Constraint Logic Programming with Hereditary Harrop Formulas

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the syntax and proof theory of HH with the help of a given constraint system, in such a way that the key property of HH as a logic programming language (namely, the existence of uniform proofs) is preserved. We also present a procedure for goal solving, showing its soundness and completeness for computing answer constraints. As a consequence of this result, we obtain a new strong completeness theorem for CLP that avoids the need to build disjunctions of computed answers, as well as a more abstract formulation of a known completeness theorem for HH.

[1]  Dale Miller,et al.  Unification Under a Mixed Prefix , 1992, J. Symb. Comput..

[2]  Dale Miller,et al.  A Logical Analysis of Modules in Logic Programming , 1989, J. Log. Program..

[3]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[4]  A. Tarski.  A Decision Method for Elementary Algebra and Geometry , 2023 .

[5]  Michael J. Maher,et al.  The Semantics of Constraint Logic Programs , 1998, J. Log. Program..

[6]  Jean-Pierre Jouannaud,et al.  Syntacticness, Cycle-Syntacticness, and Shallow Theories , 1994, Inf. Comput..

[7]  Jacques Cohen,et al.  Constraint logic programming languages , 1990, CACM.

[8]  Zohar Manna,et al.  Proving termination with multiset orderings , 1979, CACM.

[9]  Hubert Comon,et al.  Complete axiomatizations of some quotient term algebras , 1993 .

[10]  Robert A. Kowalski,et al.  The Semantics of Predicate Logic as a Programming Language , 1976, JACM.

[11]  Gert Smolka,et al.  Records for Logic Programming , 1994, J. Log. Program..

[12]  Yike Guo,et al.  Constraint Logic Programming in the Sequent Calculus , 1994, LPAR.

[13]  Michael J. Maher.  Logic Semantics for a Class of Committed-Choice Programs , 1987, ICLP.

[14]  Roland H. C. Yap,et al.  The CLP( R ) language and system , 1992, TOPL.

[15]  Vijay A. Saraswat.  The category of constraint systems is Cartesian-closed , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[16]  Gopalan Nadathur,et al.  Hereditary Harrop Formulas and Uniform Proof Systems , 1987, Logic in Computer Science.

[17]  J. S. Hodas.  Logic programming in intuitionistic linear logic: theory, design, and implementation , 1995 .

[18]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.