Monadic maps and folds for multirelations in an allegory

Authors:
Clare E. Martin;Sharon A. Curtis
Affiliations:
Oxford Brookes University, UK;Oxford Brookes University, UK
Venue:
UTP'08 Proceedings of the 2nd international conference on Unifying theories of programming
Year:
2008

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Abstract

This paper contributes to the unification of semantic models and program development techniques by making a link from multirelations and predicate transformer semantics to algebraic semantics and the derivation of programs by calculation, as used in functional programming and relational program development. Two common ways to characterise iteration, namely the functional programming operators map and fold, are extended to multirelations, using concepts from category theory, power allegories and monads.