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arXiv · 1511.09394

Proof Relevant Corecursive Resolution

Peng Fu·Ekaterina Komendantskaya·Tom Schrijvers·Andrew Pond
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Abstract

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the role of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on non-terminating type class resolution problems.

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Peng Fu, Ekaterina Komendantskaya, Tom Schrijvers, Andrew Pond. 2015-11-30. Proof Relevant Corecursive Resolution. https://arxiv.org/abs/1511.09394

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