Extensional Higher-Order Logic Programming

A Extensional Higher-Order Logic Programming

The two most prominent declarative paradigms, namely logic and functional programming, differ radically in an important aspect: logic programming is traditionally firstorder while functional programming encourages and promotes the use of higher-order functions and constructs. This difference can be partially explained by the fact that higher-order logic fails in terms of vital properties such a...

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 underlyin...

Proof Procedures for Extensional Higher-Order Logic Programming

We consider an extensional higher-order logic programming language which possesses the minimum Herbrand model property. We propose an SLD-resolution proof procedure and we demonstrate that it is sound and complete with respect to this semantics. In this way, we extend the familiar proof theory of first-order logic programming to apply to the more general higher-order case. We then enhance our s...

Higher-Order Logic Programming

Extensional Higher-Order Datalog

We define a higher-order extension of Datalog based on the Horn fragment of higher-order logic introduced in [Wad91]. Programs of Higher-Order Datalog can be understood declaratively as formulas in extensional higher-order logic, in which (for example) a unary predicate of unary predicates is a set of sets of data objects. The language retains all the basic principles of first-order logic progr...