Beating the Productivity Checker Using Embedded Languages

Nils Anders Danielsson
(University of Nottingham)

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.

In Ana Bove, Ekaterina Komendantskaya and Milad Niqui: Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010), Edinburgh, UK, 15th July 2010, Electronic Proceedings in Theoretical Computer Science 43, pp. 29–48.
Published: 21st December 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.43.3 bibtex PDF

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