Species, profunctors and Taylor expansion weighted by SMCC: a unified framework for modelling nondeterministic, probabilistic and quantum programs

Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show...

Повний опис

Бібліографічні деталі
Автори: Tsukada, T, Asada, K, Ong, C
Формат: Conference item
Опубліковано: Association for Computing Machinery 2018
Опис
Резюме:Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show that the category of W-weighted profunctors is a Lafont category, a categorical model of linear logic with exponential. As a model of programming languages, the construction of this paper gives a unified framework that induces adequate models of nondeterministic, probabilistic, algebraic and quantum programming languages by an appropriate choice of the weight SMCC.