We set up a framework for the study of extensionality in the context of higher-order logic programming. For simply typed logic programs we propose a novel declarative semantics, consisting of a model class with a semi-computable initial model, and a notion of extensionality. We show that the initial model of a simply typed logic program, in case the program is extensional, collapses into a simple, set-theoretic representation. Given the undecidability of extensionality in general, we develop a decidable, syntactic criterion which is sufficient for extensionality. Some typical examples of higher-order logic programs are shown to be extensional.

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CWI
CWI. Probability, Networks and Algorithms [PNA]

Bezem, M.A. (1999). Extensionality of simply typed logic programs. CWI. Probability, Networks and Algorithms [PNA]. CWI.