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External Rewriting for Skeptical Proof Assistants
, 2002
"... This paper presents the design, the implementation and experiments of the integration of syntactic, conditional possibly associativecommutative term rewriting into proof assistants based on constructive type theory. Our approach is called external since it consists in performing term rewriting in a ..."
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Cited by 18 (3 self)
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This paper presents the design, the implementation and experiments of the integration of syntactic, conditional possibly associativecommutative term rewriting into proof assistants based on constructive type theory. Our approach is called external since it consists in performing term rewriting in a speci c and ecient environment and to check the computations later in a proof assistant.
On Using Ground Joinable Equations in Equational Theorem Proving
 PROC. OF THE 3RD FTP, ST. ANDREWS, SCOTTLAND, FACHBERICHTE INFORMATIK. UNIVERSITAT KOBLENZLANDAU
, 2000
"... When rewriting and completion techniques are used for equational theorem proving, the axiom set is saturated with the aim to get a rewrite system that is terminating and confluent on ground terms. To reduce the computational effort it should (1) be powerful for rewriting and (2) create not too ma ..."
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Cited by 10 (2 self)
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When rewriting and completion techniques are used for equational theorem proving, the axiom set is saturated with the aim to get a rewrite system that is terminating and confluent on ground terms. To reduce the computational effort it should (1) be powerful for rewriting and (2) create not too many critical pairs. These problems become especially important if some operators are associative and commutative (AC ). We show in this paper how these two goals can be reached to some extent by using ground joinable equations for simplification purposes and omitting them from the generation of new facts. For the special case of AC operators we present a simple redundancy criterion which is easy to implement, efficient, and effective in practice, leading to significant speedups.
Citius altius fortius: Lessons learned from the Theorem Prover Waldmeister
 Proceedings of the 4th International Workshop on FirstOrder Theorem Proving, number 86.1 in Electronic Notes in Theoretical Computer Science
, 2003
"... In the last years, the development of automated theorem provers has been advancing in a so to speak Olympic spirit, following the motto "faster, higher, stronger"; and the Waldmeister system has been a part of that endeavour. We will survey the concepts underlying this prover, which implements Knuth ..."
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Cited by 8 (0 self)
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In the last years, the development of automated theorem provers has been advancing in a so to speak Olympic spirit, following the motto "faster, higher, stronger"; and the Waldmeister system has been a part of that endeavour. We will survey the concepts underlying this prover, which implements KnuthBendix completion in its unfailing variant. The system architecture is based on a strict separation of active and passive facts, and is realized via speci cally tailored representations for each of the central data structures: indexing for the active facts, setbased compression for the passive facts, successor sets for the conjectures. In order to cope with large search spaces, specialized redundancy criteria are employed, and the empirically gained control knowledge is integrated to ease the use of the system. We conclude with a discussion of strengths and weaknesses, and a view of future prospects.
The HOL Light manual (1.1)
, 2000
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 6 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...
Deriving Focused Calculi For Transitive Relations
 Rewriting Techniques and Applications, 12th International Conference, volume 2051 of LNCS
, 2001
"... We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi ..."
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Cited by 4 (4 self)
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We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi then follows from correctness of this synthesis. Our method clearly separates deductive and procedural aspects: relating ordered chaining to KnuthBendix completion for transitive relations provides the semantic background that drives the synthesis towards its goal. This yields a more restrictive and transparent chaining calculus. The method also supports the development of approximate focused calculi and a modular approach to theory hierarchies.
A Phytography of Waldmeister
"... The architecture of the Waldmeister prover is based on a strict separation of active and passice facts... ..."
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Cited by 3 (1 self)
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The architecture of the Waldmeister prover is based on a strict separation of active and passice facts...
Noncomputational Equations and Rewriting Techniques
"... this report we present an overview of dierent rewriting methods which allow one to automatically construct decision procedures for such kind of theories. The next section reviews main denitions and techniques in rewriting (rewriting, normal forms, termination, conuence, and completion); section 2 in ..."
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this report we present an overview of dierent rewriting methods which allow one to automatically construct decision procedures for such kind of theories. The next section reviews main denitions and techniques in rewriting (rewriting, normal forms, termination, conuence, and completion); section 2 introduces noncomputational equations; in section 3 we describe three main extensions of rewriting (as well as their combinations) for handling of noncomputational equations; the report is concluded with a summary
A constructive decision procedure for equalities modulo AC
"... this paper an optimised constructive decision procedure for AC equalities based on the syntacticness of AC theories. The original motivation for it comes from our work [5] to incorporate term rewriting into the Coq proof assistant [3] using ELAN [7]. The main idea is to perform term rewriting in ELA ..."
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this paper an optimised constructive decision procedure for AC equalities based on the syntacticness of AC theories. The original motivation for it comes from our work [5] to incorporate term rewriting into the Coq proof assistant [3] using ELAN [7]. The main idea is to perform term rewriting in ELAN and to only use Coq for checking purpose. When considering AC rewriting, proof checking requires an ecient method to prove AC equality in Coq using two axioms of associativity and commutativity or possibly a nite set of equalities derived from them