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Increasing limits of bounded evaluators — unchecked contract

Lax755887.LimitDeciderContract · concepts/Lax755887/LimitDeciderContract.lean · lax-755887

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    Natural Language Statement

    Theorem

    Bounded acceptance is computable and increases with fuel. Its union is the halting predicate; computability does not pass to this increasing limit.

    This is an intentionally false contract, retained as an open proof obligation.

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    Lean source view on GitHub

    1import Lax755887.LimitDecider
    2
    3/-!
    4---
    5title: Increasing limits of bounded evaluators — unchecked contract
    6type: theorem
    7---
    8Bounded acceptance is computable and increases with fuel. Its union is the halting predicate; computability does not pass to this increasing limit.
    9
    10This is an intentionally false contract, retained as an open proof obligation.
    11-/
    12
    13namespace Lax755887.LimitDeciderContract
    14
    15open Lax755887.LimitDecider
    16
    17open Nat.Partrec (Code)
    18open Nat.Partrec.Code
    19
    20axiom monotone_limit (p : ℕ → Code → Prop)
    21 (step : ∀ n c, p n c → p (n + 1) c)
    22 (deciders : ∀ n, ComputablePred (p n)) : ComputablePred (fun c => ∃ n, p n c)
    23
    24end Lax755887.LimitDeciderContract
    25
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