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49
E  A Brainiac Theorem Prover
, 2002
"... We describe the superpositionbased theorem prover E. E is a sound and complete... ..."
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Cited by 179 (23 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
LEOII — A cooperative automatic theorem prover for higherorder logic
 In Fourth International Joint Conference on Automated Reasoning (IJCAR’08), volume 5195 of LNAI
, 2008
"... Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved pe ..."
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Cited by 56 (26 self)
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Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved performance of LEOII, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level. LEOII is implemented in Objective Caml and its problem representation language is the new TPTP THF language. 1
Caching and Lemmaizing in Model Elimination Theorem Provers
, 1992
"... Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduc ..."
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Cited by 52 (2 self)
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Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduced by more than an order of magnitude the time required to find proofs of several problems and that have enabled the prover to prove theorems previously unobtainable by topdown model elimination theorem provers.
Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 51 (15 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
Efficient Access Mechanisms For Tabled Logic Programs
, 1999
"... This article describes the design, implementation, and experimental evaluation of data structures and algorithms for highperformance table access. Our approach uses tries as the basis for tables. Tries, a variant of discrimination nets, provide complete discrimination for terms, and permit a lookup ..."
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Cited by 48 (16 self)
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This article describes the design, implementation, and experimental evaluation of data structures and algorithms for highperformance table access. Our approach uses tries as the basis for tables. Tries, a variant of discrimination nets, provide complete discrimination for terms, and permit a lookup and possible insertion to be performed in a single pass through a term. In addition, a novel technique of substitution factoring is proposed. When substitution factoring is used, the access cost for answers is proportional to the size of the answer substitution, rather than to the size of the answer itself. Answer tries can be implemented both as interpreted structures and as compiled WAMlike code. When they are compiled, the speed of computing substitutions through answer tries is competitive with the speed of unit facts compiled or asserted as WAM code. Because answer tries can also be created an order of magnitude more quickly than asserted code, they form a promising alternative for representing certain types of dynamic code, even in Prolog systems without tabling. / Address correspondence to I.V. Ramakrishnan, D.S. Warren, Dept. of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 117944400, U.S.A., email: fram,warreng@cs.sunysb.edu; P. Rao, Bellcore, 445 South Street, Morristown, NJ 079606438, U.S.A., email: prasadr@bellcore.com; K. Sagonas, Dept. of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B3001, Heverlee, Belgium, email:
Promoting Rewriting to a Programming Language: A Compiler for NonDeterministic Rewrite Programs in AssociativeCommutative Theories
, 2001
"... Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation ..."
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Cited by 40 (7 self)
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Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation techniques for such languages based on rewriting have to be designed. This is the topic addressed in this paper. The proposed techniques are independent from the rewriting language and may be useful to build a compiler for any system using rewriting modulo associative and commutative (AC) theories. An algorithm for manytoone AC matching is presented, that works efficiently for a restricted class of patterns. Other patterns are transformed to fit into this class. A refined data structure, namely compact bipartite graph, allows encoding all matching problems relative to a set of rewrite rules. A few optimisations concerning the construction of the substitution and of the reduced term are described. We also address the problem of nondeterminism related to AC rewriting and show how to handle it through the concept of strategies. We explain how an analysis of the determinism can be performed at compile time and we illustrate the benefits of this analysis for the performance of the compiled evaluation process. Then we briefly introduce the ELAN system and its compiler, in order to give some experimental results and comparisons with other languages or rewrite engines.
Substitution Tree Indexing
, 1994
"... The performance of a theorem prover crucially depends on the speed of the basic retrieval operations, such as finding terms that are unifiable with (instances of, or more general than) a given query term. In this paper a new indexing method is presented, which outperforms traditional methods such as ..."
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Cited by 39 (1 self)
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The performance of a theorem prover crucially depends on the speed of the basic retrieval operations, such as finding terms that are unifiable with (instances of, or more general than) a given query term. In this paper a new indexing method is presented, which outperforms traditional methods such as path indexing, discrimination tree indexing and abstraction trees. Additionally, the new index not only supports term indexing but also provides maintenance and efficient retrieval of substitutions. As confirmed in multiple experiments, substitution trees combine maximal search speed and minimal memory requirements.
Principles and Practice of Unification Factoring
 ACM Transactions on Programming Languages and Systems
, 1996
"... Devices]: Models of Computationautomata; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problemspattern matching General Terms: Algorithms, Languages, Theory Additional Key Words and Phrases: Indexing, logic programming, trie minimization, unification 1. IN ..."
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Cited by 17 (6 self)
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Devices]: Models of Computationautomata; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problemspattern matching General Terms: Algorithms, Languages, Theory Additional Key Words and Phrases: Indexing, logic programming, trie minimization, unification 1. INTRODUCTION In logic programming languages, such as Prolog, a predicate is defined by a sequence of Horn clauses. A clause becomes applicable for resolution if its head unifies with a selected goal; and each applicable clause is invoked in textual order. Unification of a clause head with a goal involves two basic types of operations: elementary match operations and substitution operations for variables in the two A preliminary version of this article was presented at POPL '95. This work was supported in part by NSF grants CCR9102159, CCR9102989, CCR9404921, CDA9303181, CDA9504275, INT9314412, and ONR grant 400X116YIP01. Authors' addresses: S. Dawson, Computer Science Laboratory, SRI In...
WALDMEISTER: Development of a High Performance CompletionBased Theorem Prover
, 1996
"... : In this report we give an overview of the development of our new Waldmeister prover for equational theories. We elaborate a systematic stepwise design process, starting with the inference system for unfailing KnuthBendix completion and ending up with an implementation which avoids the main dise ..."
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Cited by 14 (0 self)
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: In this report we give an overview of the development of our new Waldmeister prover for equational theories. We elaborate a systematic stepwise design process, starting with the inference system for unfailing KnuthBendix completion and ending up with an implementation which avoids the main diseases today's provers suffer from: overindulgence in time and space. Our design process is based on a logical threelevel system model consisting of basic operations for inference step execution, aggregated inference machine, and overall control strategy. Careful analysis of the inference system for unfailing completion has revealed the crucial points responsible for time and space consumption. For the low level of our model, we introduce specialized data structures and algorithms speeding up the running system and cutting it down in size  both by one order of magnitude compared with standard techniques. Flexible control of the midlevel aggregation inside the resulting prover is made po...
System Description: E 1.8
"... Abstract. E is a theorem prover for full firstorder logic with equality. It reduces firstorder problems to clause normal form and employs a saturation algorithm based on the equational superposition calculus. E is built on shared terms with cached rewriting, and employs several innovations for eff ..."
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Cited by 14 (3 self)
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Abstract. E is a theorem prover for full firstorder logic with equality. It reduces firstorder problems to clause normal form and employs a saturation algorithm based on the equational superposition calculus. E is built on shared terms with cached rewriting, and employs several innovations for efficient clause indexing. Major strengths of the system are automatic problem analysis and highly flexible search heuristics. The prover can provide verifiable proof objects and answer substitutions with very little overhead. E performs well, solving more than 69 % of TPTP5.4.0 FOF and CNF problems in automatic mode. 1