Partial higher-order specifications
In this paper we study the classes of extensional models of higher-order partial conditional specifications. After investigating the closure properties of these classes, we show that an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models, can be obtained from any equationally complete inference system for partial conditional specifications. Then, applying some previous results, we propose a deduction system, equationally complete for the class of extensional models of a partial conditional specification.
Finally, turning the attention to the special important case of term-extensional models, we first show a sound and equationally complete inference system and then give necessary and sufficient conditions for the existence of free models, which are also free in the class of term-generated extensional models.
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