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 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
ACM
02.08.2020
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| Subjects: | |
| ISSN: | 2475-1421, 2475-1421 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 2475-1421 2475-1421 |
| DOI: | 10.1145/3409001 |