%0 Conference Proceedings
%T Container Combinatorics: Monads and Lax Monoidal Functors
%+ Tallinn University of Technology (TTÜ)
%A Uustalu, Tarmo
%Z Part 3: Logic, Semantics, and Programming Theory
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 2nd International Conference on Topics in Theoretical Computer Science (TTCS)
%C Tehran, Iran
%Y Mohammad Reza Mousavi
%Y Jiří Sgall
%I Springer International Publishing
%3 Topics in Theoretical Computer Science
%V LNCS-10608
%P 91-105
%8 2017-09-12
%D 2017
%R 10.1007/978-3-319-68953-1_8
%Z Computer Science [cs]Conference papers
%X Abbott et al.’s containers are a “syntax” for a wide class of set functors in terms of shapes and positions. Containers whose “denotation” carries a comonad structure can be characterized as directed containers, or containers where a shape and a position in it determine another shape, intuitively a subshape of this shape rooted by this position. In this paper, we develop similar explicit characterizations for container functors with a monad structure and container functors with a lax monoidal functor structure as well as some variations. We argue that this type of characterizations make a tool, e.g., for enumerating the monad structures or lax monoidal functors that some set functor admits. Such explorations are of interest, e.g., in the semantics of effectful functional programming languages.
%G English
%Z TC 1
%Z WG 1.8
%2 https://inria.hal.science/hal-01760638/document
%2 https://inria.hal.science/hal-01760638/file/440117_1_En_8_Chapter.pdf
%L hal-01760638
%U https://inria.hal.science/hal-01760638
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-WG1-8
%~ IFIP-TTCS
%~ IFIP-LNCS-10608