The Undecidability of Pattern Matching in Calculi where Primitive Recursive Functions are Representable

Gilles Dowek

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arXiv · 2306.05876

The Undecidability of Pattern Matching in Calculi where Primitive Recursive Functions are Representable

Gilles Dowek

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Abstract

We prove that the pattern matching problem is undecidable in polymorphic lambda-calculi (as Girard's system F) and calculi supporting inductive types (as G{\"o}del's system T) by reducing Hilbert's tenth problem to it. More generally pattern matching is undecidable in all the calculi in which primitive recursive functions can be fairly represented in a precised sense.

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Gilles Dowek. 2023-06-09. The Undecidability of Pattern Matching in Calculi where Primitive Recursive Functions are Representable. https://arxiv.org/abs/2306.05876

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