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32
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: an ‘LCFstyle’ logical kernel for clausal firstorder logic. This allows the choice of different logical mappings between higherorder logic and firstorder logic to be used depending on the subgoal, and also enables several different firstorder proof procedures to cooperate on constructing the proof. This work was carried out using the HOL4 theorem prover; we comment on the ease of transferring the technology to other higherorder logic theorem provers. 1
Integrating Gandalf and HOL
 Theorem Proving in Higher Order Logics: TPHOLs ’99, LNCS 1690
, 1999
"... Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a ..."
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Cited by 49 (2 self)
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Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a Gandalf server may be set up servicing multiple HOL clients. In addition, the translation of the Gandalf proof into HOL fits in with the LCF model and guarantees logical consistency.
Lightweight relevance filtering for machinegenerated resolution problems
 In ESCoR: Empirically Successful Computerized Reasoning
, 2006
"... Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial set ..."
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Cited by 48 (9 self)
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Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial settings. We have designed these techniques as part of a project to link automatic theorem provers to the interactive theorem prover Isabelle. They should be applicable to other situations where the resolution problems are produced mechanically and where completeness is less important than achieving a high success rate with limited processor time. 1
The KEY Approach: Integrating Object Oriented Design and Formal Verification
, 2000
"... This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification. A distinctive feature of our approach is the use of a commercial CASE tool enhanced with functionality for formal specifiation an ..."
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Cited by 47 (19 self)
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This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification. A distinctive feature of our approach is the use of a commercial CASE tool enhanced with functionality for formal specifiation and deductive verification.
Extending Sledgehammer with SMT Solvers
"... Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sl ..."
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Cited by 47 (11 self)
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Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture. Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs ’ reach. Remarkably, the best SMT solver performs better than the best ATP on most of our benchmarks. 1
Three Years of Experience with Sledgehammer, a Practical Link between Automatic and Interactive Theorem Provers
"... Sledgehammer is a highly successful subsystem of Isabelle/HOL that calls automatic theorem provers to assist with interactive proof construction. It requires no user configuration: it can be invoked with a single mouse gesture at any point in a proof. It automatically finds relevant lemmas from all ..."
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Cited by 42 (6 self)
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Sledgehammer is a highly successful subsystem of Isabelle/HOL that calls automatic theorem provers to assist with interactive proof construction. It requires no user configuration: it can be invoked with a single mouse gesture at any point in a proof. It automatically finds relevant lemmas from all those currently available. An unusual aspect of its architecture is its use of unsound translations, coupled with its delivery of results as Isabelle/HOL proof scripts: its output cannot be trusted, but it does not need to be trusted. Sledgehammer works well with Isar structured proofs and allows beginners to prove challenging theorems.
Structured Specifications and Interactive Proofs with KIV
, 1998
"... The aim of this chapter is to describe the integrated specification and theorem proving environment of KIV. KIV is an advanced tool for developing high assurance systems. It supports:  hierarchical formal specification of software and system designs  specification of safety/security models  ..."
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Cited by 36 (28 self)
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The aim of this chapter is to describe the integrated specification and theorem proving environment of KIV. KIV is an advanced tool for developing high assurance systems. It supports:  hierarchical formal specification of software and system designs  specification of safety/security models  proving properties of specifications  modular implementation of specification components  modular verification of implementations  incremental verification and error correction  reuse of specifications, proofs, and verified components KIV supports the entire design process from formal specifications to verified code. It supports functional as well as statebased modeling. KIV is ready for use, and has been tested in a number of indu...
Automation for interactive proof: First prototype
 Information and Computation
"... Interactive theorem provers require too much effort from their users. We have been developing a system in which Isabelle users obtain automatic support from automatic theorem provers (ATPs) such as Vampire and SPASS. An ATP is invoked at suitable points in the interactive session, and any proof foun ..."
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Cited by 30 (8 self)
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Interactive theorem provers require too much effort from their users. We have been developing a system in which Isabelle users obtain automatic support from automatic theorem provers (ATPs) such as Vampire and SPASS. An ATP is invoked at suitable points in the interactive session, and any proof found is given to the user in a window displaying an Isar proof script. There are numerous differences between Isabelle (polymorphic higherorder logic with type classes, natural deduction rule format) and classical ATPs (firstorder, untyped, clause form). Many of these differences have been bridged, and a working prototype that uses background processes already provides much of the desired functionality. 1