Tropical Mathematics and the Lambda-Calculus I: Metric and Differential Analysis of Effectful Programs
Résumé
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program metrics, based on the analysis of program sensitivity via Lipschitz conditions, on the other hand resource analysis, based on linear logic and higher-order program differentiation. To do that, we focus on the semantics arising from the relational model weighted over the tropical semiring, and we discuss its application to the study of "best case" program behavior for languages with probabilistic and non-deterministic effects. Finally, we show that a general foundation for this approach is provided by an abstract correspondence between tropical algebra and Lawvere's theory of generalized metric spaces.
Mots clés
Relational semantics
Differential lambda-calculus
Tropical semiring
Program metrics
Lawvere quantale
Theory of computation → Lambda calculus
Theory of computation → Categorical semantics
Theory of computation → Linear logic
2012 ACM Subject Classification Theory of computation Ñ Lambda calculus Theory of computation Ñ Categorical semantics Theory of computation Ñ Linear logic Relational semantics
Lawvere quantale Digital Object Identifier 10.4230/LIPIcs.CSL.2024.14
2012 ACM Subject Classification Theory of computation Ñ Lambda calculus
Theory of computation Ñ Categorical semantics
Theory of computation Ñ Linear logic Relational semantics
Domaines
Informatique [cs]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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