This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. Then we focus on the actual logical foundations of the language at two different levels: basic specification and structured specification, including also the definition of the CafeOBJ institution. We survey some novel or more classical theoretical concepts supporting the logical foundations of CafeOBJ together with pointing to the main results but without giving proofs and without discussing all mathematical details. Novel theoretical concepts include the coherent hidden algebra formalism and its combination with rewriting logic, and Grothendieck (or fibred) institutions. However for proofs and for some of the mathematical details not discussed here we give pointers to relevant publications. ...

CafeOBJ is an executable industrial strength multi-logic algebraic speci cation language which is a modern successor of OBJ and incorporates several new algebraic speci cation paradigms.

This paper gives an overview of the main features and methodologies of CafeOBJ by means of a collection of elegant examples. Therefore, this paper may also serve as a tutorial introduction to CafeOBJ. We hope that besides the strength of CafeOBJ, the reader will also appreciate the beauty of this language.

this paper, we present techniques for composing specification components which enables to represent patterns of system architectures such as client-server computing, multicasting, etc. Our object composition technique enables to reuse not only component specifications but also the verification proofs of them.