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Integration in Cones

Ehrhard, Thomas ; Geoffroy, Guillaume

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Título:
Integration in Cones
Autor: Ehrhard, Thomas ; Geoffroy, Guillaume
Assuntos: Computer Science ; Logic in Computer Science
Descrição: 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 thesecond based on a new notion of integrable analytic function on cones.
Data de criação/publicação: 2022
Idioma: Inglês

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