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### Algorithm = Logic + Control

Declarative programming has a long history yielding languages such as LISP, Prolog and other purer functional and logic programming languages, and of course it underpinned the introduction of relational databases and produced SQL which, for all its faults, is today's most commercially successful declarative programming language.

There has been a recognition that declarative programming has problems with performance and scaleability. One consequence has been a swing back to traditional procedural programming. However, constraint programming, whilst recognising that efficiency is an important issue, retains the underlying declarative approach. The idea is not to abandon declarative programming (that would amount to throwing away the baby with the bathwater), but to augment it with explicit facilities to control evaluation. Hence Kowalski's maxim that Algorithm = Logic + Control.

When constraints are used in an application, both the issues of modelling and performance are considered. An early use of constraints was in the modelling of electrical circuits. Such circuits involve a variety of constraints from simple equations (the current at any two points in a sequential circuit is the same), to linear equations (when a circuit divides, the current flowing in is the sum of the currents flowing out), to quadratic equations (voltage equals current multiplied by resistance) and so on. A constraint solver that can handle all the constraints on a circuit would be prohibitively inefficient. Consequently Sussmann sought to model circuits using only a simple class of constraints. He showed that the lack of expressive power of simple constraints can be compensated for by using multiple orthogonal models of the circuit. The different constraints of the different models interact to produce more information than could be extracted from the models independently.

Mark Wallace
Wed Sep 3 18:36:40 BST 1997