Coalgebraic Operational Semantics for an Imperative Language

Abstract

Operational semantics is a known and popular semantic method for describing the execution of programs in detail. The traditional definition of this method defines each step of a program as a transition relation. We present a new approach on how to define operational semantics as a coalgebra over a category of configurations. Our approach enables us to deal with a program that is written in a small but real imperative language containing also the common program constructs as input and output statements, and declarations. A coalgebra enables to define operational semantics in a uniform way and it describes the behavior of the programs. The state space of our coalgebra consists of the configurations modeling the actual states; the morphisms in a base category of the coalgebra are the functions defining particular steps during the program's executions. Polynomial endofunctor determines this type of systems. Another advantage of our approach is its easy implementation and graphical representation, which we illustrate on a simple program.

Visualization of Formal Semantics - Possibilities of Attracting Formal Methods in Teaching

“…Categories have a strong expressive ability and allow to model relationships between mathematical structures in a very elegant way. The software tool we presented in this work allows us to visualize and model the coalgebraic operational semantics defined in [20].…”

The visualization of a graph semantics of imperative languages

“…An environment that expresses the context dependencies known from operational semantics (Plotkin, 2004) is now a part of category objects and is given by the level of nesting. Hence each state is represented as a function, that assigns to a variable on a given level of nesting its value (Steingartner et al, 2019). These states are objects in the category of states.…”

“…As a modeling language, we present a simple imperative language named Jane. The language Jane (Steingartner et al, 2019) is an abstract language embodying a tiny core fragment of conventional mainstream languages such as C and Java. We note that this concept of abstract imperative language is well-known and is also mentioned as language While or IMP, presented e.g., in (Nielson and Nielson, 2007;Roșu and Șerbănută, 2010).…”

Δrle

“…Some are discarded after they are created, transferred, and used, but a large portion is subsequently archived, extending the total amount of data currently included in ICT. The data transfer itself represents a significant burden for ICT, so we are looking for ways how to model, optimize and minimize it [1] [2]. A large amount of data exists in multiple copies -in uncompressed or compressed forms.…”