Container Combinatorics: Monads and Lax Monoidal Functors

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10608)


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.


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© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Department of Software ScienceTallinn University of TechnologyTallinnEstonia

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