Type-Based Termination, Inflationary Fixed-Points, and Mixed Inductive-Coinductive Types

TL;DR

This paper introduces a novel type system based on inflationary fixed-points that guarantees termination and productivity of programs, with a prototype implementation demonstrating its effectiveness for corecursive and mixed recursive-corecursive functions.

Contribution

It presents a new type system utilizing inflationary iteration for termination and productivity guarantees, advancing the theoretical foundation and practical certification methods.

Findings

Proposes a type system based on inflationary fixed-points.

Demonstrates certification of productivity in corecursive functions.

Provides a prototype implementation, MiniAgda.

Abstract

Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away. Termination and productivity are non-trivial yet desired program properties, and several type systems have been put forward that guarantee termination, compositionally. These type systems are intimately connected to the definition of least and greatest fixed-points by ordinal iteration. While most type systems use conventional iteration, we consider inflationary iteration in this article. We demonstrate how this leads to a more principled type system, with recursion based on well-founded induction. The type system has a prototypical implementation, MiniAgda, and we show in particular how it certifies productivity of corecursive and mixed recursive-corecursive functions.