Fusion in Coq

Abstract

Fusion theorem is a classical result that allows the simplification of the morphisms among homogeneus structures [10]. We present this theorem and some generalizations in the context of the constructive proof assistant tool Coq [2] where we have dependent types and parametric polymorphism. The work is organised as follows: afther the classical interpretation of the fusion law for catamorphisms in a categoric context, examples of fusion for programs defined with recursive types in Coq are analysed and the theorems of corresponding optimisation are shown. Finally, a generalisation of fusion law for inductive types is presented which is applied to a specific case. © 2011 Springer-Verlag Berlin Heidelberg.