The Size-Change Principle for Mixed Inductive and Coinductive types

TL;DR

This paper adapts the size-change principle to verify totality in recursive functions involving mixed inductive and coinductive types, ensuring correctness in languages like ML and Haskell.

Contribution

It introduces a novel adaptation of the size-change principle to handle nested inductive and coinductive types for totality checking.

Findings

The adapted size-change principle correctly verifies totality in mixed types.

Naive application of the size-change principle is unsound for nested types.

The method ensures correctness with respect to (co)inductive 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.