Making Functionality More General

The definition for the notion of a "function" is not cast in stone, but depends upon what we adopt as types in our language. With partial equivalence relations (pers) as types in a relational language, we show that the functional relations are precisely those satisfying the simple equation f = f o fu o f, where "o" and "u" are respectively the composition and converse operators for relations. This article forms part of "A calculational theory of pers as types".

Functional Programming With Relations

While programming in a relational framework has much to offer over the functional style in terms of expressiveness, computing with relations is less efficient, and more semantically troublesome. In this paper we propose a novel blend of the functional and relational styles. We identify a class of "causal relations", which inherit some of the bi-directionality properties of relations, but retain the efficiency and semantic foundations of the functional style.

A Relational Derivation of a Functional Program

This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard $quot;column of half-adders$quot;, but the derivation illustrates a number of points about working with relations rather than with functions.