Static semantic analysis and theorem proving for CASL

This paper presents a static semantic analysis for CASL, the Common Algebraic Speciication Language. Abstract syntax trees are generated including subsorts and overloaded functions and predicates. The static semantic analysis, through the implementation of an overload resolution algorithm, checks and qualiies these abstract syntax trees. The result is a fully qualiied CASL abstract syntax tree where the overloading has been resolved. This abstract syntax tree corresponds to a theory in the institution underlying CASL, subsorted partial rst-order logic with sort generation constraints (SubPCFOL). Two ways of embedding SubPCFOL in higher-order logic (HOL) of the logical framework Isabelle are discussed: the rst one from SubPFOL to HOL via PFOL (partial rst-order logic) rst drops subsorting and then partiality, and the second one is the counterpart via SubFOL (sub-sorted rst-order logic). The C in SubPCFOL stands for sort generation constraints, which are translated separately. Finally, we sketch an integration of the embedding of CASL into the UniForM Workbench.