A Logical Framework to Prove Properties of Alpha Programs
Résumé
We present an assertional approach to prove properties of Alpha programs. Alpha is a functional language based on affine recurrence equations. We first present two kinds of operational semantics for Alpha together with some equivalence andconfluence properties of these semantics. We then present an attempt to provide Alpha with an external logical framework. We therefore define a proof method based on invariants. We focus on a particular class of invariants, namely canonical invariants, that are a logical expression of the program's semantics. We finally show that this framework is well-suited to prove equivalence properties between Alpha programs.