Inductive, coinductive, and pointed types

Abstract

An extension of the simply-typed lambda calculus is presented which contains both well-structured inductive and coinductive types, and which also identifies a class of types for which general recursion is possible. The motivations for this work are certain natural constructions in category theory, in particular the notion of an algebraically bounded functor, due to Freyd. We propose that this is a particularly elegant core language in which to work with recursive objects, since the potential for general recursion is contained in a single operator which interacts well with the facilities for bounded iteration and coiteration.