:test whether bsimp(bders(r, s)) == ders_simp(r,s) This does not hold. As illustrated by the output of the example where string is abaa and regex is (a* + ab)* this property still holds when s = aba but after the derivative of the last character a, the result is negative. However this seems easily fixable as the difference is relatively small, it might be possible to find where the difference happens and by taking that difference into accound we have some function f s.t. f(bsimp(r,s)) = ders_simp(r,s) and mkeps(f(r)) = mkeps(r) This will complete the correctness proof. Even if finding such f is hard, it would still provide insights for the real difference between simp(der(simp(der(simp(der...... and simp(ders

removing PRED why should it still be there after so many rounds of experiments? It should have been removed long ago since its existence will always make the compiler report errors. mysterious.: