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Processing programs as data is one of the successes of functional and logicprogramming. Higher-order functions, as program-processing programs are calledin functional programming, and meta-programs, as they are called in logicprogramming, are widespread declarative programming techniques. In logicprogramming, there is a gap between the meta-programming practice and itstheory: The formalisations of meta-programming do not explicitly address itsimpredicativity and are not fully adequate. This article aims at overcomingthis unsatisfactory situation by discussing the relevance of impredicativity tometa-programming, by revisiting former formalisations of meta-programming andby defining Reflective Predicate Logic, a conservative extension of first-orderlogic, which provides a simple formalisation of meta-programming.

In Praise of Impredicativity: A Contribution to the Formalisation of Meta-Programming