Verifying the unification algorithm in LCF
Science of Computer Programming - Ellis Horwood series in artificial intelligence
Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Information and Computation - Semantics of Data Types
Foundations of deductive databases and logic programming
Proofs and types
Declarative modeling of the operational behavior of logic languages
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
Partial evaluation in logic programming
Journal of Logic Programming
Computation as logic
The role of standardising apart in logic programming
Theoretical Computer Science
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)
Logic, Programming and PROLOG
Verification of Compiler Correctness for the WAM
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Formalizing Basic First Order Model Theory
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Logic Programming and Co-inductive Definitions
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Hi-index | 0.00 |
This paper presents a full formalization of the semantics of definite programs, in the calculus of inductive constructions. First, we describe a formalization of the proof of first-order terms unification: this proof is obtained from a similar proof dealing with quasi-terms, thus showing how to relate an inductive set with a subset defined by a predicate. Then, SLD-resolution is explicitely defined: the renaming process used in SLD-derivations is made explicit, thus introducing complications, usually overlooked, during the proofs of classical results. Last, switching and lifting lemmas and soundness and completeness theorems are formalized. For this, we present two lemmas, usually omitted, which are needed. This development also contains a formalization of basic results on operators and their fixpoints in a general setting. All the proofs of the results, presented here, have been checked with the proof assistant Coq.