The Guarded Lambda-Calculus: Programming and Reasoning with Guarded Recursion for Coinductive Types
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-forme...
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| Vydáno v: | Logical methods in computer science Ročník 12, Issue 3 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
01.01.2016
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| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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 introduce a program logic with L\"ob induction for
reasoning about the contextual equivalence of programs. We demonstrate the
expressiveness of the calculus by showing the definability of solutions to
Rutten's behavioural differential equations. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.2168/LMCS-12(3:7)2016 |