Section: New Results
Exp-log normal form of types and the axioms for -equality of the -calculus with sums
Participant : Danko Ilik.
In the presence of sum types, the -calculus has but one implemented (and incomplete) heuristic for deciding -equality of terms, in spite of a dozen of meta-theoretic works showing that the equality is decidable.
In the work discussed here, we first used the exp-log decomposition of the arrow type—inspired from the analytic transformation —to obtain a type normal form for the type languages . We then made a quotient of the -equality of terms modulo the terms coerced into their representation at the exp-log normal form of their type. This allows to obtain a simplification of the so far standard axioms for -equality.
Moreover, we provided a Coq implementation of a heuristic decision procedure for this equality. Although a heuristic, this implementation manages to tackle examples of equal terms that need a complex program analysis in the only previously implemented heuristic of Vincent Balat.
This work is described in a paper accepted for presentation at POPL 2017, .