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The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (49 self)
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. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment
Can a higherorder and a firstorder theorem prover cooperate?
 IN FRANZ BAADER AND ANDREI VORONKOV, EDITORS, LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING — 11TH INTERNATIONAL WORKSHOP, LPAR 2004, LNAI 3452
, 2005
"... Stateoftheart firstorder automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about ..."
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Cited by 10 (7 self)
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of clauses prevent these systems from solving a whole range of problems. We present a solution to this challenge by combining a higherorder and a firstorder automated theorem prover, both based on the resolution principle, in a flexible and distributed environment. By this we can exploit concise problem
Firstorder proof tactics in higherorder logic theorem provers
 Design and Application of Strategies/Tactics in Higher Order Logics, number NASA/CP2003212448 in NASA Technical Reports
, 2003
"... Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology: an ‘ ..."
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Cited by 73 (4 self)
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Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology
Combining Proofs of HigherOrder and FirstOrder Automated Theorem Provers
"... Abstract. Ωants is an agentoriented environment for combining inference systems. A characteristics of the Ωants approach is that a common proof object is generated by the cooperating systems. This common proof object can be inspected by verification tools to validate the correctness of the proof. Ω ..."
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Abstract. Ωants is an agentoriented environment for combining inference systems. A characteristics of the Ωants approach is that a common proof object is generated by the cooperating systems. This common proof object can be inspected by verification tools to validate the correctness of the proof
Translating HigherOrder Clauses to FirstOrder Clauses
"... Abstract. Interactive provers typically use higherorder logic, while automatic provers typically use firstorder logic. In order to integrate interactive provers with automatic ones, it is necessary to translate higherorder formulae to firstorder form. The translation should ideally be both sound ..."
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Cited by 47 (4 self)
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Abstract. Interactive provers typically use higherorder logic, while automatic provers typically use firstorder logic. In order to integrate interactive provers with automatic ones, it is necessary to translate higherorder formulae to firstorder form. The translation should ideally be both
HigherOrder Abstract Syntax
"... We describe motivation, design, use, and implementation of higherorder abstract syntax as a central representation for programs, formulas, rules, and other syntactic objects in program manipulation and other formal systems where matching and substitution or syntax incorporates name binding informat ..."
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Cited by 358 (18 self)
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We describe motivation, design, use, and implementation of higherorder abstract syntax as a central representation for programs, formulas, rules, and other syntactic objects in program manipulation and other formal systems where matching and substitution or syntax incorporates name binding
Translating higherorder problems to firstorder clauses
 ESCoR (CEUR Workshop Proceedings
, 2006
"... Proofs involving large specifications are typically carried out through interactive provers that use higherorder logic. A promising approach to improve the automation of interactive provers is by integrating them with automatic provers, which are usually based on firstorder logic. Consequently, it ..."
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Cited by 19 (5 self)
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Proofs involving large specifications are typically carried out through interactive provers that use higherorder logic. A promising approach to improve the automation of interactive provers is by integrating them with automatic provers, which are usually based on firstorder logic. Consequently
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
On the Translation of HigherOrder Problems into FirstOrder Logic
 Proceedings of ECAI94
, 1994
"... . In most cases higherorder logic is based on the  calculus in order to avoid the infinite set of socalled comprehension axioms. However, there is a price to be paid, namely an undecidable unification algorithm. If we do not use the calculus, but translate higherorder expressions into firstor ..."
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Cited by 8 (4 self)
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to certain problem classes. This paper will show how the infinite class of comprehension axioms can be represented by a finite subclass, so that an automatic translation of finite higherorder problems into finite firstorder problems is possible. This translation is sound and complete with respect to a
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