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412
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
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A lambdacalculus à la de Bruijn with explicit substitutions
, 1995
"... The aim of this paper is to present the scalculus which is a very simple calculus with explicit substitutions and to prove its confluence on closed terms and the preservation of strong normalisation of terms. We shall prove strong normalisation of the corresponding calculus of substitution by tra ..."
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Cited by 89 (31 self)
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The aim of this paper is to present the scalculus which is a very simple calculus with explicit substitutions and to prove its confluence on closed terms and the preservation of strong normalisation of terms. We shall prove strong normalisation of the corresponding calculus of substitution by translating it into the oecalculus [ACCL91], and therefore the relation between both calculi will be made explicit. The confluence of the scalculus is obtained by the "interpretation method" ([Har89], [CHL92]). The proof of the preservation of normalisation follows the lines of an analogous result for the AEcalculus (cf. [BBLRD95]). The relation between s and AE is also studied.
Natural termination
 Theoretical Computer Science
"... Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1 ..."
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Cited by 86 (11 self)
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Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1
Behavior of database production rules: Termination, con and observable determinism
 IBM Research Report RJ 8562, IBM Almaden Research
, 1992
"... Abstract. Static analysis methods are given for determining whether arbitrary sets of database production rules are (1) guaranteed to terminate; (2) guaranteed to produce a unique nal database state; (3) guaranteed to produce a unique stream of observable actions. When the analysis determines that ..."
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Cited by 83 (10 self)
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Abstract. Static analysis methods are given for determining whether arbitrary sets of database production rules are (1) guaranteed to terminate; (2) guaranteed to produce a unique nal database state; (3) guaranteed to produce a unique stream of observable actions. When the analysis determines that one of these properties is not guaranteed, it isolates the rules responsible for the problem and determines criteria that, if satised, guarantee the property. The analysis methods are presented in the context of the Starburst Rule System; they will form the basis of an interactive development environment for Starburst rule programmers. 1
ContextSensitive Computations in Functional and Functional Logic Programs
 JOURNAL OF FUNCTIONAL AND LOGIC PROGRAMMING
, 1998
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Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection
 IN CSN95: COMPUTER SCIENCE IN THE NETHERLANDS
, 1995
"... In this paper we introduce and study a new lambdacalculus with explicit substitution, lambdaxgc, which has two distinguishing features: first, it retains the use of traditional variable names, specifying terms modulo renaming; this simplifies the reduction system. Second, it includes reduction rul ..."
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Cited by 81 (7 self)
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In this paper we introduce and study a new lambdacalculus with explicit substitution, lambdaxgc, which has two distinguishing features: first, it retains the use of traditional variable names, specifying terms modulo renaming; this simplifies the reduction system. Second, it includes reduction rules for explicit garbage collection; this simplifies several proofs. We show that lambdaxgc is a conservative extension which preserves strong normalisation (PSN) of the untyped lambdacalculus. The result is obtained in a modular way by first proving it for garbagefree reduction and then extending to `reductions in garbage'. This provides insight into the counterexample to PSN for lambdasigma of Melliès (1995); we exploit the abstract nature of lambdaxgc to show how PSN is in conflict with any reasonable substitution composition rule (except for trivial composition rules of which we mention one). Key words: lambda calculus, explicit substitution, strong normalisation, garbage collection.
Basic Paramodulation
 Information and Computation
, 1995
"... We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions bas ..."
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Cited by 70 (12 self)
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We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences.
Completion of Rewrite Systems with Membership Constraints Part II: Constraint Solving
 J. Symbolic Computation
, 1992
"... this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. Thi ..."
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Cited by 70 (2 self)
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this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. This can also be compared with unification of term schemes of various kind (Chen & Hsiang, 1991; Salzer, 1992; Comon, 1995; R. Galbav'y and M. Hermann, 1992). Indeed,
Automatically Checking an Implementation against Its Formal Specification
 IEEE Transactions on Software Engineering
, 2000
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