  That the Haskell Compiler GHC is capable of proving non-trivial equalities
between Haskell code, by virtue of its aggressive optimizer, in particular the
term rewriting engine in the simplifier. We demonstrate this with a surprising
little code in a GHC plugin, explains the knobs we had to turn, discuss the
limits of the approach and related applications of the same idea, namely
testing that promises from Haskell libraries with domain-specific optimizations
hold.
