Add correctness of the term creators in SMT/Factory.lean#1103
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joscoh
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Haven't gone through it all yet but I'd love to know your thoughts on whether the theorem conclusions should be existentially quantified or direct.
… switch to a simple equality version
tautschnig
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I like how nice the theorem statements turn out!
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(Creating a new pull request because for some reason pushing to a branch didn't update #1088)
This proves that the term creators in SMT (which are also called 'Factory') are sound with respect to the denotational semantics. Initially the patch was defining a cleaner inductive predicate
DenotePredthat is analogous todenoteTermbut avoids carrying data structures that are necessary to construct the Lean goals.However, this turned out to introduce a big amount of boilerplate code because soundness/completeness of
DenotePredw.r.t.denoteTermturned out to be very big proofs.Instead, this pull request directly uses the
denoteTermand its family functions to state & prove correctnesses.There is one operation in Factory.lean which could not be proven:
quant. Thequantoperation does the following simplification:forall x, forall y, e==>forall x y, e. Proving this was hard because the result ofdenoteTermisTermDenoteResult ctxwhich is a dependent type (ctx : Context)... And rewriting the dependent type position was challenging.By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.