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

Conference item

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.

Authors: Tsukada, T; Asada, K; Ong, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Association for Computing Machinery
• Host title: LICS '18 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
• Journal: Thirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• Pages: 889-898
• Publication date: 2018-07-09
• Acceptance date: 2018-04-03
• DOI: 10.1145/3209108.3209157
• ISBN: 9781450355834
• Keywords: rigid resource calculus; quantitative model; weighted species; generalised species; quantum computation