--experimental-lossy-unification enables an
experimental heuristic in the unification checker intended to improve
its performance for unification problems of the form
f es₀ = f es₁,
i.e. unifying two applications of the same defined function, here
f, to possibly different lists of arguments and projections
The heuristic is sound but not complete.
In particular if Agda accepts code with the flag enabled it should
also accept it without the flag (with enough resources, and possibly
needing extra type annotations).
The option can be used either globally or in an
OPTIONS pragma, in the latter
case it applies only to the current module.
When trying to solve the unification problem
f es₀ = f es₁ the
heuristic proceeds by trying to solve
es₀ = es₁, if that succeeds
the original problem is also solved, otherwise unification proceeds as
without the flag, likely by reducing both
f es₀ and
100 to its input as defined below
f : ℕ → ℕ f n = 100 + n
then to unify
f 2 and
f (1 + 1) the heuristic would proceed by
(1 + 1), which quickly succeeds. Without the
flag we might instead first reduce both
f 2 and
f (1 + 1) to
102 and then compare those results.
The performance will improve most dramatically when reducing an
f would produce a large term, perhaps an element of
a record type with several fields and/or large embedded proof terms.
The main drawback is that the heursitic is not complete, i.e. it will cause Agda to
ignore some possible solutions to unification variables.
For example if
f is a constant function, then the constraint
?0 = f 1 does not uniquely determine
?0, but the heuristic will
end up assigning
Such assignments can lead to Agda to report a type error which would
not have been reported without the heuristic. This is because committing to
?0 = 1 might make other constraints unsatifiable.
The other drawback is that in some cases performance of
unification will be worse with the heuristic. Specifically, if
the heuristic will repeatedly attempt to unify lists of arguments
= es₁ while failing.