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feat: topological characterization of safety and liveness properties of infinite sequences#704

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leanprover:mainfrom
ctchou:topo-safe-live
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feat: topological characterization of safety and liveness properties of infinite sequences#704
ctchou wants to merge 2 commits into
leanprover:mainfrom
ctchou:topo-safe-live

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@ctchou

@ctchou ctchou commented Jul 9, 2026

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This PR formalizes some results in the following classic paper:

Alpern, Bowen; Schneider, Fred B. (1985). "Defining liveness". Information Processing Letters. 21 (4): 181–185.

To wit:

  • By viewing an infinite sequence as an infinite product, we define a topology on infinite sequences using the product topology.
  • We identify safety and liveness properties with closed and dense sets in this topology and justify these identifications.
  • We prove that every property is the intersection of a safety property and a liveness property and give explicit formulas for both.

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