English

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

Logic in Computer Science 2023-06-12 v1

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.

Keywords

Cite

@article{arxiv.2306.05876,
  title  = {The Undecidability of Pattern Matching in Calculi where Primitive Recursive Functions are Representable},
  author = {Gilles Dowek},
  journal= {arXiv preprint arXiv:2306.05876},
  year   = {2023}
}