perf: better isDefEq cache in the presence of metavariables #8883
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This PR fixes the problem that unification in the presence of metavariables is often exponentially slow. This comes up every now and then in mathlib, and could get worse as mathlib continues to grow. This is implemented by handling the
defEqTranscache more carefully: we keep the cache as long as no metavariables are assigned.To know when to invalidate the cache, we keep track of the number of assignments inside of a
MetavarContext. We also store this number inCache.defEqTrans, so if this number doesn't match the number in the currentMetavarContext, we invalidate the cache. We also revert the transient cache incheckpointDefEqwhen needed (instead of emptying it).Alternatively, to identify if the
MetavarContexthas progressed, it would be possible to define and usePersistentHashMap.sizeto find the number of assignments in theMetavarContext, but I didn't go for this option.For this to work, in unification we need to wrap a
checkpointDefEqaround each branch that is backtracked on if it returnsfalse. This was already meant to be like this, but some of these checkpoints were missing. In particular the addition in line 1932 (checkpointDefEq (isDefEqProjDelta t s i)) was needed to build mathlib. I added it in other places where I deemed this necessary.The test file shows some examples improved by this fix.
The mathilb speedup from the fix is:
buildlintOnly one proof in mathlib had to be fixed. That particular failure was a unification that I think should not have been expected to work, and the fix was just a small change.
Zulip#lean4 > Exponential blowup in unification with metavariables @ 💬