The art of Prolog: advanced programming techniques
The art of Prolog: advanced programming techniques
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Natural deduction as higher-order resolution
Journal of Logic Programming
Higher-order logic programming
Proceedings on Third international conference on logic programming
A higher-order logic as the basis for logic programming
A higher-order logic as the basis for logic programming
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Partial polymorphic type inference and higher-order unification
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
A logical analysis of modules in logic programming
Journal of Logic Programming
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Contributions to the Theory of Logic Programming
Journal of the ACM (JACM)
The Expressiveness of Simple and Second-Order Type Structures
Journal of the ACM (JACM)
Specifying Theorem Provers in a Higher-Order Logic Programming Language
Proceedings of the 9th International Conference on Automated Deduction
Some uses of higher-order logic in computational linguistics
ACL '86 Proceedings of the 24th annual meeting on Association for Computational Linguistics
Automated Software Engineering
Higher-Order Quantification and Proof Search
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
Using Decision Procedures with a Higher-Order Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Higher Order Unification 30 Years Later
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
A new framework for declarative programming
Theoretical Computer Science
ACM Transactions on Computational Logic (TOCL)
A treatment of higher-order features in logic programming
Theory and Practice of Logic Programming
Automated deduction for verification
ACM Computing Surveys (CSUR)
Medical knowledge induction with higher-order horn clauses and meta-programming
SMO'09 Proceedings of the 9th WSEAS international conference on Simulation, modelling and optimization
On the algebraic structure of declarative programming languages
Theoretical Computer Science
Knowledge induction from medical databases with higher-order programming
WSEAS Transactions on Information Science and Applications
Is observational congruence on μ-expressions axiomatisable in equational Horn logic?
Information and Computation
ILP'10 Proceedings of the 20th international conference on Inductive logic programming
Hiord: a type-free higher-order logic programming language with predicate abstraction
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
Representing and reasoning with operational semantics
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Is observational congruence axiomatisable in equational horn logic?
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
Extensional Higher-Order Logic Programming
ACM Transactions on Computational Logic (TOCL)
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A generalization of Horn clauses to a higher-order logic is described and examined as a basis for logic programming. In qualitative terms, these higher-order Horn clauses are obtained from the first-order ones by replacing first-order terms with simply typed &lgr;-terms and by permitting quantification over all occurrences of function symbols and some occurrences of predicate symbols. Several proof-theoretic results concerning these extended clauses are presented. One result shows that although the substitutions for predicate variables can be quite complex in general, the substitutions necessary in the context of higher-order Horn clauses are tightly constrained. This observation is used to show that these higher-order formulas can specify computations in a fashion similar to first-order Horn clauses. A complete theorem-proving procedure is also described for the extension. This procedure is obtained by interweaving higher-order unification with backchaining and goal reductions, and constitutes a higher-order generalization of SLD-resolution. These results have a practical realization in the higher-order logic programming language called &lgr;Prolog.