A new formalism, called Hiord, for defining type-free higherorder logic programming languages with predicate abstraction is introduced. A model theory, based on partial combinatory algebras, is presented, with respect to which the formalism is shown sound. A programming language built on a subset of Hiord, and its implementation are discussed. A new proposal for defining modules in this framework is considered,#R##N#along with several examples.
['Daniel Cabeza Gras', 'Manuel V. Hermenegildo', 'James Lipton']
Hiord: A type-free higher-order logic programming language with predicate abstraction