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I'm not talking about proving theorems. I'm talking about creating axioms and creating primitives from axioms.

For that any programming language can do it.




You are using the word Axiom in a non-standard way.

Can you give an example of how you would state an Axiom in Haskell? Here is an example of how it is done in LEAN:

axiom propext {a b : Prop} : (a <-> b) → a = b

It declares Propositional Extensionality to be true with no evidence/proof.




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