{codeblock}
namespace std::execution {
  template<class Sndr, class Promise>
    concept @\defexposconcept{awaitable-sender}@ =
      @\exposconcept{single-sender}@<Sndr, env_of_t<Promise>> &&
      @\libconcept{sender_to}@<Sndr, @\exposid{awaitable-receiver}@> &&    // \seebelow
      requires (Promise& p) {
        { p.unhandled_stopped() } -> @\libconcept{convertible_to}@<coroutine_handle<>>;
      };

  template<class Sndr>
    concept @\defexposconcept{has-queryable-await-completion-adaptor}@ =            // \expos
      @\libconcept{sender}@<Sndr> &&
      requires(Sndr&& sender) {
        get_await_completion_adaptor(get_env(sender));
      };

  template<class Sndr, class Promise>
    class @\exposidnc{sender-awaitable}@;                                     // \expos
}
\end{codeblock}

\pnum
The type \tcode{\exposid{sender-awaitable}<Sndr, Promise>} is equivalent to:

\begin{codeblock}
namespace std::execution {
  template<class Sndr, class Promise>
  class @\exposidnc{sender-awaitable}@ {
    struct @\exposidnc{unit}@ {};                                             // \expos
    using @\exposidnc{value-type}@ =                                          // \expos
      @\exposidnc{single-sender-value-type}@<Sndr, env_of_t<Promise>>;
    using @\exposidnc{result-type }@=                                         // \expos
      conditional_t<is_void_v<@\exposid{value-type}@>, unit, @\exposid{value-type}@>;
    struct @\exposidnc{awaitable-receiver}@;                                  // \expos

    variant<monostate, @\exposidnc{result-type}@, exception_ptr> @\exposidnc{result}@{};    // \expos
    connect_result_t<Sndr, @\exposidnc{awaitable-receiver}@> @\exposidnc{state}@;           // \expos

  public:
    @\exposid{sender-awaitable}@(Sndr&& sndr, Promise& p);
    static constexpr bool await_ready() noexcept { return false; }
    void await_suspend(coroutine_handle<Promise>) noexcept { start(@\exposid{state}@); }
    @\exposid{value-type}@ await_resume();
  };
}
\end{codeblock}

\pnum
\exposid{awaitable-receiver} is equivalent to:
\begin{codeblock}
struct @\exposid{awaitable-receiver}@ {
  using receiver_concept = receiver_t;
  variant<monostate, @\exposidnc{result-type}@, exception_ptr>* @\exposidnc{result-ptr}@;   // \expos
  coroutine_handle<Promise> @\exposidnc{continuation}@;                       // \expos
  // \seebelow
};
\end{codeblock}

\pnum
Let \tcode{rcvr} be an rvalue expression of type \exposid{awaitable-receiver},
let \tcode{crcvr} be a const lvalue that refers to \tcode{rcvr},
let \tcode{vs} be a pack of subexpressions, and
let \tcode{err} be an expression of type \tcode{Err}. Then:
\begin{itemize}
\item
If \tcode{\libconcept{constructible_from}<\exposid{result-type}, decltype((vs))...>}
is satisfied,
the expression \tcode{set_value(\newline rcvr, vs...)} is equivalent to:
\begin{codeblock}
try {
  rcvr.@\exposid{result-ptr}@->template emplace<1>(vs...);
} catch(...) {
  rcvr.@\exposid{result-ptr}@->template emplace<2>(current_exception());
}
rcvr.@\exposid{continuation}@.resume();
\end{codeblock}
Otherwise, \tcode{set_value(rcvr, vs...)} is ill-formed.
\item
The expression \tcode{set_error(rcvr, err)} is equivalent to:
\begin{codeblock}
rcvr.@\exposid{result-ptr}@->template emplace<2>(@\exposid{AS-EXCEPT-PTR}@(err));    // see \ref{exec.general}
rcvr.@\exposid{continuation}@.resume();
\end{codeblock}
\item
The expression \tcode{set_stopped(rcvr)} is equivalent to:
\begin{codeblock}
static_cast<coroutine_handle<>>(rcvr.@\exposid{continuation}@.promise().unhandled_stopped()).resume();
\end{codeblock}
\item
For any expression \tcode{tag}
whose type satisfies \exposconcept{forwarding-query} and
for any pack of subexpressions \tcode{as},
\tcode{get_env(crcvr).query(tag, as...)} is expression-equivalent to:
\begin{codeblock}
tag(get_env(as_const(crcvr.@\exposid{continuation}@.promise())), as...)
\end{codeblock}
\end{itemize}

\begin{itemdecl}
@\exposid{sender-awaitable}@(Sndr&& sndr, Promise& p);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Initializes \exposid{state} with
\begin{codeblock}
connect(std::forward<Sndr>(sndr),
        @\exposid{awaitable-receiver}@{addressof(result), coroutine_handle<Promise>::from_promise(p)})
\end{codeblock}
\end{itemdescr}

\begin{itemdecl}
@\exposid{value-type}@ await_resume();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
if (@\exposid{result}@.index() == 2)
  rethrow_exception(get<2>(@\exposid{result}@));
if constexpr (!is_void_v<@\exposid{value-type}@>)
  return std::forward<@\exposid{value-type}@>(get<1>(@\exposid{result}@));
\end{codeblock}
\end{itemdescr}

\pnum
\tcode{as_awaitable} is a customization point object.
For subexpressions \tcode{expr} and \tcode{p}
where \tcode{p} is an lvalue,
\tcode{Expr} names the type \tcode{decltype((expr))} and
\tcode{Promise} names the type \tcode{decay_t<decltype((p))>},
\tcode{as_awaitable(expr, p)} is expression-equivalent to,
except that the evaluations of \tcode{expr} and \tcode{p}
are indeterminately sequenced:
\begin{itemize}
\item
\tcode{expr.as_awaitable(p)} if that expression is well-formed.

\mandates
\tcode{\exposconcept{is-awaitable}<A, Promise>} is \tcode{true},
where \tcode{A} is the type of the expression above.
\item
Otherwise, \tcode{(void(p), expr)}
if \tcode{\exposconcept{is-awaitable}<Expr, U>} is \tcode{true},
where \tcode{U} is an unspecified class type
that is not \tcode{Promise} and
that lacks a member named \tcode{await_transform}.

\expects
\tcode{\exposconcept{is-awaitable}<Expr, Promise>} is \tcode{true} and
the expression \tcode{co_await expr}
in a coroutine with promise type \tcode{U} is expression-equivalent to
the same expression in a coroutine with promise type \tcode{Promise}.
\item
Otherwise, \tcode{\exposid{sender-awaitable}\{\exposid{adapted-expr}, p\}}
if
\begin{codeblock}
@\exposid{has-queryable-await-completion-adaptor}@<Expr>
\end{codeblock}
and
\begin{codeblock}
@\exposid{awaitable-sender}@<decltype((@\exposid{adapted-expr}@)), Promise>
\end{codeblock}
are both satisfied, where \exposid{adapted-expr} is
\tcode{get_await_completion_adaptor(get_env(expr))(expr)},
except that \tcode{expr} is evaluated only once.
\item
Otherwise, \tcode{\exposid{sender-awaitable}\{expr, p\}}
if \tcode{\exposconcept{awaitable-sender}<Expr, Promise>} is \tcode{true}.
\item
Otherwise, \tcode{(void(p), expr)}.
\end{itemize}

\rSec2[exec.with.awaitable.senders]{\tcode{execution::with_awaitable_senders}}

\pnum
\tcode{with_awaitable_senders},
when used as the base class of a coroutine promise type,
makes senders awaitable in that coroutine type.

In addition, it provides a default implementation of \tcode{unhandled_stopped}
such that if a sender completes by calling \tcode{set_stopped},
it is treated as if an uncatchable "stopped" exception were thrown
from the \grammarterm{await-expression}.
\begin{note}
The coroutine is never resumed, and
the \tcode{unhandled_stopped} of the coroutine caller's promise type is called.
\end{note}

\begin{codeblock}
namespace std::execution {
  template<@\exposconcept{class-type}@ Promise>
    struct @\libglobal{with_awaitable_senders}@ {
      template<class OtherPromise>
        requires (!@\libconcept{same_as}@<OtherPromise, void>)
      void set_continuation(coroutine_handle<OtherPromise> h) noexcept;

      coroutine_handle<> @\libmember{continuation}{with_awaitable_senders}@() const noexcept { return @\exposid{continuation}@; }

      coroutine_handle<> @\libmember{unhandled_stopped}{with_awaitable_senders}@() noexcept {
        return @\exposid{stopped-handler}@(@\exposid{continuation}@.address());
      }

      template<class Value>
      @\seebelow@ await_transform(Value&& value);

    private:
      [[noreturn]] static coroutine_handle<>
        @\exposid{default-unhandled-stopped}@(void*) noexcept {             // \expos
        terminate();
      }
      coroutine_handle<> @\exposid{continuation}@{};                        // \expos
      coroutine_handle<> (*@\exposid{stopped-handler}@)(void*) noexcept =   // \expos
        &@\exposid{default-unhandled-stopped}@;
    };
}
\end{codeblock}

\indexlibrarymember{set_continuation}{with_awaitable_senders}%
\begin{itemdecl}
template<class OtherPromise>
  requires (!@\libconcept{same_as}@<OtherPromise, void>)
void set_continuation(coroutine_handle<OtherPromise> h) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
@\exposid{continuation}@ = h;
if constexpr ( requires(OtherPromise& other) { other.unhandled_stopped(); } ) {
  @\exposid{stopped-handler}@ = [](void* p) noexcept -> coroutine_handle<> {
    return coroutine_handle<OtherPromise>::from_address(p)
      .promise().unhandled_stopped();
  };
} else {
  @\exposid{stopped-handler}@ = &@\exposid{default-unhandled-stopped}@;
}
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{await_transform}{with_awaitable_senders}%
\begin{itemdecl}
template<class Value>
@\exposid{call-result-t}@<as_awaitable_t, Value, Promise&> await_transform(Value&& value);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
return as_awaitable(std::forward<Value>(value), static_cast<Promise&>(*this));
\end{codeblock}
\end{itemdescr}

\rSec2[exec.affine.on]{\tcode{execution::affine_on}}

\pnum
\tcode{affine_on} adapts a sender into one that completes on
the specified scheduler.
If the algorithm determines that the adapted sender already completes
on the correct scheduler it can avoid any scheduling operation.

\pnum
The name \tcode{affine_on} denotes a pipeable sender adaptor
object.
For subexpressions \tcode{sch} and \tcode{sndr}, if \tcode{decltype((sch))}
does not satisfy \libconcept{scheduler}, or \tcode{decltype((sndr))}
does not satisfy \libconcept{sender}, \tcode{affine_on(sndr, sch)}
is ill-formed.

\pnum
Otherwise, the expression \tcode{affine_on(sndr, sch)} is
expression-equivalent to:
\begin{codeblock}
transform_sender(@\exposid{get-domain-early}@(sndr), @\exposid{make-sender}@(affine_on, sch, sndr))
\end{codeblock}
except that \tcode{sndr} is evaluated only once.

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \tcode{affine_on_t} as follows:

\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<affine_on_t> : @\exposid{default-impls}@ {
    static constexpr auto @\exposid{get-attrs}@ =
      [](const auto& data, const auto& child) noexcept -> decltype(auto) {
        return @\exposid{JOIN-ENV}@(@\exposid{SCHED-ATTRS}@(data), @\exposid{FWD-ENV}@(get_env(child)));
      };
  };
}
\end{codeblock}

\pnum
Let \tcode{\placeholder{out_sndr}} be a subexpression denoting a sender
returned from \tcode{affine_on(sndr, sch)} or one equal to such,
and let \tcode{\placeholder{OutSndr}} be the type \tcode{decltype((\placeholder{out_sndr}))}.
Let \tcode{\placeholder{out_rcvr}} be a subexpression denoting a receiver that
has an environment of type \tcode{Env} such that \tcode{\libconcept{sender_in}<\placeholder{OutSndr}, Env>}
is \tcode{true}.
Let \tcode{\placeholder{op}} be an lvalue referring to the operation state that
results from connecting \tcode{\placeholder{out_sndr}} to \tcode{\placeholder{out_rcvr}}.
Calling \tcode{start(\placeholder{op})} will start \tcode{sndr} on the current
execution agent and execute completion operations on \tcode{\placeholder{out_rcvr}}
on an execution agent of the execution resource associated with
\tcode{sch}.
If the current execution resource is the same as the execution
resource associated with \tcode{sch}, the completion operation on
\tcode{\placeholder{out_rcvr}} may be called before \tcode{start(\placeholder{op})} completes.
If scheduling onto \tcode{sch} fails, an error completion on
\tcode{\placeholder{out_rcvr}} shall be executed on an unspecified execution
agent.

\rSec2[exec.inline.scheduler]{\tcode{execution::inline_scheduler}}

\begin{codeblock}
namespace std::execution {
  class @\libglobal{inline_scheduler}@ {
    class @\exposidnc{inline-sender}@;                // \expos

    template<@\libconcept{receiver}@ R>
      class @\exposidnc{inline-state}@;               // \expos

  public:
    using scheduler_concept = scheduler_t;

    constexpr @\exposid{inline-sender}@ schedule() noexcept { return {}; }
    constexpr bool operator==(const inline_scheduler&) const noexcept = default;
  };
}
\end{codeblock}

\pnum
\tcode{inline_scheduler} is a class that models
\libconcept{scheduler}\iref{exec.sched}.
All objects of type \tcode{inline_scheduler} are equal.

\pnum
\exposid{inline-sender} is an exposition-only type that satisfies
\libconcept{sender}.
The type \tcode{completion_signatures_of_t<\exposid{inline-sender}>}
is \tcode{completion_signatures<set_value_t()>}.

\pnum
Let \tcode{sndr} be an expression of type \exposid{inline-sender},
let \tcode{rcvr} be an expression such that
\tcode{\libconcept{receiver_of}<decltype((rcvr)), CS>} is \tcode{true}
where \tcode{CS} is \tcode{completion_signatures<set_value_t()>},
then:
\begin{itemize}
\item the expression \tcode{connect(sndr, rcvr)} has
type \tcode{\exposid{inline-state}<remove_cvref_t<decltype((rcvr))>>}
and is potentially-throwing if and only if
\tcode{((void)sndr, auto(rcvr))} is potentially-throwing, and
\item the expression
\tcode{get_completion_scheduler<set_value_t>(get_env(sndr))} has
type\brk{} \tcode{inline_\-sched\-ul\-er} and is potentially-throwing
if and only if \tcode{get_env(sndr)} is potentially-throwing.
\end{itemize}

\pnum
Let \tcode{\placeholder{o}} be a non-\tcode{const} lvalue of type
\tcode{\exposid{inline-state}<Rcvr>}, and let \tcode{REC(\placeholder{o})} be
a non-\tcode{const} lvalue reference to an object of type \tcode{Rcvr} that
was initialized with the expression \tcode{rcvr} passed to an
invocation of \tcode{connect} that returned \tcode{\placeholder{o}}, then:
\begin{itemize}
\item the object to which \tcode{REC(\placeholder{o})} refers remains valid for
the lifetime of the object to which \tcode{\placeholder{o}} refers, and
\item the expression \tcode{start(\placeholder{o})} is equivalent to
\tcode{set_value(std::move(REC(\placeholder{o})))}.
\end{itemize}

\rSec2[exec.task.scheduler]{\tcode{execution::task_scheduler}}

\begin{codeblock}
namespace std::execution {
  class @\libglobal{task_scheduler}@ {
    class @\exposidnc{ts-sender}@;                    // \expos

    template<@\libconcept{receiver}@ R>
      class @\exposidnc{state}@;                      // \expos

  public:
    using scheduler_concept = scheduler_t;

    template<class Sch, class Allocator = allocator<void>>
      requires (!@\libconcept{same_as}@<task_scheduler, remove_cvref_t<Sch>>)
        && @\libconcept{scheduler}@<Sch>
    explicit task_scheduler(Sch&& sch, Allocator alloc = {});

    @\exposid{ts-sender}@ schedule();

    friend bool operator==(const task_scheduler& lhs, const task_scheduler& rhs)
        noexcept;
    template<class Sch>
      requires (!@\libconcept{same_as}@<task_scheduler, Sch>)
      && @\libconcept{scheduler}@<Sch>
    friend bool operator==(const task_scheduler& lhs, const Sch& rhs) noexcept;

  private:
    shared_ptr<void> @\exposidnc{sch_}@; // \expos
  };
}
\end{codeblock}

\pnum
\tcode{task_scheduler} is a class that models
\libconcept{scheduler}\iref{exec.sched}.
Given an object \tcode{s} of type \tcode{task_scheduler}, let
\tcode{\exposid{SCHED}(s)} be the object owned by \tcode{s.\exposid{sch_}}.

\indexlibraryctor{task_scheduler}
\begin{itemdecl}
template<class Sch, class Allocator = allocator<void>>
  requires(!@\libconcept{same_as}@<task_scheduler, remove_cvref_t<Sch>>) && @\libconcept{scheduler}@<Sch>
explicit task_scheduler(Sch&& sch, Allocator alloc = {});
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Initialize \exposid{sch_} with
\tcode{allocate_shared<remove_cvref_t<Sch>>(alloc,\brk{} std::forward<Sch>\brk{}(sch))}.

\pnum
\recommended
Implementations should avoid the use of dynamically
allocated memory for small scheduler objects.

\pnum
\remarks
Any allocations performed by construction of \exposid{ts-sender} or
\exposid{state} objects resulting from calls on \tcode{*this} are
performed using a copy of \tcode{alloc}.
\end{itemdescr}

\indexlibrarymember{scheduler}{task_scheduler}%
\begin{itemdecl}
@\exposid{ts-sender}@ schedule();
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Returns an object of type \exposid{ts-sender} containing a sender
initialized with \tcode{sched\-ule(\brk{}\exposid{SCHED}\brk{}(*this))}.
\end{itemdescr}

\indexlibrarymember{operator==}{task_scheduler}%
\begin{itemdecl}
bool operator==(const task_scheduler& lhs, const task_scheduler& rhs) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Equivalent to: \tcode{return lhs == \exposid{SCHED}(rhs);}
\end{itemdescr}

\indexlibrarymember{operator==}{task_scheduler}%
\begin{itemdecl}
template<class Sch>
  requires (!@\libconcept{same_as}@<task_scheduler, Sch>)
        && @\libconcept{scheduler}@<Sch>
bool operator==(const task_scheduler& lhs, const Sch& rhs) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
\tcode{false} if the type of \tcode{\exposid{SCHED}(lhs)} is not \tcode{Sch},
otherwise \tcode{\exposid{SCHED}(lhs) == rhs}.
\end{itemdescr}

\pnum
\begin{codeblock}
namespace std::execution {
  class task_scheduler::@\exposidnc{ts-sender}@ {     // \expos
  public:
    using sender_concept = sender_t;

    template<@\libconcept{receiver}@ Rcvr>
      @\exposid{state}@<Rcvr> connect(Rcvr&& rcvr);
  };
}
\end{codeblock}
\exposid{ts-sender} is an exposition-only class that models
\libconcept{sender}\iref{exec.snd} and for which
\tcode{completion_signatures_of_t<\exposid{ts-sender}>} denotes:
\begin{codeblock}
completion_signatures<
  set_value_t(),
  set_error_t(error_code),
  set_error_t(exception_ptr),
  set_stopped_t()>
\end{codeblock}

\pnum
Let \tcode{\placeholder{sch}} be an object of type \tcode{task_scheduler}
and let \tcode{sndr} be an object of type \exposid{ts-sender} obtained
from \tcode{schedule(\placeholder{sch})}.
Then \tcode{get_completion_scheduler<set_value_t>(get_env(sndr)) == \placeholder{sch}}
is \tcode{true}.
The object \tcode{\exposid{SENDER}(sndr)} is the sender object contained by
\tcode{sndr} or an object move constructed from it.

\indexlibrarymember{connect}{task_scheduler::\exposid{ts-sender}}%
\begin{itemdecl}
template<@\libconcept{receiver}@ Rcvr>
  @\exposid{state}@<Rcvr> connect(Rcvr&& rcvr);
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Let \tcode{\placeholder{r}} be an object of a type that models \libconcept{receiver}
and whose completion handlers result in invoking the corresponding
completion handlers of \tcode{rcvr} or copy thereof.
Returns an object of type \tcode{\exposid{state}<Rcvr>} containing
an operation state object initialized with \tcode{connect(\exposid{SENDER}(*this),
std::move(\placeholder{r}))}.
\end{itemdescr}

\pnum
\begin{codeblock}
namespace std::execution {
  template<@\libconcept{receiver}@ R>
  class task_scheduler::@\exposidnc{state}@ {         // \expos
  public:
    using operation_state_concept = operation_state_t;

    void start() & noexcept;
  };
}
\end{codeblock}
\exposid{state} is an exposition-only class template whose
specializations model \libconcept{operation_state}\iref{exec.opstate}.

\indexlibrarymember{start}{task_scheduler::\exposid{state}}%
\begin{itemdecl}
void start() & noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Equivalent to \tcode{start(st)} where \tcode{st} is the operation
state object contained by \tcode{*this}.
\end{itemdescr}

\rSec2[exec.task]{\tcode{execution::task}}

\rSec3[task.overview]{\tcode{task} overview}

\pnum
The \tcode{task} class template represents a sender that can
be used as the return type of coroutines.
The first template parameter \tcode{T} defines the type of the value
completion datum\iref{exec.async.ops} if \tcode{T} is not \tcode{void}.
Otherwise, there are no value completion datums.
Inside coroutines returning \tcode{task<T, E>} the operand of
\tcode{co_return} (if any) becomes the argument of \tcode{set_value}.
The second template parameter \tcode{Environment} is used to customize
the behavior of \tcode{task}.

\rSec3[task.class]{Class template \tcode{task}}

\begin{codeblock}
namespace std::execution {
  template<class T, class Environment>
  class @\libglobal{task}@ {
    // \ref{task.state}
    template<@\libconcept{receiver}@ Rcvr>
      class @\exposidnc{state}@;                              // \expos

  public:
    using sender_concept = sender_t;
    using completion_signatures = @\seebelow@;
    using allocator_type = @\seebelow@;
    using scheduler_type = @\seebelow@;
    using stop_source_type = @\seebelow@;
    using stop_token_type = decltype(declval<stop_source_type>().get_token());
    using error_types = @\seebelow@;

    // \ref{task.promise}
    class promise_type;

    task(task&&) noexcept;
    ~task();

    template<@\libconcept{receiver}@ Rcvr>
      @\exposid{state}@<Rcvr> connect(Rcvr&& rcvr);

  private:
    coroutine_handle<promise_type> @\exposidnc{handle}@;      // \expos
  };
}
\end{codeblock}

\pnum
\tcode{task<T, E>} models \libconcept{sender}\iref{exec.snd}
if \tcode{T} is \tcode{void}, a reference type, or a \cv{}-unqualified
non-array object type and \tcode{E} is a class type.
Otherwise a program that instantiates the definition of \tcode{task<T, E>}
is ill-formed.

\pnum
The nested types of \tcode{task} template specializations
are determined based on the \tcode{Environment} parameter:
\begin{itemize}
\item \tcode{allocator_type} is \tcode{Environment::allocator_type}
if that \grammarterm{qualified-id} is valid and denotes a type,
\tcode{allocator<byte>} otherwise.
\item \tcode{scheduler_type} is \tcode{Environment::scheduler_type}
if that \grammarterm{qualified-id} is valid and denotes a type,
\tcode{task_scheduler} otherwise.
\item \tcode{stop_source_type} is \tcode{Environment::stop_source_type}
if that \grammarterm{qualified-id} is valid and denotes a type,
\tcode{inplace_stop_source} otherwise.
\item \tcode{error_types} is \tcode{Environment::error_types} if
that \grammarterm{qualified-id} is valid and denotes a type,
\tcode{com\-pletion_sign\-atures<set_error_t(exception_ptr)>} otherwise.
\end{itemize}

\pnum
 A program is ill-formed if \tcode{error_types} is not a
specialization of \tcode{completion_signatures<ErrorSigs...>} or
\tcode{ErrorSigs} contains an element which is not of the form
\tcode{set_error_t(E)} for some type \tcode{E}.

\pnum
The type alias \tcode{completion_signatures} is a specialization
of \tcode{execution::completion_signatures} with the template
arguments (in unspecified order):
\begin{itemize}
\item \tcode{set_value_t()} if \tcode{T} is \tcode{void},
and \tcode{set_value_t(T)} otherwise;
\item template arguments of the specialization of
\tcode{execution::completion_signatures} denoted by \tcode{error_types};
and
\item \tcode{set_stopped_t()}.
\end{itemize}

\pnum
\tcode{allocator_type} shall meet the \oldconcept{Allocator}
requirements.

\rSec3[task.members]{\tcode{task} members}

\indexlibraryctor{task}%
\begin{itemdecl}
task(task&& other) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Initializes \exposid{handle} with \tcode{exchange(other.\exposid{handle},
\{\})}.
\end{itemdescr}

\indexlibrarydtor{task}%
\begin{itemdecl}
~task();
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
if (@\exposid{handle}@)
  @\exposid{handle}@.destroy();
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{connect}{task}%
\begin{itemdecl}
template<@\libconcept{receiver}@ Rcvr>
  @\exposid{state}@<Rcvr> connect(Rcvr&& recv);
\end{itemdecl}
\begin{itemdescr}
\pnum
\expects
\tcode{bool(\exposid{handle})} is \tcode{true}.

\pnum
\effects
Equivalent to:
\begin{codeblock}
return @\exposid{state}@<Rcvr>(exchange(@\exposid{handle}@, {}), std::forward<Rcvr>(recv));
\end{codeblock}
\end{itemdescr}

\rSec3[task.state]{\tcode{Class template \tcode{task::state}}}

\begin{codeblock}
namespace std::execution {
  template<class T, class Environment>
  template<@\libconcept{receiver}@ Rcvr>
  class task<T, Environment>::@\exposidnc{state}@ {           // \expos
  public:
    using operation_state_concept = operation_state_t;

    template<class R>
      @\exposid{state}@(coroutine_handle<promise_type> h, R&& rr);

    ~@\exposid{state}@();

    void start() & noexcept;

  private:
    using @\exposidnc{own-env-t}@ = @\seebelownc@;                // \expos
    coroutine_handle<promise_type> @\exposidnc{handle}@;      // \expos
    remove_cvref_t<Rcvr>           @\exposidnc{rcvr}@;        // \expos
    @\exposidnc{own-env-t}@                      @\exposidnc{own-env}@;     // \expos
    Environment                    @\exposidnc{environment}@; // \expos
  };
}
\end{codeblock}

\pnum
The type \exposid{own-env-t} is \tcode{Environment::template
env_type<decltype(get_env(\brk{}declval\brk{}<Rcvr>(\brk{})))\brk{}>} if that
\grammarterm{qualified-id} is valid and denotes a type, \tcode{env<>} otherwise.

\indexlibraryctor{task::\exposid{state}}%
\begin{itemdecl}
template<class R>
  @\exposid{state}@(coroutine_handle<promise_type> h, R&& rr);
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Initializes
\begin{itemize}
\item \exposid{handle} with \tcode{std::move(h)};
\item \exposid{rcvr} with \tcode{std::forward<R>(rr)};
\item \exposid{own-env}
with \tcode{\exposid{own-env-t}(get_env(\exposid{rcvr}))} if that expression
is valid and \tcode{\exposid{own-env-t}()} otherwise.
If neither of these expressions is valid, the program is ill-formed.
\item \exposid{environment} with
\tcode{Environment(\exposid{own-env})} if that expression is
valid, otherwise \tcode{Environment(\brk{}get_env(\exposid{rcvr}))}
if this expression is valid, otherwise \tcode{Environment()}.
If neither of these expressions is valid, the program is ill-formed.
\end{itemize}
\end{itemdescr}

\indexlibrarydtor{task::\exposid{state}}%
\begin{itemdecl}
~@\exposid{state}@();
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
if (@\exposid{handle}@)
  @\exposid{handle}@.destroy();
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{start}{task::\exposid{state}}%
\begin{itemdecl}
void start() & noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Let \tcode{\placeholder{prom}} be the object \tcode{\exposid{handle}.promise()}.
Associates \tcode{\exposid{STATE}(\placeholder{prom})}, \tcode{\exposid{RCVR}(\placeholder{prom})}, and \tcode{\exposid{SCHED}(\placeholder{prom})}
with \tcode{*this} as follows:
\begin{itemize}
\item \tcode{\exposid{STATE}(\placeholder{prom})} is \tcode{*this}.
\item \tcode{\exposid{RCVR}(\placeholder{prom})} is \exposid{rcvr}.
\item \tcode{\exposid{SCHED}(\placeholder{prom})} is the object initialized
with \tcode{scheduler_type(get_scheduler(get_env(\exposid{rcvr})))}
if that expression is valid and \tcode{scheduler_type()} otherwise.
If neither of these expressions is valid, the program is ill-formed.
\end{itemize}
Let \tcode{\placeholder{st}} be \tcode{get_stop_token(get_env(\exposid{rcvr}))}.
Initializes \tcode{\placeholder{prom}.\exposid{token}} and
\tcode{\placeholder{prom}.\exposid{source}} such that
\begin{itemize}
\item
\tcode{\placeholder{prom}.\exposid{token}.stop_requested()} returns
\tcode{\placeholder{st}.stop_requested()};
\item
\tcode{\placeholder{prom}.\exposid{token}.stop_possible()} returns
\tcode{\placeholder{st}.stop_possible()}; and
\item
for types \tcode{Fn} and \tcode{Init} such that both
\tcode{\libconcept{invocable}<Fn>} and
\tcode{\libconcept{constructible_from}<Fn, Init>} are modeled,
\tcode{stop_token_type::callback_type<Fn>} models
\tcode{\exposconcept{stoppable-callback-for}<Fn,\brk{} stop\-_token_type, Init>}.
\end{itemize}
After that invokes \tcode{\exposid{handle}.resume()}.
\end{itemdescr}

\rSec3[task.promise]{Class \tcode{task::promise_type}}

\begin{codeblock}
namespace std::execution {
  template<class T, class Environment>
  class task<T, Environment>::promise_type {
  public:
    template<class... Args>
      promise_type(const Args&... args);

    task get_return_object() noexcept;

    auto initial_suspend() noexcept;
    auto final_suspend() noexcept;

    void uncaught_exception();
    coroutine_handle<> unhandled_stopped();

    void return_void();                 // present only if \tcode{is_void_v<T>} is \tcode{true}
    template<class V>
      void return_value(V&& value);     // present only if \tcode{is_void_v<T>} is \tcode{false}

    template<class E>
      @\unspec@ yield_value(with_error<E> error);

    template<class A>
      auto await_transform(A&& a);
    template<class Sch>
      auto await_transform(change_coroutine_scheduler<Sch> sch);

    @\unspec@ get_env() const noexcept;

    template<class... Args>
      void* operator new(size_t size, Args&&... args);

    void operator delete(void* pointer, size_t size) noexcept;

  private:
    using @\exposidnc{error-variant}@ = @\seebelownc@;    // \expos

    allocator_type    @\exposidnc{alloc}@;            // \expos
    stop_source_type  @\exposidnc{source}@;           // \expos
    stop_token_type   @\exposidnc{token}@;            // \expos
    optional<T>       @\exposidnc{result}@;           // \expos; present only if \tcode{is_void_v<T>} is \tcode{false}
    @\exposidnc{error-variant}@     @\exposidnc{errors}@;           // \expos
  };
}
\end{codeblock}

\pnum
Let \tcode{\placeholder{prom}} be an object of \tcode{promise_type}
and let \tcode{\placeholder{tsk}} be the \tcode{task} object
created by \tcode{\placeholder{prom}.get_return_object()}.
The description below
refers to objects \tcode{\exposid{STATE}(\placeholder{prom})},
\tcode{\exposid{RCVR}(\placeholder{prom})},
and \tcode{\exposid{SCHED}(\placeholder{prom})}
associated with \tcode{\placeholder{tsk}}
during evaluation of \tcode{task::\exposid{state}<Rcvr>::start}
for some receiver \tcode{Rcvr}.

\pnum
\exposid{error-variant} is a \tcode{variant<monostate,
remove_cvref_t<E>...>}, with duplicate types removed, where \tcode{E...}
are the parameter types of the template arguments of the specialization of
\tcode{execution::completion_signatures} denoted by
\tcode{error_types}.

\indexlibraryctor{task::promise_type}%
\begin{itemdecl}
template<class... Args>
  promise_type(const Args&... args);
\end{itemdecl}
\begin{itemdescr}
\pnum
\mandates
The first parameter of type \tcode{allocator_arg_t} (if any) is not
the last parameter.

\pnum
\effects
If \tcode{Args} contains an element of type \tcode{allocator_arg_t}
then \exposid{alloc} is initialized with the corresponding next
element of \tcode{args}.
Otherwise, \exposid{alloc} is initialized with \tcode{allocator_type()}.
\end{itemdescr}

\indexlibrarymember{get_return_object}{task::promise_type}%
\begin{itemdecl}
task get_return_object() noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
A \tcode{task} object whose member \exposid{handle} is
\tcode{coroutine_handle<promise_type>::\brk{}from_promise\brk{}(*this)}.
\end{itemdescr}

\indexlibrarymember{initial_suspend}{task::promise_type}%
\begin{itemdecl}
auto initial_suspend() noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
An awaitable object of unspecified type\iref{expr.await} whose
member functions arrange for
\begin{itemize}
\item the calling coroutine to be suspended,
\item the coroutine to be resumed on an execution agent of the
execution resource associated with \tcode{\exposid{SCHED}(*this)}.
\end{itemize}
\end{itemdescr}

\indexlibrarymember{final_suspend}{task::promise_type}%
\begin{itemdecl}
auto final_suspend() noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
An awaitable object of unspecified type\iref{expr.await} whose
member functions arrange for the completion of the asynchronous
operation associated with \tcode{\exposid{STATE}(*this)} by invoking:
\begin{itemize}
\item
\tcode{set_error(std::move(\exposid{RCVR}(*this)), std::move(e))}
if \tcode{\exposid{errors}.index()} is greater than zero and
\tcode{e} is the value held by \exposid{errors}, otherwise
\item
\tcode{set_value(std::move(\exposid{RCVR}(*this)))} if \tcode{is_void<T>} is \tcode{true},
and otherwise
\item
 \tcode{set_value(std::move(\exposid{RCVR}(*this)), *\exposid{result})}.
\end{itemize}
\end{itemdescr}

\indexlibrarymember{yield_value}{task::promise_type}%
\begin{itemdecl}
template<class Err>
  auto yield_value(with_error<Err> err);
\end{itemdecl}
\begin{itemdescr}
\pnum
\mandates
\tcode{std::move(err.error)} is convertible to exactly one of the
\tcode{set_error_t} argument types of \tcode{error_types}.
Let \tcode{\placeholder{Cerr}} be that type.

\pnum
\returns
An awaitable object of unspecified type\iref{expr.await} whose
member functions arrange for the calling coroutine to be suspended
and then completes the asynchronous operation associated with
\tcode{\exposid{STATE}(*this)} by invoking \tcode{set_error(std::move(\exposid{RCVR}(*this)),
\placeholder{Cerr}(std::move(err.error)))}.
\end{itemdescr}

\indexlibrarymember{await_transform}{task::promise_type}%
\begin{itemdecl}
template<@\libconcept{sender}@ Sender>
  auto await_transform(Sender&& sndr) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
If \tcode{\libconcept{same_as}<inline_scheduler, scheduler_type>} is \tcode{true}
returns \tcode{as_awaitable(\brk{}std::\brk{}for\-ward<Sender>(sndr), *this)};
otherwise returns
\tcode{as_awaitable(affine_on(\brk{}std::\brk{}for\-ward<Sen\-der>(sndr), \exposid{SCHED}(*this)), *this)}.
\end{itemdescr}

\indexlibrarymember{await_transform}{task::promise_type}%
\begin{itemdecl}
template<class Sch>
  auto await_transform(change_coroutine_scheduler<Sch> sch) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
return await_transform(just(exchange(@\exposid{SCHED}@(*this), scheduler_type(sch.scheduler))), *this);
\end{codeblock}
\end{itemdescr}

\indexlibrarymember{uncaught_exception}{task::promise_type}%
\begin{itemdecl}
void uncaught_exception();
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
If the signature \tcode{set_error_t(exception_ptr)} is not an element
of \tcode{error_types}, calls \tcode{terminate()}\iref{except.terminate}.
Otherwise, stores \tcode{current_exception()} into \exposid{errors}.
\end{itemdescr}

\indexlibrarymember{unhandled_stopped}{task::promise_type}%
\begin{itemdecl}
coroutine_handle<> unhandled_stopped();
\end{itemdecl}
\begin{itemdescr}
\pnum
\effects
Completes the asynchronous operation associated with \tcode{\exposid{STATE}(*this)}
by invoking \tcode{set_stopped(std::move(\exposid{RCVR}(*this)))}.
\end{itemdescr}
\begin{itemdescr}
\pnum
\returns
\tcode{noop_coroutine()}.
\end{itemdescr}

\indexlibrarymember{get_env}{task::promise_type}%
\begin{itemdecl}
@\unspec@ get_env() const noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\returns
An object \tcode{env} such that queries are forwarded as follows:
\begin{itemize}
\item \tcode{env.query(get_scheduler)} returns \tcode{scheduler_type(\exposid{SCHED}(*this))}.
\item \tcode{env.query(get_allocator)} returns \exposid{alloc}.
\item \tcode{env.query(get_stop_token)} returns \exposid{token}.
\item For any other query \tcode{q} and arguments \tcode{a...} a
call to \tcode{env.query(q, a...)} returns
\tcode{\exposid{STATE}(*this)}. \tcode{environment.query(q, a...)} if this expression
is well-formed and \tcode{forwarding_query(q)} is well-formed and is \tcode{true}.
Otherwise \tcode{env.query(q, a...)} is ill-formed.
\end{itemize}
\end{itemdescr}

\indexlibrarymember{operator new}{task::promise_type}%
\begin{itemdecl}
template<class... Args>
  void* operator new(size_t size, const Args&... args);
\end{itemdecl}
\begin{itemdescr}
\pnum
If there is no parameter with type \tcode{allocator_arg_t} then let
\tcode{alloc} be \tcode{allocator_type()}.
Otherwise, let \tcode{arg_next} be the parameter
following the first \tcode{allocator_arg_t} parameter,
and let \tcode{alloc} be \tcode{allocator_type(arg_next)}.
Let \tcode{PAlloc} be \tcode{allocator_traits<allocator_type>::template
rebind_alloc<U>}, where \tcode{U} is an unspecified type
whose size and alignment are both \mname{STDCPP_DEFAULT_NEW_ALIGNMENT}.

\pnum
\mandates
\begin{itemize}
\item The first parameter of type \tcode{allocator_arg_t} (if any) is not the last parameter.
\item \tcode{allocator_type(arg_next)} is a valid expression if there is a parameter
of type \tcode{allocator_arg_t}.
\item \tcode{allocator_traits<PAlloc>::pointer} is a pointer type.
\end{itemize}

\pnum
\effects
Initializes an allocator \tcode{palloc} of type \tcode{PAlloc} with
\tcode{alloc}.
Uses \tcode{palloc} to allocate storage for the
smallest array of \tcode{U} sufficient to provide storage for a
coroutine state of size \tcode{size}, and unspecified additional
state necessary to ensure that \tcode{operator delete} can later
deallocate this memory block with an allocator equal to \tcode{palloc}.

\pnum
\returns
A pointer to the allocated storage.
\end{itemdescr}

\indexlibrarymember{operator delete}{task::promise_type}%
\begin{itemdecl}
void operator delete(void* pointer, size_t size) noexcept;
\end{itemdecl}
\begin{itemdescr}
\pnum
\expects
\tcode{pointer} was returned from an invocation of the above overload
of \tcode{operator new} with a size argument equal to \tcode{size}.

\pnum
\effects
Deallocates the storage pointed to by \tcode{pointer} using an
allocator equal to that used to allocate it.
\end{itemdescr}

\rSec1[exec.scope]{Execution scope utilities}

\rSec2[exec.scope.concepts]{Execution scope concepts}

\pnum
The \libconcept{scope_token} concept defines the requirements on
a type \tcode{Token} that can be used to create associations
between senders and an async scope.

\pnum
Let \placeholder{test-sender} and \placeholder{test-env}
be unspecified types such that
\tcode{\libconcept{sender_in}<\placeholder{test-sender}, \placeholder{test-env}>}
is modeled.

\begin{codeblock}
namespace std::execution {
  template<class Token>
    concept @\deflibconcept{scope_token}@ =
      @\libconcept{copyable}@<Token> &&
      requires(const Token token) {
        { token.try_associate() } -> @\libconcept{same_as}@<bool>;
        { token.disassociate() } noexcept -> @\libconcept{same_as}@<void>;
        { token.wrap(declval<@\placeholder{test-sender}@>()) } -> @\libconcept{sender_in}@<@\placeholder{test-env}@>;
      };
}
\end{codeblock}

\pnum
A type \tcode{Token} models \libconcept{scope_token} only if:

\begin{itemize}
\item
no exceptions are thrown from
copy construction,
move construction,
copy assignment, or
move assignment
of objects of type \tcode{Token}; and

\item
given an lvalue \tcode{token} of type (possibly const) \tcode{Token},
for all expressions \tcode{sndr} such that
\tcode{decltype((\linebreak{}sndr))} models \libconcept{sender}:
  \begin{itemize}
  \item
  \tcode{token.wrap(sndr)} is a valid expression,
  \item
  \tcode{decltype(token.wrap(sndr))} models \libconcept{sender}, and
  \item
  \tcode{completion_signatures_of_t<decltype(token.wrap(sndr)), E>}
  contains the same completion signatures as
  \tcode{completion_signatures_of_t<decltype((sndr)), E>}
  for all types \tcode{E} such that
  \tcode{\libconcept{sender_in}<decltype((sndr)), E>} is modeled.
  \end{itemize}
\end{itemize}

\rSec2[exec.counting.scopes]{Counting Scopes}

\rSec3[exec.counting.scopes.general]{General}

\pnum
Scopes of type \tcode{simple_counting_scope} and \tcode{counting_scope}
maintain counts of associations.
Let:
\begin{itemize}
\item
\tcode{Scope} be either \tcode{simple_counting_scope} or \tcode{counting_scope},
\item
\tcode{scope} be an object of type \tcode{Scope},
\item
\tcode{tkn} be an object of type \tcode{Scope::token}
obtained from \tcode{scope.get_token()},
\item
\tcode{jsndr} be a sender obtained from \tcode{scope.join()}, and
\item
\tcode{op} be an operation state obtained from
connecting \tcode{jsndr} to a receiver.
\end{itemize}
During its lifetime \tcode{scope} goes through different states
which govern what operations are allowed and the result of these operations:

\begin{itemize}
\item
\exposid{unused}:
a newly constructed object starts in the \exposid{unused} state.

\item
\exposid{open}:
when \tcode{tkn.try_associate()} is called
while \tcode{scope} is in the \exposid{unused} state,
\tcode{scope} moves to the \exposid{open} state.

\item
\exposid{open-and-joining}:
when the operation state \tcode{op} is started
while \tcode{scope} is in the \exposid{unused} or \exposid{open} state,
\tcode{scope} moves to the \exposid{open-and-joining} state.

\item
\exposid{closed}:
when \tcode{scope.close()} is called
while \tcode{scope} is in the \exposid{open} state,
\tcode{scope} moves to the \exposid{closed} state.

\item
\exposid{unused-and-closed}:
when \tcode{scope.close()} is called
while \tcode{scope} is in the \exposid{unused} state,
\tcode{scope} moves to the \exposid{unused-and-closed} state.

\item
\exposid{closed-and-joining}:
when \tcode{scope.close()} is called
while \tcode{scope} is in the \exposid{open-and-joining} state or
the operation state \tcode{op} is started
while \tcode{scope} is in
the \exposid{closed} or \exposid{unused-and-closed} state,
\tcode{scope} moves to the \exposid{closed-and-joining} state.

\item
\exposid{joined}:
when the count of associations drops to zero
while \tcode{scope} is in
the \exposid{open-and-joining} or \exposid{closed-and-joining} state,
\tcode{scope} moves to the \exposid{joined} state.
\end{itemize}

\pnum
\recommended
For \tcode{simple_counting_scope} and \tcode{counting_scope},
implementations should store the state and the count of associations
in a single member of type \tcode{size_t}.

\pnum
Subclause \ref{exec.counting.scopes} makes use of
the following exposition-only entities:

\begin{codeblock}
struct @\exposid{scope-join-t}@ {};     // \expos

enum @\exposid{scope-state-type}@ {     // \expos
  @\exposid{unused}@,                   // \expos
  @\exposid{open}@,                     // \expos
  @\exposid{closed}@,                   // \expos
  @\exposid{open-and-joining}@,         // \expos
  @\exposid{closed-and-joining}@,       // \expos
  @\exposid{unused-and-closed}@,        // \expos
  @\exposid{joined}@,                   // \expos
};
\end{codeblock}

\pnum
The exposition-only class template \exposid{impls-for}\iref{exec.snd.expos}
is specialized for \exposid{scope-join-t} as follows:

\indexlibraryglobal{execution::\exposid{impls-for}<\exposid{scope-join-t}>}%
%%FIXME: The declarations of "receiver" below hide the \libconcept of the same name
\begin{codeblock}
namespace std::execution {
  template<>
  struct @\exposid{impls-for}@<@\exposid{scope-join-t}@> : @\exposid{default-impls}@ {
    template<class Scope, class Rcvr>
    struct @\exposid{state}@ {                          // \expos
      struct @\exposid{rcvr-t}@ {                       // \expos
        using receiver_concept = receiver_t;

        Rcvr& @\exposid{rcvr}@;                         // \expos

        void set_value() && noexcept {
          execution::set_value(std::move(@\exposid{rcvr}@));
        }

        template<class E>
          void set_error(E&& e) && noexcept {
            execution::set_error(std::move(@\exposid{rcvr}@), std::forward<E>(e));
          }

        void set_stopped() && noexcept {
          execution::set_stopped(std::move(@\exposid{rcvr}@));
        }

        decltype(auto) get_env() const noexcept {
          return execution::get_env(@\exposid{rcvr}@);
        }
      };

      using @\exposid{sched-sender}@ =                  // \expos
        decltype(schedule(get_scheduler(get_env(declval<Rcvr&>()))));
      using @\exposid{op-t}@ =                          // \expos
        connect_result_t<@\exposid{sched-sender}@, @\exposid{rcvr-t}@>;

      Scope* @\exposid{scope}@;                         // \expos
      Rcvr& @\exposid{receiver}@;                       // \expos
      @\exposid{op-t}@ @\exposid{op}@;                              // \expos

      @\exposid{state}@(Scope* scope, Rcvr& rcvr)       // \expos
        noexcept(@\exposconcept{nothrow-callable}@<connect_t, @\exposid{sched-sender}@, @\exposid{rcvr-t}@>)
        : @\exposid{scope}@(scope),
          @\exposid{receiver}@(rcvr),
          @\exposid{op}@(connect(schedule(get_scheduler(get_env(rcvr))), @\exposid{rcvr-t}@(rcvr))) {}

      void @\exposid{complete}@() noexcept {            // \expos
        start(@\exposid{op}@);
      }

      void @\exposid{complete-inline}@() noexcept {     // \expos
        set_value(std::move(@\exposid{receiver}@));
      }
    };

    static constexpr auto @\exposid{get-state}@ =       // \expos
      []<class Rcvr>(auto&& sender, Rcvr& receiver)
        noexcept(is_nothrow_constructible_v<@\exposid{state}@<Rcvr>, @\exposid{data-type}@<decltype(sender)>, Rcvr&>) {
        auto[_, self] = sender;
        return @\exposid{state}@(self, receiver);
      };

    static constexpr auto @\exposid{start}@ =           // \expos
      [](auto& s, auto&) noexcept {
        if (s.@\exposid{scope}@->@\exposid{start-join-sender}@(s))
          s.@\exposid{complete-inline}@();
      };
  };
}
\end{codeblock}

\rSec3[exec.scope.simple.counting]{Simple Counting Scope}

\rSec4[exec.scope.simple.counting.general]{General}

\indexlibraryglobal{execution::simple_counting_scope}%
\begin{codeblock}
namespace std::execution {
  class simple_counting_scope {
  public:
    // \ref{exec.simple.counting.token}, token
    struct token;

    static constexpr size_t max_associations = @\UNSP{\impldef{value of \tcode{std::execution::simple_counting_scope::max_associations}}}@;

    // \ref{exec.simple.counting.ctor}, constructor and destructor
    simple_counting_scope() noexcept;
    simple_counting_scope(simple_counting_scope&&) = delete;
    ~simple_counting_scope();

    // \ref{exec.simple.counting.mem}, members
    token get_token() noexcept;
    void close() noexcept;
    @\libconcept{sender}@ auto join() noexcept;

  private:
    size_t @\exposid{count}@;                                       // \expos
    @\exposid{scope-state-type}@ @\exposid{state}@;                             // \expos

    bool @\exposid{try-associate}@() noexcept;                      // \expos
    void @\exposid{disassociate}@() noexcept;                       // \expos
    template<class State>
      bool @\exposid{start-join-sender}@(State& state) noexcept;    // \expos
  };
}
\end{codeblock}

\pnum
For purposes of determining the existence of a data race,
\tcode{get_token},
\tcode{close},
\tcode{join},
\exposid{try-associate},
\exposid{disassociate}, and
\exposid{start-join-sender}
behave as atomic operations\iref{intro.multithread}.
These operations on a single object of
type \tcode{simple_counting_scope} appear to occur in a single total order.

\rSec4[exec.simple.counting.ctor]{Constructor and Destructor}

\indexlibraryctor{execution::simple_counting_scope}%
\begin{itemdecl}
simple_counting_scope() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\ensures
\exposid{count} is \tcode{0} and \exposid{state} is \exposid{unused}.
\end{itemdescr}

\indexlibrarydtor{execution::simple_counting_scope}%
\begin{itemdecl}
~simple_counting_scope();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \exposid{state} is not one of
\exposid{joined}, \exposid{unused}, or \exposid{unused-and-closed},
invokes \tcode{terminate}\iref{except.terminate}.
Otherwise, has no effects.
\end{itemdescr}

\rSec4[exec.simple.counting.mem]{Members}

\indexlibrarymember{get_token}{execution::simple_counting_scope}%
\begin{itemdecl}
token get_token() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\returns
An object \tcode{t} of type \tcode{simple_counting_scope::token} such that
\tcode{t.\exposid{scope} == this} is \tcode{true}.
\end{itemdescr}

\indexlibrarymember{close}{execution::simple_counting_scope}%
\begin{itemdecl}
void close() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \exposid{state} is
\begin{itemize}
\item
\exposid{unused}, then changes \exposid{state} to \exposid{unused-and-closed};
\item
\exposid{open}, then changes \exposid{state} to \exposid{closed};
\item
\exposid{open-and-joining},
then changes \exposid{state} to \exposid{closed-and-joining};
\item
otherwise, no effects.
\end{itemize}

\pnum
\ensures
Any subsequent call to \tcode{\exposid{try-associate}()} on \tcode{*this}
returns \tcode{false}.
\end{itemdescr}

\indexlibrarymember{join}{execution::simple_counting_scope}%
\begin{itemdecl}
@\libconcept{sender}@ auto join() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\returns
\tcode{\exposid{make-sender}(\exposid{scope-join-t}(), this)}.
\end{itemdescr}

\indexlibrarymember{\exposid{try-associate}}{execution::simple_counting_scope}%
\begin{itemdecl}
bool @\exposid{try-associate}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \exposid{count} is equal to \tcode{max_associations}, then no effects.
Otherwise, if \exposid{state} is
\begin{itemize}
\item
\exposid{unused},
then increments \exposid{count} and changes \exposid{state} to \exposid{open};
\item
\exposid{open} or \exposid{open-and-joining},
then increments \exposid{count};
\item
otherwise, no effects.
\end{itemize}

\pnum
\returns
\tcode{true} if \exposid{count} was incremented, \tcode{false} otherwise.
\end{itemdescr}

\indexlibrarymember{\exposid{disassociate}}{execution::simple_counting_scope}%
\begin{itemdecl}
void @\exposid{disassociate}@() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
\exposid{count} is greater than zero.

\pnum
\effects
Decrements \exposid{count}.
If \exposid{count} is zero after decrementing and
\exposid{state} is \exposid{open-and-joining} or \exposid{closed-and-joining},
changes \exposid{state} to \exposid{joined} and
calls \tcode{\exposid{complete}()} on all objects registered with \tcode{*this}.
\begin{note}
Calling \tcode{\exposid{complete}()} on any registered object
can cause \tcode{*this} to be destroyed.
\end{note}
\end{itemdescr}

\indexlibrarymember{\exposid{start-join-sender}}{execution::simple_counting_scope}%
\begin{itemdecl}
template<class State>
  bool @\exposid{start-join-sender}@(State& st) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
If \exposid{state} is
\begin{itemize}
\item
\exposid{unused}, \exposid{unused-and-closed}, or \exposid{joined}, then
changes \exposid{state} to \exposid{joined} and returns \tcode{true};
\item
\exposid{open} or \exposid{open-and-joining}, then
changes \exposid{state} to \exposid{open-and-joining},
registers \tcode{st} with \tcode{*this} and returns \tcode{false};
\item
\exposid{closed} or \exposid{closed-and-joining}, then
changes \exposid{state} to \exposid{closed-and-joining},
registers \tcode{st} with \tcode{*this} and returns \tcode{false}.
\end{itemize}
\end{itemdescr}

\rSec4[exec.simple.counting.token]{Token}

\indexlibraryglobal{execution::simple_counting_scope::token}%
\begin{codeblock}
namespace std::execution {
  struct simple_counting_scope::token {
    template<@\libconcept{sender}@ Sender>
      Sender&& wrap(Sender&& snd) const noexcept;
    bool try_associate() const noexcept;
    void disassociate() const noexcept;

  private:
    simple_counting_scope* @\exposid{scope}@;   // \expos
  };
}
\end{codeblock}

\indexlibrarymember{wrap}{execution::simple_counting_scope::token}%
\begin{itemdecl}
template<@\libconcept{sender}@ Sender>
  Sender&& wrap(Sender&& snd) const noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\returns
\tcode{std::forward<Sender>(snd)}.
\end{itemdescr}

\indexlibrarymember{try_associate}{execution::simple_counting_scope::token}%
\begin{itemdecl}
bool try_associate() const noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to: \tcode{return \exposid{scope}->\exposid{try-associate}();}
\end{itemdescr}

\indexlibrarymember{disassociate}{execution::simple_counting_scope::token}%
\begin{itemdecl}
void disassociate() const noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to \tcode{\exposid{scope}->\exposid{disassociate}()}.
\end{itemdescr}

\rSec3[exec.scope.counting]{Counting Scope}

\indexlibraryglobal{execution::counting_scope}%
\indexlibrarymember{token}{execution::counting_scope}%
\begin{codeblock}
namespace std::execution {
  class counting_scope {
  public:
    struct token {
      template<@\libconcept{sender}@ Sender>
        @\libconcept{sender}@ auto wrap(Sender&& snd) const noexcept(@\seebelow@);
      bool try_associate() const noexcept;
      void disassociate() const noexcept;

    private:
      counting_scope* @\exposid{scope}@;                            // \expos
    };

    static constexpr size_t max_associations = @\UNSP{\impldef{value of \tcode{std::execution::counting_scope::max_associations}}}@;

    counting_scope() noexcept;
    counting_scope(counting_scope&&) = delete;
    ~counting_scope();

    token get_token() noexcept;
    void close() noexcept;
    @\libconcept{sender}@ auto join() noexcept;
    void request_stop() noexcept;

  private:
    size_t @\exposid{count}@;                                       // \expos
    @\exposid{scope-state-type}@ @\exposid{state}@;                             // \expos
    inplace_stop_source @\exposid{s_source}@;                       // \expos

    bool @\exposid{try-associate}@() noexcept;                      // \expos
    void @\exposid{disassociate}@() noexcept;                       // \expos

    template<class State>
      bool @\exposid{start-join-sender}@(State& state) noexcept;    // \expos
  };
}
\end{codeblock}

\pnum
\tcode{counting_scope} differs from \tcode{simple_counting_scope} by
adding support for cancellation.
Unless specified below, the semantics of members of \tcode{counting_scope}
are the same as the corresponding members of \tcode{simple_counting_scope}.

\indexlibrarymember{get_token}{execution::counting_scope}%
\begin{itemdecl}
token get_token() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\returns
An object \tcode{t} of type \tcode{counting_scope::token} such that
\tcode{t.\exposid{scope} == this} is \tcode{true}.
\end{itemdescr}

\indexlibrarymember{request_stop}{execution::counting_scope}%
\begin{itemdecl}
void request_stop() noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to \tcode{\exposid{s_source}.request_stop()}.

\pnum
\remarks
Calls to \tcode{request_stop} do not introduce data races.
\end{itemdescr}

\indexlibrarymember{wrap}{execution::counting_scope::token}%
\begin{itemdecl}
template<@\libconcept{sender}@ Sender>
  @\libconcept{sender}@ auto counting_scope::token::wrap(Sender&& snd) const
    noexcept(is_nothrow_constructible_v<remove_cvref_t<Sender>, Sender>);
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Equivalent to:
\begin{codeblock}
return @\exposid{stop-when}@(std::forward<Sender>(snd), @\exposid{scope}@->@\exposid{s_source}@.get_token());
\end{codeblock}
\end{itemdescr}

\rSec1[exec.par.scheduler]{Parallel scheduler}

\pnum
\tcode{parallel_scheduler} models \libconcept{scheduler}.

\pnum
Let \tcode{sch} be an object of type \tcode{parallel_scheduler}, and
let \tcode{\exposid{BACKEND-OF}(sch)} be \tcode{*ptr},
where \tcode{sch} is associated with \tcode{ptr}.

\pnum
The expression \tcode{get_forward_progress_guarantee(sch)} has the value
\tcode{forward_progress_guarantee::\brk{}parallel}.

\pnum
Let \tcode{sch2} be an object of type \tcode{parallel_scheduler}.
Two objects \tcode{sch} and \tcode{sch2} compare equal if and only if
\tcode{\exposid{BACKEND-OF}(sch)} and
\tcode{\exposid{BACKEND-OF}(sch2)} refer to the same object.

\pnum
Let \tcode{rcvr} be a receiver.
A \defnx{proxy for \tcode{rcvr} with base \tcode{B}}{proxy} is
an lvalue \tcode{r} of type \tcode{B} such that:
\begin{itemize}
\item
\tcode{r.set_value()} has effects equivalent to
\tcode{set_value(std::move(rcvr))}.
\item
\tcode{r.set_error(e)}, where \tcode{e} is an \tcode{exception_ptr} object,
has effects equivalent to \tcode{set_error(std::move(\brk{}rcvr), std::move(e))}.
\item
\tcode{r.set_stopped()} has effects equivalent to
\tcode{set_stopped(std::move(rcvr))}.
\end{itemize}

\pnum
A \defn{preallocated backend storage for a proxy} \tcode{r} is
an object \tcode{s} of type \tcode{span<byte>}
such that the range \tcode{s} remains valid and may be overwritten
until one of \tcode{set_value}, \tcode{set_error}, or \tcode{set_stopped}
is called on \tcode{r}.
\begin{note}
The storage referenced by \tcode{s} can be used as temporary storage
for operations launched via calls to \tcode{parallel_scheduler_backend}.
\end{note}

\pnum
A \defnx{bulk chunked proxy for \tcode{rcvr}
with callable \tcode{f} and arguments \tcode{args}}{proxy!bulk chunked}
is a proxy \tcode{r} for \tcode{rcvr}
with base \tcode{system_context_replaceability::bulk_item_receiver_proxy}
such that
\tcode{r.execute(i, j)} for indices \tcode{i} and \tcode{j}
has effects equivalent to \tcode{f(i, j, args...)}.

\pnum
A \defnx{bulk unchunked proxy for \tcode{rcvr}
with callable \tcode{f} and arguments \tcode{args}}{proxy!bulk unchunked}
is a proxy \tcode{r} for \tcode{rcvr}
with base \tcode{system_context_replaceability::bulk_item_receiver_proxy}
such that
\tcode{r.execute(i, i + 1)} for index \tcode{i}
has effects equivalent to \tcode{f(i, args...)}.

\pnum
Let \tcode{b} be \tcode{\exposid{BACKEND-OF}(sch)},
let \tcode{sndr} be the object returned by \tcode{schedule(sch)}, and
let \tcode{rcvr} be a receiver.
If \tcode{rcvr} is connected to \tcode{sndr} and
the resulting operation state is started, then:
\begin{itemize}
\item
If \tcode{sndr} completes successfully,
then \tcode{b.schedule(r, s)} is called, where
\begin{itemize}
\item
\tcode{r} is a proxy for \tcode{rcvr}
with base \tcode{system_context_replaceability::receiver_proxy} and
\item
\tcode{s} is a preallocated backend storage for \tcode{r}.
\end{itemize}
\item
All other completion operations are forwarded unchanged.
\end{itemize}

\pnum
\tcode{parallel_scheduler} provides a customized implementation of
the \tcode{bulk_chunked} algorithm\iref{exec.bulk}.
If a receiver \tcode{rcvr} is connected to the sender
returned by \tcode{bulk_chunked(sndr, pol, shape, f)} and
the resulting operation state is started, then:
\begin{itemize}
\item
If \tcode{sndr} completes with values \tcode{vals},
let \tcode{args} be a pack of lvalue subexpressions designating \tcode{vals},
then \tcode{b.schedule_bulk_chunked(shape, r, s)} is called, where
\begin{itemize}
\item
\tcode{r} is a bulk chunked proxy for \tcode{rcvr}
with callable \tcode{f} and arguments \tcode{args} and
\item
\tcode{s} is a preallocated backend storage for \tcode{r}.
\end{itemize}
\item
All other completion operations are forwarded unchanged.
\end{itemize}
\begin{note}
Customizing the behavior of \tcode{bulk_chunked}
affects the default implementation of \tcode{bulk}.
\end{note}

\pnum
\tcode{parallel_scheduler} provides a customized implementation of
the \tcode{bulk_unchunked} algorithm\iref{exec.bulk}.
If a receiver \tcode{rcvr} is connected to the sender
returned by \tcode{bulk_unchunked(sndr, pol, shape, f)} and
the resulting operation state is started, then:
\begin{itemize}
\item
If \tcode{sndr} completes with values \tcode{vals},
let \tcode{args} be a pack of lvalue subexpressions designating \tcode{vals},
then \tcode{b.schedule_bulk_unchunked(shape, r, s)} is called, where
\begin{itemize}
\item
\tcode{r} is a bulk unchunked proxy for \tcode{rcvr}
with callable \tcode{f} and arguments \tcode{args} and
\item
\tcode{s} is a preallocated backend storage for \tcode{r}.
\end{itemize}
\item
All other completion operations are forwarded unchanged.
\end{itemize}

\indexlibraryglobal{get_parallel_scheduler}%
\begin{itemdecl}
parallel_scheduler get_parallel_scheduler();
\end{itemdecl}

\begin{itemdescr}
\pnum
\effects
Let \tcode{eb} be the result of \tcode{system_context_replaceability::query_parallel_scheduler_backend()}.
If \tcode{eb == nullptr} is \tcode{true},
calls \tcode{terminate}\iref{except.terminate}.
Otherwise, returns a \tcode{parallel_scheduler} object
associated with \tcode{eb}.
\end{itemdescr}

\rSec1[exec.sysctxrepl]{Namespace \tcode{system_context_replaceability}}

\rSec2[exec.sysctxrepl.general]{General}

\pnum
Facilities in the \tcode{system_context_replaceability} namespace
allow users to replace the default implementation of \tcode{parallel_scheduler}.

\rSec2[exec.sysctxrepl.query]{\tcode{query_parallel_scheduler_backend}}
\indexlibraryglobal{query_parallel_scheduler_backend}%
\begin{itemdecl}
shared_ptr<parallel_scheduler_backend> query_parallel_scheduler_backend();
\end{itemdecl}

\begin{itemdescr}
\pnum
\tcode{query_parallel_scheduler_backend()} returns
the implementation object for a parallel scheduler.

\pnum
\returns
A non-null shared pointer to an object
that implements the \tcode{parallel_scheduler_backend} interface.

\pnum
\remarks
This function is replaceable\iref{term.replaceable.function}.
\end{itemdescr}

\begin{codeblock}
namespace std::execution::system_context_replaceability {
  struct @\libglobal{receiver_proxy}@ {
    virtual ~receiver_proxy() = default;

  protected:
    virtual bool @\exposidnc{query-env}@(@\unspecnc@) noexcept = 0;   // \expos

  public:
    virtual void set_value() noexcept = 0;
    virtual void set_error(exception_ptr) noexcept = 0;
    virtual void set_stopped() noexcept = 0;

    template<class P, @\exposconcept{class-type}@ Query>
      optional<P> try_query(Query q) noexcept;
  };

  struct @\libglobal{bulk_item_receiver_proxy}@ : receiver_proxy {
    virtual void execute(size_t, size_t) noexcept = 0;
  };
}
\end{codeblock}

\pnum
\tcode{receiver_proxy} represents a receiver
that will be notified
by the implementations of \tcode{parallel_scheduler_backend}
to trigger the completion operations.
\tcode{bulk_item_receiver_proxy} is derived from \tcode{receiver_proxy} and
is used for \tcode{bulk_chunked} and \tcode{bulk_unchunked} customizations
that will also receive notifications
from implementations of \tcode{parallel_scheduler_backend}
corresponding to different iterations.

\begin{itemdecl}
template<class P, @\exposconcept{class-type}@ Query>
  optional<P> @\libglobal{try_query}@(Query q) noexcept;
\end{itemdecl}

\begin{itemdescr}
\pnum
\mandates
\tcode{P} is a cv-unqualified non-array object type.

\pnum
\returns
Let \tcode{env} be the environment of the receiver represented by \tcode{*this}.
If
\begin{itemize}
\item
\tcode{Query} is not a member of an implementation-defined set
of supported queries; or
\item
\tcode{P} is not a member of an implementation-defined set
of supported result types for \tcode{Query}; or
\item
the expression \tcode{q(env)} is not well-formed or
does not have type \cv{} \tcode{P},
\end{itemize}
then returns \tcode{nullopt}.
Otherwise, returns \tcode{q(env)}.

\pnum
\remarks
\tcode{get_stop_token_t} is
in the implementation-defined set of supported queries, and
\tcode{inplace_stop_token} is a member
of the implementation-defined set of supported result types
for \tcode{get_stop_token_t}.
\end{itemdescr}

\rSec2[exec.sysctxrepl.psb]{Class \tcode{parallel_scheduler_backend}}

\begin{codeblock}
namespace std::execution::system_context_replaceability {
  struct @\libglobal{parallel_scheduler_backend}@ {
    virtual ~parallel_scheduler_backend() = default;

    virtual void schedule(receiver_proxy&, span<byte>) noexcept = 0;
    virtual void schedule_bulk_chunked(size_t, bulk_item_receiver_proxy&,
                                       span<byte>) noexcept = 0;
    virtual void schedule_bulk_unchunked(size_t, bulk_item_receiver_proxy&,
                                         span<byte>) noexcept = 0;
  };
}
\end{codeblock}

\indexlibrarymember{schedule}{parallel_scheduler_backend}%
\begin{itemdecl}
virtual void schedule(receiver_proxy& r, span<byte> s) noexcept = 0;
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
The ends of
the lifetimes of \tcode{*this},
the object referred to by \tcode{r}, and
any storage referenced by \tcode{s}
all happen after
the beginning of the evaluation of
the call to \tcode{set_value}, \tcode{set_error}, or \tcode{set_done}
on \tcode{r} (see below).

\pnum
\effects
A derived class shall implement this function such that:
\begin{itemize}
\item
One of the following expressions is evaluated:
\begin{itemize}
\item
\tcode{r.set_value()}, if no error occurs, and the work is successful;
\item
\tcode{r.set_error(eptr)}, if an error occurs,
where \tcode{eptr} is an object of type \tcode{exception_ptr};
\item
\tcode{r.set_stopped()}, if the work is canceled.
\end{itemize}
\item
Any call to \tcode{r.set_value()} happens on
an execution agent of the execution context represented by \tcode{*this}.
\end{itemize}

\pnum
\remarks
The storage referenced by \tcode{s}
may be used by \tcode{*this} as temporary storage
for the duration of the operation launched by this call.
\end{itemdescr}

\indexlibrarymember{schedule_bulk_chunked}{parallel_scheduler_backend}%
\begin{itemdecl}
virtual void schedule_bulk_chunked(size_t n, bulk_item_receiver_proxy& r,
                                   span<byte> s) noexcept = 0;
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
The ends of
the lifetimes of \tcode{*this},
the object referred to by \tcode{r}, and
any storage referenced by \tcode{s}
all happen after
the beginning of the evaluation of one of the expressions below.

\pnum
\effects
A derived class shall implement this function such that:
\begin{itemize}
\item
Eventually, one of the following expressions is evaluated:
\begin{itemize}
\item
\tcode{r.set_value()}, if no error occurs, and the work is successful;
\item
\tcode{r.set_error(eptr)}, if an error occurs,
where \tcode{eptr} is an object of type \tcode{exception_ptr};
\item
\tcode{r.set_stopped()}, if the work is canceled.
\end{itemize}
\item
If \tcode{r.execute(b, e)} is called,
then \tcode{b} and \tcode{e} are in the range \crange{0}{n} and
$\tcode{b} < \tcode{e}$.
\item
For each $i$ in \range{0}{n},
there is at most one call to \tcode{r.execute(b, e)}
such that $i$ is in the range \range{b}{e}.
\item
If \tcode{r.set_value()} is called,
then for each $i$ in \range{0}{n},
there is exactly one call to \tcode{r.execute(b, e)}
such that $i$ is in the range \range{b}{e}.
\item
All calls to \tcode{execute} on \tcode{r} happen before
the call to either \tcode{set_value}, \tcode{set_error}, or \tcode{set_stopped}
on \tcode{r}.
\item
All calls to \tcode{execute} and \tcode{set_value} on \tcode{r} are made
on execution agents of the execution context represented by \tcode{*this}.
\end{itemize}

\pnum
\remarks
The storage referenced by \tcode{s} may be used by \tcode{*this}
as temporary storage for the duration of the operation launched by this call.
\end{itemdescr}

\indexlibrarymember{schedule_bulk_unchunked}{parallel_scheduler_backend}%
\begin{itemdecl}
virtual void schedule_bulk_unchunked(size_t n, bulk_item_receiver_proxy& r,
                                     span<byte> s) noexcept = 0;
\end{itemdecl}

\begin{itemdescr}
\pnum
\expects
The ends of
the lifetimes of \tcode{*this},
the object referred to by \tcode{r}, and
any storage referenced by \tcode{s}
all happen after
the beginning of the evaluation of one of the expressions below.

\pnum
\effects
A derived class shall implement this function such that:
\begin{itemize}
\item
Eventually, one of the following expressions is evaluated:
\begin{itemize}
\item
\tcode{r.set_value()}, if no error occurs, and the work is successful;
\item
\tcode{r.set_error(eptr)}, if an error occurs,
where \tcode{eptr} is an object of type \tcode{exception_ptr};
\item
\tcode{r.set_stopped()}, if the work is canceled.
\end{itemize}
\item
If \tcode{r.execute(b, e)} is called,
then \tcode{b} is in the range \range{0}{n} and
\tcode{e} is equal to \tcode{b + 1}.
For each $i$ in \range{0}{n},
there is at most one call to \tcode{r.execute($i$, $i$ + 1)}.
\item
If \tcode{r.set_value()} is called,
then for each $i$ in \range{0}{n},
there is exactly one call to \tcode{r.execute($i$, $i$ + 1)}.
\item
All calls to \tcode{execute} on \tcode{r} happen before
the call to either \tcode{set_value}, \tcode{set_error}, or \tcode{set_stopped}
on \tcode{r}.
\item
All calls to \tcode{execute} and \tcode{set_value} on \tcode{r} are made
on execution agents of the execution context represented by \tcode{*this}.
\end{itemize}

\pnum
\remarks
The storage referenced by \tcode{s} may be used by \tcode{*this}
as temporary storage for the duration of the operation launched by this call.
\end{itemdescr}