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Add alpha equivalence #12
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This PR contributes two flavours of$\alpha$ -equivalence for foil terms:
alphaEquivRefreshed
) First approach is to compare terms after normalizing the binders by renaming each binder to the minimum possible one in the current scope (note that non-minimal binders may occur during substitution).alphaEquiv
) Second approach is to compare terms directly and only rename binders when they disagree. Moreover, renaming only happens for one of the terms (the one with a bigger binder). This relies on a new function added to the foil, calledunifyNameBinders
, as well asliftRM
, a relative analogue ofliftM
, instead of usingsubstitute
.The second approach is the cleaned up (yet at the moment less efficient due to
liftRM
) version ofunsafeAeq
that we have used in the benchmarks: https://github.com/KarinaTyulebaeva/lambda-n-ways/blob/09a995f9644f6bf29db1803eef004ddd382b823d/lib/FreeScoped/Foil.hs#L336-L401What remains in this PR:
Language.LambdaPi.Impl.Foil
.Language.LambdaPi.Impl.FoilTH
.Language.LambdaPi.Impl.FreeFoil
.