Beating the Productivity Checker Using Embedded Languages

TL;DR

This paper presents a method to transform productive programs that are not guarded into guarded programs by defining a problem-specific language and creating a guarded interpreter, enhancing the usability of guarded corecursion.

Contribution

It introduces a novel approach to convert non-guarded productive programs into guarded ones using a problem-specific language and interpreter.

Findings

Enables non-guarded productive programs to be guarded.

Provides a systematic method for program transformation.

Improves the applicability of guarded corecursion techniques.

Abstract

Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by a coinductive constructor. Guardedness ensures that programs are productive, i.e. that every finite prefix of an infinite value can be computed in finite time. However, many productive programs are not guarded, and it can be nontrivial to put them in guarded form. This paper gives a method for turning a productive program into a guarded program. The method amounts to defining a problem-specific language as a data type, writing the program in the problem-specific language, and writing a guarded interpreter for this language.