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Verification of the Completeness of Unification Algorithms à la
"... Abstract. This work presents a general methodology for verification of the completeness of firstorder unification algorithms à la Robinson developed in the higherorder proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general u ..."
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Abstract. This work presents a general methodology for verification of the completeness of firstorder unification algorithms à la Robinson developed in the higherorder proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design
Unification
"... In this note we present the basic theory of substitutions and a unification algorithm expressed in an applicative sideeffect free programming language. 1 INTRODUCTION 1 1 Introduction Unification was first introduced in theorem proving by Robinson [9], and the problem is well known in the literat ..."
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In this note we present the basic theory of substitutions and a unification algorithm expressed in an applicative sideeffect free programming language. 1 INTRODUCTION 1 1 Introduction Unification was first introduced in theorem proving by Robinson [9], and the problem is well known
AN EFFICIENT NOMINAL UNIFICATION ALGORITHM
"... Abstract. Nominal Unification is an extension of firstorder unification where terms can contain binders and unification is performed modulo αequivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearlyreduce nominal unification problems to ..."
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Cited by 6 (1 self)
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to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for firstorder unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan
Minimal and Complete Prefix Unification . . .
, 1997
"... For theorem proving in nonclassical logics two similar approaches have been established: a matrix characterization of Wallen and Ohlbach’s resolution calculus. In both cases the essential extension of the classical calculi is a need for unifying the socalled prefixes of atomic formulae or socalle ..."
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called worldpaths respectively. We present a specialized stringunification algorithm which computes a minimal set of most general unifiers. By transforming systems of equations we obtain an elegant and efficient procedure which applies to intuitionistic logic and the modal logic S4. With some modifications
Workshop Programme International Workshop on Unification (UNIF’04)
"... UNIF is the main international meeting on unification. Unification is concerned with the problem of identifying given terms, either syntactically or modulo a given logical theory. Syntactic unification is the basic operation of most automated reasoning systems, and unification modulo theories can be ..."
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UNIF is the main international meeting on unification. Unification is concerned with the problem of identifying given terms, either syntactically or modulo a given logical theory. Syntactic unification is the basic operation of most automated reasoning systems, and unification modulo theories can
Verifying the Unification Algorithm in LCF
 Science of Computer Programming
, 1985
"... Manna and Waldinger's theory of substitutions and unification has been verified using the Cambridge LCF theorem prover. A proof of the monotonicity of substitution is presented in detail, as an example of interaction with LCF. Translating the theory into LCF's domaintheoretic logic is ..."
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Cited by 11 (0 self)
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is largely straightforward. Wellfounded induction on a complex ordering is translated into nested structural inductions. Correctness of unification is expressed using predicates for such properties as idempotence and mostgenerality. The verification is presented as a series of lemmas. The LCF proofs
A Parallel Unification Algorithm
, 1989
"... We define an abstract unification algorithm which can be (and has been) implemented on a parallel SingleInstruction MultipleData (SIMD) computer. We proceed to suggest an actual representation for the unification problem and a realization of the algorithm. The representation is based on Robinson&a ..."
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We define an abstract unification algorithm which can be (and has been) implemented on a parallel SingleInstruction MultipleData (SIMD) computer. We proceed to suggest an actual representation for the unification problem and a realization of the algorithm. The representation is based on Robinson
Lazy Linear Combinatorial Unification
, 1998
"... In this paper we define a tworule reduction system for the lazy computation of unification on firstorder terms. The computation consists of a sequence of reductions which is almost linear with the size of the input. Every reduction transforms the problem into an equivalent one which is a better ap ..."
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unification is required. 1 Introduction Since 1965, when J. A. Robinson [Robinson 65, Robinson 92] defined it as the substitution rule for resolution, unification has been widely used in several areas of computer science, e.g. programming languages, automated reasoning and artificial intelligence [Siekmann
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