As the first of two methodological devices aimed at increasing the trust in the `correctness' of a specification, we develop a calculus for proving consistency of Casl specifications. It turns out to be possible to delegate large parts of the proof load to syntactical criteria by structuring consistency proofs along the given specification structure, so that only in rather few remaining focus points, actual theorem proving is required. The practical usability of the resulting calculus is demonstrated by extensive examples taken from the Casl library of basic data types.

syntax for higher-order functors (additions and changes) I 2 Int = FunIntEnv \Theta StrIntEnv \Theta Fin(var) SIE 2 StrIntEnv = strid fin ! Int FIE 2 FunIntEnv = funid fin ! Int IB 2 IntBasis = FunIntEnv \Theta SigEnv \Theta StrIntEnv ME 2 ModEnv = FunEnv \Theta ModStrEnv \Theta VarEnv MSE 2 ModStrEnv = strid fin ! ModEnv B 2 Basis = SigEnv \Theta ModEnv FIGURE 5. Semantic objects for higher-order functors (additions and changes) thinning functors. The nature of this information is discussed at length later. Interface Bases (IntBasis) These now have a new component: a functor interface environment. Module-level environments (ModEnv) These are the environments obtained as the result of evaluating structures. Since structures can contain functors, these environments contain a functor environment (FunEnv) component. In the rest of this paper we will refer to these objects as "environments" unless there is a possibility of confusion with Core-level environments. Module-lev...