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Is there a formalization in Isabelle/HOL of the strong normalization property of the simply typed lambda-calculus with pairs?

I am aware of the development in ~~/src/HOL/Proofs/Lambda/StrongNorm.thy, but that one does not support pairs. (Terms only consist of abstractions, applications, and variables.)

To be specific, by "pairs" I mean that the language should contain constructs such as Pair x y, Fst x, Snd x. And I do not need dependent pairs.

Background: The problem came up as part of a larger development where I need strong normalization of a more complex calculus which can, however, be reduced to the strong normalization of the simply typed lambda calculus with pairs by a suitable embedding.

Dominique Unruh
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  • A development in another proof assistant (Coq, HOL-light, etc.) might be helpful, too, as a basis for porting it to Isabelle/HOL. – Dominique Unruh May 28 '15 at 14:07
  • I hope you have found a solution in the mean time, but in any case, here is a Coq development proving strong normalization of the simply-typed lambda calculus with pairs: https://www.cis.upenn.edu/~bcpierce/sf/current/Norm.html – Isabelle Newbie Oct 15 '15 at 20:31
  • Thanks. But the problem with that development is: (a) It leaves out all the steps related to pairs. (b) It uses the fact that its lambda-calculus uses a deterministic evaluation strategy ("Note that in the forward direction the proof depends on the fact that our language is determinstic. This lemma might still be true for non-deterministic languages, but the proof would be harder!") – Dominique Unruh Oct 17 '15 at 13:39

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