Keeping sums under control
Résumé
This paper presents a normalization tool for the \l-calculus with sum types, based on the technique of normalization by evaluation, and more precisely techniques developed by Olivier Danvy for partial evaluation, using control operators. The main characteristic of this work is that it produces a result in a canonical form. That is to say: two beta-eta-equivalent terms will be normalized into (almost) identical terms. It was not the case with the usual algorithm, which could even lead to an explosion of the size of code. This canonical form is an eta-long beta-normal form with constraints, which captures the definition of eta-long normal form for the lambda-calculus without sums, and reduces drastically the \e-conversion possibilities for sums. We will show how this normalizer helped us to solve a problem of characterization of type isomorphisms.