The Church–Rosser theorem guarantees that the final resul... — Carmelics

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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

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Reasons For

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Reason for

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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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Reasons Against

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Reason against 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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