J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974. Home/Search Document Not in Database Summary Related Articles Check |
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A Framework for Incorporating Abstraction Mechanisms into the.. - Zachary (1987) (1 citation) (Correct)
....set of all terms. For smaller moded bases it might be necessary to devise new procedures. In any event, the body of existing unification procedures provides a rich source for implementations of the built in theories of Denali. 6.1. 2 Narrowing An approach based upon the narrowing operation of [Slagle 74] can be used to synthesize unification procedures for equational theories presented by a convergent term rewriting system [Fay 79] The narrowing approach has been improved by [Hullot 80] who gives sufficient conditions for its termination; by [Jouannaud 83] who generalizes it to equational ....
J. R. Slagle. Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity. Journal of the ACM, 21(4):622--642, October 1974.
A Generalized Approach to Equational Unification - Yelick (1985) (3 citations) (Correct)
....84] open open FPAG [Kandri Rody 85] open open BR [Kandri Rody 85] open open Figure 1 4: Known Unification Algorithms 1.5. 2 Narrowing While most of the existing unification work in unification has required human invention of each algorithm, the unification procedures based on narrowing [Slagle 74] are automatically generated, For equational theories representable by a convergent term rewriting system there is method for performing unification in the theory of the rewriting system [Fay 79] Hullot 80] gives sufficient con ditions for termination of the narrowing process, along with some ....
J.R. Slagle, "Automated Theorem-Proving for Theories with Simplifiers, Commmutativity and Associativity," JACM 21 (4):622-642, October 1974.
Conditional Equational Theories and Complete Sets of.. - Hölldobler (2 citations) (Correct)
.... for EP and (F a computed answer substitution oe which is more general modulo EP than (see [Holldobler, 1989] Of course, the search space generated by reflection, instantiation and paramodulation contains far to many redundant and irrelevant inferences and it has been proposed at 8 first by Slagle [1974] and Lankford [1975] to impose certain conditions on equational theories such that paramodulation need not to be applied to variable occurrences. This restricted form of paramodulation is often called narrowing (e.g [Hullot, 1980] Obviously, instantiation is no longer needed if it suffices to ....
J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21:622--642, 1974.
Observable Semantics and Dynamic Analysis of Computational Processes - Lucas (2000) (Correct)
....( i;s Theta , i;t ) ffi ( r;s Theta , r;t ) Narrowing [Hul80] written ; and involving a restricted class of substitutions for instantiation, namely most general unifiers) is a restriction of , narr , i.e. narr . Narrowing, which is extensively used in automated deduction [Sla74] and functional logic programming [Han94] is usually described as a combination of instantiation and reduction. Here we have given an algebraic expression for this combination. 3.2 Progress of computational processes By the computational process issued by , we mean its reflexive transitive ....
J.R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622-642, 1974.
An Implementation of Narrowing Strategies - Antoy, Hanus, Massey, Steiner (2001) (Correct)
....computations are amalgamated with the exible use of logical variables, providing for function inversion and search for solutions. Functional logic languages with a sound and complete operational semantics are usually based on narrowing (originally introduced in automated theorem proving [32]) which combines reduction (from the functional part) and variable instantiation (from the logic part) A narrowing step instantiates variables of an expression and applies a reduction step to a redex of the instantiated expression. The instantiation of variables is usually computed by unifying a ....
J. Slagle. Automated theorem-proving for theories with simpliers, commutativity, and associativity. Journal of the ACM, 21(4):622-642, 1974.
Towards the Global Optimization of Functional Logic Programs - Hanus (1994) (Correct)
....logic languages with a sound and complete operational semantics are based on narrowing (e.g. 10, 12, 26, 28] a combination of the reduction principle of functional languages and the resolution principle of logic languages. Narrowing, originally introduced in automated theorem proving [29], is used to solve equations by finding appropriate values for variables occurring in arguments of functions. This is done by unifying (rather than matching) an input term with the left hand side of some rule and then replacing the instantiated input term by the instantiated right hand side of the ....
J.R. Slagle. Automated Theorem-Proving for Theories with Simplifiers, Commutativity, and Associativity. Journal of the ACM, Vol. 21, No. 4, pp. 622--642, 1974.
A Needed Narrowing Strategy - Antoy, Echahed, Hanus (1994) (95 citations) (Correct)
....matching. 1 Introduction In recent years, most proposals with a sound and complete operational semantics for the integration of functional and logic programming languages [5, 10] were based on narrowing, e.g. 6, 15, 17, 19, 37, 44] Narrowing, originally introduced in automated theorem proving [46], solves equations by computing unifiers with respect to an equational theory [14] Informally, narrowing unifies a term with the left hand side of a rewrite rule and fires the rule on the instantiated term. Example 1 Consider the following rewrite rules defining the operations less than or ....
J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974.
Cancellative Superposition Decides the Theory of Divisible.. - Waldmann (1999) (5 citations) (Correct)
....Associativity, Commutativity, Variable Elimination, Term Rewriting, Divisible Torsion free Abelian Groups, Decision Problem. 1 Introduction Equational reasoning in the presence of the associativity and commutativity axioms is known to be dicult theoretically [4, 8] as well as practically [1, 9, 10, 11, 12, 13, 17]. Using AC uni cation and extended clauses the worst ineciencies of a na ve approach can be avoided, but still the extended clauses lead to numerous variable overlaps one of the most proli c types of inferences in resolution or superposition style calculi. Besides, minimal complete set of ....
James R. Slagle. Automated theorem-proving for theories with simpli- ers, commutativity, and associativity. Journal of the ACM, 21(4):622{ 642, October 1974.
Combining Lazy Narrowing and Simplification - Hanus (1994) (10 citations) (Correct)
....languages [19] Functional logic languages with a sound and complete operational semantics are based on narrowing, a combination of the reduction principle of functional languages and the resolution principle of logic languages. Narrowing, originally introduced in automated theorem proving [34], is used to solve equations by finding appropriate values for variables occurring in arguments of functions. This is done by unifying (rather than matching) an input term with the left hand side of some rule and then replacing the instantiated input term by the instantiated right hand side of the ....
J.R. Slagle. Automated Theorem-Proving for Theories with Simplifiers, Commutativity, and Associativity. Journal of the ACM, Vol. 21, No. 4, pp. 622--642, 1974. 15
The Integration of Functions into Logic Programming: A Survey - Hanus (1994) (14 citations) (Correct)
....[1,2,3] If there is a function call containing free variables in arguments, then it is generally necessary to instantiate these variables to appropriate terms in order to apply a rewrite step. This can be done by using unification instead of matching in the rewrite step which is called narrowing [119]. Hence in a narrowing step we unify a (non variable) subterm of the goal with the left hand side of a rule and then we replace the instantiated subterm by the instantiated right hand side of the rule. To be precise we say a term t is narrowable into a term t 0 if 1. p is a non variable ....
....to implementations on sequential architectures. Similarly to logic programming, functional logic languages can also be implemented on distributed architectures using concepts like AND and OR parallelism (see, for instance, 16, 81, 113] 26 Operational principle Requirements simple narrowing [69, 119] C, T basic narrowing [69] C, T left to right basic narrowing [64] C, T LSE narrowing [12] C, T innermost narrowing [41] C, T, CB, TD; complete w.r.t. ground substitutions innermost basic narrowing [66] C, T, CB selection narrowing [18] C, T, CB normalizing narrowing [40] C, T, CB ....
J.R. Slagle. Automated Theorem-Proving for Theories with Simplifiers, Commutativity, and Associativity. Journal of the ACM, Vol. 21, No. 4, pp. 622--642, 1974.
A Needed Narrowing Strategy - Antoy, Echahed, Hanus (1994) (95 citations) (Correct)
....matching. 1 Introduction In recent years, most proposals with a sound and complete operational semantics for the integration of functional and logic programming languages [5, 10] were based on narrowing, e.g. 6, 15, 17, 19, 37, 44] Narrowing, originally introduced in automated theorem proving [46], solves equations by computing uni ers with respect to an equational theory [14] Informally, narrowing uni es a term with the left hand side of a rewrite rule and res the rule on the instantiated term. Example 1 Consider the following rewrite rules de ning the operations less than or equal ....
J. R. Slagle. Automated theorem-proving for theories with simpliers, commutativity, and associativity. Journal of the ACM, 21(4):622-642, 1974.
A Generic Rewrite Method for Proving Self-Stabilization - Beauquier, Bérard.. (1998) (Correct)
....t i of t reduces to r i . We will disregard unifiers j which instantiate t at a nonvariable position . We then say that t is minimally reducible at a nonvariable position via the set of unifiers f 1 ; k g. This corresponds to the operation called narrowing in first order rewrite systems [29,11,18]. The corresponding set of minimal reduction steps is ft i r i g i=1; k . Example Suppose we have a rule of the form #X11Y # #X22Y #. The word t : #1W1# unifies with lefthand side #X11Y # via most general unifiers 1 : fW=1W 0 g [ fX= Y=W 0 1g, 2 : fW=W 0 1g [ fX=1W 0 ; Y = g, ....
J.R. Slagle. "Automated Theorem-Proving for Theories with Simplifiers, Commutativity, and Associativity." J. ACM 21:4, 1974, pp. 622-642.
Nominal Logic Programming - Cheney (2004) (Correct)
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J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974.
The Narrowing-Driven Approach to Functional Logic Program.. - Albert, Vidal (2002) (2 citations) (Correct)
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) Slagle J., "Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity," Journal of the ACM, 21, 4, pp. 622--642, 1974.
Unfolding of Equational Logic Programs - Alpuente, Falaschi, Ramis, Vidal (1994) (Correct)
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J.R. Slagle. Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity. journal of the ACM, 21(4):622--642, 1974. 3
Logic Programs with Functions - And Default Values (Correct)
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J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity and associativity. Journal of the ACM, 21(4):622--642, 1974.
Refining Weakly Outermost-Needed Rewriting and Narrowing - Escobar (2003) (Correct)
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J. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974.
Decision Procedures and Model - Building In Equational (Correct)
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J.R. Slagle, Automated Theorem Proving for Theories with Simplifiers, Commutativity, and Associativity. J. of the ACM 21(4):622--642, October 1974.
Logic Programs with Functions - And Default Values (Correct)
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J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity and associativity. Journal of the ACM, 21(4):622--642, 1974.
Higher-Order Narrowing with Definitional Trees - Michael Hanus And (1996) (25 citations) (Correct)
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J.R. Slagle. Automated theorem-proving for theories withsimplifi, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974.
Decision Procedures and Model - Building In Equational (Correct)
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J.R. Slagle, Automated Theorem Proving for Theories with Simplifiers, Commutativity, and Associativity. J. of the ACM 21(4):622--642, October 1974.
Inductive Theorem Proving for Design Specifications - Padawitz (1997) (3 citations) (Correct)
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J.R. Slagle, Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity, Journal ACM 21 (1974) 622-642
Swinging Data Types - The dielectic between actions and.. - Padawitz (1998) (Correct)
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J.R. Slagle, Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity, Journal ACM 21 (1974) 622-642
An Implementation of Narrowing Strategies - Antoy, Hanus, Massey, Steiner (2001) (Correct)
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J. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622--642, 1974.
Context-Sensitive Rewriting Strategies - Lucas (2000) (2 citations) (Correct)
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J.R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity, and associativity. Journal of the ACM, 21(4):622-642, 1974.
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