Monadic Maps and Folds for Multirelations in an Allegory

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.