Abstract

We present a programming paradigm based upon the notion of binary relations as programs, and partial equivalence relations (pers) as types. Our method is calculational , in that programs are derived from specifications by algebraic manipulation. Working with relations as programs generalises the functional paradigm, admiting non--determinism and the use of relation converse. Working with pers as types, we have a more general notion than normal of what constitutes an element of a type; this leads to a more general class of functional relations, the so--called difunctional relations. Our basic method of defining types is to take the fixpoint of a relator , a simple strengthening of the categorical notion of a functor. Further new types can be made by imposing laws and restrictions on the constructors of other types. Having pers as types is fundamental to our treatment of types with laws. Contents 1 Introduction 2 2 Relational calculus 4 2.1 Powerset lattice structure : : : : : : : : :...

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