Behavioral abstraction is hiding information

We show that for any behavioral Σ-specification B there is an ordinary algebraic specification B˜ over a larger signature, such that a model behaviorally satisfies B iff it satisfies, in the ordinary sense, the Σ-theorems of B˜. The idea is to add machinery for contexts and experiments (sorts, operations and equations), use it, and then hide it. We develop a procedure, called unhiding, which takes a finite B and produces a finite B˜. The practical aspect of this procedure is that one can use any standard equational inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.