Categorical semantics of programming languages
William Steingartner, Valerie Novitzká · Publishing Office of Czestochowa University of Technology eBooks · 2017
Computer science uses still more formal models to aid the understanding of complex software systems and to reason about their behavior, in particular to verify the correctness of a system or at least some desired aspects of its behavior with respect to a formal specification.All these techniques are grounded in formal models of system execution which are themselves rooted in the formal semantics of the underlying programming languages.Denotational semantics expresses the meaning of programs by functions from syntactical domains to semantic domains which can be non-trivial mathematical structures.We present in this document representation of denotational semanitcs based on category theory.We consider memory states as objects of category and semantic functions as morphisms.Category is then a model and semantics of a program written in our language Jane is modeled in this category as a path, i.e. a composition of morphisms.