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FirstOrder Unification by Structural Recursion
, 2001
"... Firstorder unification algorithms (Robinson, 1965) are traditionally implemented via general recursion, with separate proofs for partial correctness and termination. The latter tends to involve counting the number of unsolved variables and showing that this total decreases each time a substitution ..."
Abstract

Cited by 12 (4 self)
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Firstorder unification algorithms (Robinson, 1965) are traditionally implemented via general recursion, with separate proofs for partial correctness and termination. The latter tends to involve counting the number of unsolved variables and showing that this total decreases each time a substitution enlarges the terms. There are many such proofs in the literature, for example, (Manna & Waldinger, 1981; Paulson, 1985; Coen, 1992; Rouyer, 1992; Jaume, 1997; Bove, 1999). This paper
A Full Formalization of SLDResolution in the Calculus of Inductive Constructions
"... 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 quasiterms, thus showing how to rela ..."
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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 quasiterms, thus showing how to relate an inductive set with a subset defined by a predicate. Then, SLDresolution is explicitely defined: the renaming process used in SLDderivations 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.
Formalisation of General Logics in the Calculus of Inductive Constructions: Towards an Abstract . . .
, 1999
"... Formal specifications of logics share many standard concepts and in order to avoid repetitious works, it seems desirable to express these specifications in a uniform framework. General logics à la J. Meseguer provide an uniform and modular way of encoding a logical language, its semantics and its in ..."
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Formal specifications of logics share many standard concepts and in order to avoid repetitious works, it seems desirable to express these specifications in a uniform framework. General logics à la J. Meseguer provide an uniform and modular way of encoding a logical language, its semantics and its inference system. Hence, we describe here a formalisation of general logics in the calculus of inductive constructions thus providing a generic and modular set of speci cations (with the proofs of s...