In Praise of Impredicativity: A Contribution to the Formalisation of Meta-Programming
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Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic programming, are widespread declarative programming techniques. In logic programming, there is a gap between the meta-programming practice and its theory: The formalisations of meta-programming do not explicitly address its impredicativity and are cumbersome. This article aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former logics and by defining Reflective Predicate Logic, a conservative extension of first-order logic, that provides a simple formalisation of meta-programming. Under consideration for publication in Theory and Practice of Logic Programming
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