Stable relations and abstract interpretation of higher-order programs

We present a novel denotational semantics for the untyped call-by-value λ-calculus, where terms are interpreted as stable relations , i.e. as binary relations between substitutions and values, enjoying a monotonicity property. The denotation captures the input-output behaviour of higher-order progra...

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Published in:Proceedings of ACM on programming languages Vol. 4; no. ICFP; pp. 1 - 30
Main Authors: Montagu, Benoît, Jensen, Thomas
Format: Journal Article
Language:English
Published: ACM 02.08.2020
Subjects:
Computer Science
Programming Languages
ISSN:2475-1421, 2475-1421
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Abstract We present a novel denotational semantics for the untyped call-by-value λ-calculus, where terms are interpreted as stable relations , i.e. as binary relations between substitutions and values, enjoying a monotonicity property. The denotation captures the input-output behaviour of higher-order programs, and is proved sound and complete with respect to the operational semantics. The definition also admits a presentation as a program logic. Following the principles of abstract interpretation, we use our denotational semantics as a collecting semantics to derive a modular relational analysis for higher-order programs. The analysis infers equalities between the arguments of a program and its result—a form of frame condition for functional programs.
AbstractList We present a novel denotational semantics for the untyped call-by-value λ-calculus, where terms are interpreted as stable relations , i.e. as binary relations between substitutions and values, enjoying a monotonicity property. The denotation captures the input-output behaviour of higher-order programs, and is proved sound and complete with respect to the operational semantics. The definition also admits a presentation as a program logic. Following the principles of abstract interpretation, we use our denotational semantics as a collecting semantics to derive a modular relational analysis for higher-order programs. The analysis infers equalities between the arguments of a program and its result—a form of frame condition for functional programs.
Author Jensen, Thomas
Montagu, Benoît
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Snippet We present a novel denotational semantics for the untyped call-by-value λ-calculus, where terms are interpreted as stable relations , i.e. as binary relations...
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Title Stable relations and abstract interpretation of higher-order programs
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