ORDER-SORTED ALGEBRA SOLVES THE CONSTRUCTOR-SELECTOR, MULTIPLE REPRESENTATION AND COERCION PROBLEMS.

Structured data are generally composed from constituent parts by constructors and decomposed by selectors. The authors prove that the usual many-sorted algebra approach to abstract data types cannot capture the simple intuition in a satisfactory way. They also show that order-sorted algebra does solve this problem, and many others concerning ill-defined and erroneous expressions, in a simple and natural way. In particular, they show how order-sorted algebra supports an elegant solution to the problems of multiple representations and coercions. The essence of order-sorted algebra is that sorts have subsorts, whose semantic interpretation is the subset relation on the carriers of algebras.