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Elaboration of subtyping rule of struct and variant in SpecTec IL #2111

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2067e36
fix: typo
jihongmin63 Mar 10, 2026
3791634
Merge branch 'WebAssembly:main' into main
jihongmin63 Mar 12, 2026
8cd0346
[spectec] elaborate subtyping rules for struct and variant
jihongmin63 Mar 13, 2026
f12cda1
Merge branch 'WebAssembly:main' into subtyp
jihongmin63 Mar 13, 2026
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5 changes: 5 additions & 0 deletions spectec/doc/semantics/il/0-aux.spectec
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Original file line number Diff line number Diff line change
Expand Up @@ -13,3 +13,8 @@ def $equiv_(syntax X, x_1*, x_2*) = false -- otherwise
def $transpose_(syntax X, X**) : X**
def $transpose_(syntax X, eps^n) = eps
def $transpose_(syntax X, (x_1 x*)*) = x_1* $transpose_(X, x**)


def $forall(bool*) : bool
def $forall(eps) = true
def $forall(bool_1 bool*) = bool_1 /\ $forall(bool*)
8 changes: 4 additions & 4 deletions spectec/doc/semantics/il/6-typing.spectec
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Expand Up @@ -45,16 +45,16 @@ rule Sub_typ/struct:
E |- t_1 <: t_2
-- Expand_typ: E |- t_1 => STRUCT tf_1*
-- Expand_typ: E |- t_2 => STRUCT tf_2*
-- (if (a `: t_2a `- `{q*} pr*) = tf_2)*
-- (if (a `: t_1a `- `{q*} pr*) <- tf_1*)*
-- (if (a `: t_2a `- `{q*} pr_2*) = tf_2)*
-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1* /\ $forall((pr_2 <- pr_1*)*))*
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@rossberg rossberg Mar 16, 2026

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Does this not work without the auxiliary forall?

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-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1* /\ $forall((pr_2 <- pr_1*)*))*
-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1*)*
-- (if pr_2 <- pr_1*)**

-- (Sub_typ: E |- t_1a <: t_2a)*

rule Sub_typ/variant:
E |- t_1 <: t_2
-- Expand_typ: E |- t_1 => VARIANT tc_1*
-- Expand_typ: E |- t_2 => VARIANT tc_2*
-- (if (m `: t_1a `- `{q*} pr*) = tc_1)*
-- (if (m `: t_2a `- `{q*} pr*) <- tc_2*)*
-- (if (m `: t_1a `- `{q*} pr_1*) = tc_1)*
-- (if (m `: t_2a `- `{q*} pr_2*) <- tc_2* /\ $forall((pr_2 <- pr_1*)*))*
-- (Sub_typ: E |- t_1a <: t_2a)*

rule Sub_typ/iter:
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