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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| Veröffentlicht in: | Logical methods in computer science Jg. 12, Issue 3 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Logical Methods in Computer Science e.V
01.01.2016
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| ISSN: | 1860-5974, 1860-5974 |
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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 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Grathwohl, Hans Bugge Clouston, Ranald Birkedal, Lars Bizjak, Aleš |
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| Snippet | We present the guarded lambda-calculus, an extension of the simply typed
lambda-calculus with guarded recursive and coinductive types. The use of
guarded... We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded... |
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| Title | The Guarded Lambda-Calculus: Programming and Reasoning with Guarded Recursion for Coinductive Types |
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