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Distributive Laws in Programming Structures

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If you have a question about this talk, please contact Paul Levy.

Generalised Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse formal approaches. However, the lack of a formal notion of distributive laws in their full generality has been to date hindering their further development.

In this talk, an approach to formalisation of distributive laws will be presented based on the functorial approach to formal Category Theory pioneered by Lawvere and others, notably Gray. The proposed formalism, based on lax 2-naturality and Gray’s tensor product, discloses a rather simple nature of distributive laws of the kind found in programming structures. General notions of products, coproducts and composition of distributive laws will be presented and conditions for their construction given.

The presentation will be geometrical as much as possible making use of the wonderful three-dimensional nature of 2-categories.

This talk is part of the Theoretical computer science seminar series.

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