Some aspects about coalgebras as foundation for expressing the semantics of imperative languages

Abstract

Copyright by the paper’s authors. The semantics of programs written in some languages is concerned with the interpretation in various types of models. Denotational semantics expresses the meaning of programs by functions from syntactical domains to semantic domains which can be non-trivial mathematical structures. On the other hand, structural operational semantics describes the program behaviour in the form of states’ changes caused by the execution of elementary steps. We present in this paper categorical representation of denotational semantics in category of states as objects and semantic functions as morphisms. We present also categorical representation of structural operational semantics in category as a transition system where states are objects and morphisms are elementary transitions. We also sketch how to define endofunctor on the category of states and how to construct a Q-coalgebra of the functor.