This paper presents a reflection about function construction through well-founded recursion in the type theory known as Calculus of Inductive Constructions. It shows the expressive power of this calculus when dealing with concepts as accesibility and noetherianity among others. The properties of the General Recursion Scheme ([2]) and its relation with Structural Recursion in inductive types are analyzed. As a consequence, a methodology arises which is illustrated with some examples.We use the INRIA's compiler of the Calculus of Inductive Constructions: Coq[6].
['José Luis Freire', 'Enrique Xavier Garcés Freire', 'Antonio Martínez Blanco']
On recursive functions and well-founded relations in the calculus of constructions