STAE TOULOUSE

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Distributive laws of directed containers

Le 1er juin 2012, Conférence.

Le 12 juin 2012

Tarmo Uustalu de l'Institut de Cybernétique de l'Université technique de Tallinn visite l'équipe ACADIE du 12 au 15 juin dans le cadre d'un accord de partenariat Hubert Curien avec l'Estonie.

Celui-ci donnera un séminaire pour le chantier IFSE du RTRA STAE

le mardi 12 juin à 14 heures,
dans la salle 175 du bâtiment IRIT2 sur le site UPS.

Containers are an elegant representation of a wide class of datatypes in terms of positions and shapes. We have recently introduced directed containers as a special case to account for the common situation where every position in a shape determines another shape, informally the subshape rooted by that position. While containers interpret into set functors via a fully faithful functor, directed containers denote comonads fully faithfully. In fact, directed containers correspond to exactly those containers that carry a comonad structure. Directed containers can be seen as a generalization (a dependently typed version) of monoids.

While the category of containers (just as the category of set functors) carries a composition monoidal structure, directed containers (just as comonads) do not generally compose. In this talk, I develop a concept of a distributive law between two directed containers matching that of a distributive law between two comonads and spell out the distributive-law based composition construction of directed containers. This turns out to generalize the Zappa-Szép product of two monoids.

This is joint work with Danel Ahman.

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