Logical closures

Uniform proof procedures for hereditary Harrop formulae have been proposed as a foundation for logic programming. A non-standard approach to defining hereditary Harrop formula is given, allowing quantification over predicate variables but distinguishing the forms of predicate quantification. The benefits of this approach include a treatment of higher order procedures which avoids some scoping problems with languages such as λ-Prolog, and the possibility of extending the language straightforwardly with a module system such as that developed for Standard ML. To enable a style of programming found in existing logic programming languages, a form of implementation inheritance is introduced into the language. Combining this with explicit type quantification provides a form of dynamic dispatching similar to CLOS generic procedures in a statically typed language.