October 17

The semantics of programs written in some languages is concerned with the interpretation in various types of models. We present a new approach to semantics: behavior of programs, i.e. changes of states is modeled in the category of states. Category morphisms express elementary execution steps and program execution is an oriented path in the category, i.e. composition of morphisms. Our categorical model is constructed for a simple procedural language that contains all basic van Dijkstra's constructs. We enrich our approach also with procedures forming a collection of categories interconnected by functors. This method enables the repeated call of procedures, nesting of procedure calls and recursive calls. Moreover, it allows us to illustrate and accentuate dynamics of program execution.