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Coq is a formal proof management system, also called an interactive theorem prover. It is used to express mathematical assertions, mechanically check proofs of these assertions, find formal proofs, and extract certified programs.

17 votes

Function extensionality: does it make a difference? why would one keep it out of the axioms?

You will lose canonicity, which is - mathematically - not that much of a problem, but when you want to extract programs, you want it. The problem is that not every proof of equality reduces to reflexi …
Christoph-Simon Senjak's user avatar