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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The claim that the Church–Rosser theorem guarantees a unique final result is a slight overstatement

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Uniqueness of a final result implies termination of every reduction sequence
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    • 2.The Church–Rosser theorem does not itself guarantee termination—a term may diverge rather than reach a normal form
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The Church–Rosser property guarantees confluence: if a term has a normal form, that normal form is unique.
      ?

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    • 2.Guaranteeing uniqueness only under the condition of existence is logically weaker than guaranteeing a unique final result simpliciter.
      ?

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    • 3.Conflating conditional uniqueness with unconditional uniqueness is a semantic overstatement, as Barendregt's lambda calculus treatment explicitly distinguishes these properties.
      ?

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    Reason against 2 of 2
    ?
    • 1.In proof-theoretic semantics, a 'result' presupposes termination; Church–Rosser is silent on whether reduction terminates for arbitrary terms.
      ?

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    • 2.Curry and Feys's original combinatory logic literature treats normalization and confluence as independent properties requiring separate proofs.
      ?

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    • 3.Describing Church–Rosser as guaranteeing a 'unique final result' elides this independence, making the claim a genuine overstatement rather than mere imprecision.
      ?

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