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[Coq-Club] Why are my terms not reducing?


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  • From: Agnishom Chattopadhyay <agnishom AT cmi.ac.in>
  • To: coq-club AT inria.fr
  • Subject: [Coq-Club] Why are my terms not reducing?
  • Date: Wed, 17 Jan 2024 16:40:33 -0600
  • Authentication-results: mail3-smtp-sop.national.inria.fr; spf=None smtp.pra=agnishom AT cmi.ac.in; spf=Pass smtp.mailfrom=agnishom AT cmi.ac.in; spf=None smtp.helo=postmaster AT mail.cmi.ac.in
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Hi Coq-club;

I recently came across the proof pearl titled "Well-founded recursion done right" by Xavier Leroy, and considered applying it to a proof I previously tried to attempt.

I wish to define the function described in this Haskell program, and I have tried three different approaches.

Approach 1(Method1.v) : This uses the mentioned proof-pearl. In this case, the _expression_ refuses to reduce.
Approach 2(Method2.v): Uses the refine tactic and this technique (from Pit-Claudel) to get rid of opaque proofs. Much of this code is thanks to Mukesh Tiwari. However, even in this case, the _expression_ refuses to reduce.
Approach 3(GitHub Issue): Uses the Equations package. This crashes coqtop.

Any ideas on why these refuse to reduce? In Page 2 of the proof-pearl, the author says "Now, the hole [...] is any proof of [...],and it can be opaque.". So, I assume that the error is not due to me providing opaque proofs.

--Agnishom



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