Abstract

The notion of functionality is not cast in stone, but depends upon what we have as types in our language. With partial equivalence relations (pers) as types we show that the functional relations are precisely those satisfying the simple equation f = f ffi f [ ffi f , where " [ " is the relation converse operator. This article forms part of "A calculational theory of pers as types" [1]. 1 Introduction In calculational programming, programs are derived from specifications by a process of algebraic manipulation. Perhaps the best known calculational paradigm is the Bird--Meertens formalism, or to use its more colloquial name, Squiggol [2]. Programs in the Squiggol style work upon trees, lists, bags and sets, the so--called Boom hierarchy. The framework was uniformly extended to cover arbitrary recursive types by Malcolm in [3], by means of the F--algebra paradigm of type definition, and resulting catamorphic programming style. More recently, Backhouse et al [4] have made a further ...

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