Sketches and computation – II: dynamic evaluation and applications

Abstract

In the first part of this paper (Duval and Reynaud 1994), we defined a categorical framework, based on the notion of sketch, for specification and evaluation in the senses of algebraic specifications and algebraic programming. Static evaluation in quasi-projective sketches was defined in Part I; in this paper, dynamic evaluation is introduced. It deals with more general structures, which may have no initial model. Until now, this process has not been used in algebraic specification systems, but computer algebra systems are beginning to use it as a basic tool. Finally, we give some applications of dynamic evaluation to computation in field extensions.