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arXiv · 1501.02925

Programming and Reasoning with Guarded Recursion for Coinductive Types

Ranald Clouston·Aleš Bizjak·Hans Bugge Grathwohl·Lars Birkedal
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Abstract

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive types may be transformed into coinductive types by a type-former inspired by modal logic and Atkey-McBride clock quantification, allowing the typing of acausal functions. We give a call-by-name operational semantics for the calculus, and define adequate denotational semantics in the topos of trees. The adequacy proof entails that the evaluation of a program always terminates. We demonstrate the expressiveness of the calculus by showing the definability of solutions to Rutten's behavioural differential equations. We introduce a program logic with Löb induction for reasoning about the contextual equivalence of programs.

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Ranald Clouston, Aleš Bizjak, Hans Bugge Grathwohl, Lars Birkedal. 2015-01-15. Programming and Reasoning with Guarded Recursion for Coinductive Types. https://arxiv.org/abs/1501.02925

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