CafeOBJ is a most advanced formal specification language which inherits many advanced features (e.g. flexible mix-fix syntax,powerful and clear typing system with ordered sorts, parameteric modules and views for instantiating the parameters, and module expressions, etc.) from OBJ (or more exactly OBJ3 ) algebraic specification language.
CafeOBJ is a language for writing formal (i.e. mathematical) specifications of models for wide varieties of software and systems, and verifying properties of them. CafeOBJ implements equational logic by rewriting and can be used as a powerful interactive theorem proving system. Specifiers can write proof scores also in CafeOBJ and doing proofs by executing the proof scores.
CafeOBJ has state-of-art rigorous logical semantics based on institutions. The CafeOBJ cube shows the structure of the various logics underlying the combination of the various paradigms implemented by the language. Proof scores in CafeOBJ are also based on institution based rigorous semantics, and can be constructed using a complete set of proof rules.
See the home page of CafeOBJ for details: http://www.cafeobj.org/