Abstract : 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.
https://hal.inria.fr/hal-01760638 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Friday, April 6, 2018 - 3:07:57 PM Last modification on : Friday, April 6, 2018 - 3:08:59 PM