The Size-Change Principle for Mixed Inductive and Coinductive types

Abstract

This paper shows how to use Lee, Jones and Ben Amram's size-change principle to check correctness of arbitrary recursive definitions in an ML / Haskell like programming language with inductive and coinductive types. Naively using the size-change principle to check productivity and termination is straightforward but unsound when inductive and coinductive types are nested. We can however adapt the size-change principle to check ``totality'', which corresponds exactly to correctness with respect to the corresponding (co)inductive type.