Article Dans Une Revue Logical Methods in Computer Science Année : 2025

Integration in Cones

Résumé

Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates ``continuous data types'' such as the real line. So far however, they lacked a major feature to make them a model of more general probabilistic programming languages (notably call-by-value and call-by-push-value languages): a theory of integration for functions whose codomain is a cone, which is the key ingredient for interpreting the sampling programming primitives. The goal of this paper is to develop such a theory: our definition of integrals is an adaptation to cones of Pettis integrals in topological vector spaces. We prove that such integrable cones, with integral-preserving linear maps as morphisms, form a model of Linear Logic for which we develop two exponential comonads: the first based on a notion of stable functions introduced in earlier work and the second based on a new notion of integrable analytic function on cones.

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Dates et versions

hal-03883861 , version 1 (04-12-2022)
hal-03883861 , version 2 (08-01-2023)
hal-03883861 , version 3 (12-03-2024)
hal-03883861 , version 4 (24-09-2024)

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Thomas Ehrhard, Guillaume Geoffroy. Integration in Cones. Logical Methods in Computer Science, 2025, 21 (1). ⟨hal-03883861v4⟩
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