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    Home/Original/inverse
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    Inverse View

    It is not the case that The Church–Rosser theorem guarantees that the final result of a series of reductions on a term is unique, independently of the order of reduction steps

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Confluence guarantees uniqueness of normal forms when they exist, but does not guarantee that any normal form exists at all for a given term.
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    • 2.Wittgenstein's rule-following considerations (Philosophical Investigations §201) suggest that the determinacy of a computational rule's outcome cannot be read off the rule itself without presupposing a practice of application.
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    • 3.The theorem's guarantee of uniqueness is therefore conditional on facts about termination that are undecidable in general, undermining any unconditional epistemic confidence in unique results.
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    Reason for 2 of 2
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    • 1.The Church–Rosser theorem applies only to normalizing terms; non-terminating reductions (like Ω = (λx.xx)(λx.xx)) have no unique normal form.
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    • 2.A theorem that guarantees uniqueness only when reduction terminates cannot ground a general claim about uniqueness 'independently of reduction order'.
      ?

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    Reasons Against

    1 perspective
    Reason against
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    • 1.Reduction can be modeled as computing the value of a function
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    • 2.The Church–Rosser theorem states that reduction results are confluent—different reduction paths lead to the same normal form
      ?

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