Constructive Negation in Extensional Higher-Order Logic Programming

Extensional higher-order logic programming has been recently proposed as an interesting extension of classical logic programming. An important characteristic of the new paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we enhance extensional higher-order logic programming with constructive negation. We argue that the main ideas underlying constructive negation are quite close to the existing proof procedure for extensional higher-order logic programming and for this reason the two notions amalgamate quite conveniently. We demonstrate the soundness of the resulting proof procedure and describe an actual implementation of a language that embodies the above ideas. In this way we obtain the first (to our knowledge) higher-order logic programming language supporting constructive negation and offering a new style of programming that genuinely extends that of traditional logic programming.