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34
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 50 (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
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
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 29 (10 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
Experiments on supporting interactive proof using resolution
 In Basin and Rusinowitch [4
"... Abstract. Interactive theorem provers can model complex systems, but require much effort to prove theorems. Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications. This paper reports a series of experiments designed to determine whethe ..."
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Cited by 28 (8 self)
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Abstract. Interactive theorem provers can model complex systems, but require much effort to prove theorems. Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications. This paper reports a series of experiments designed to determine whether resolution can support interactive proof as it is currently done. In particular, we present a sound and practical encoding in firstorder logic of Isabelle’s type classes. 1
Expressiveness + automation + soundness: Towards combining SMT solvers and interactive proof assistants
 In Tools and Algorithms for Construction and Analysis of Systems (TACAS
, 2006
"... Abstract. Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proofpr ..."
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Cited by 23 (5 self)
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Abstract. Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proofproducing SMT (Satisfiability Modulo Theories) solver that contains a SAT engine and a decision procedure for quantifierfree firstorder logic with equality. As a result, a user benefits from the expressiveness of Isabelle/HOL when modeling a system, but obtains much better automation for those fragments of the proofs that fall within the scope of the (automatic) SMT solver. Soundness is not compromised because all proofs are submitted to the trusted kernel of Isabelle for certification. This architecture is straightforward to extend for other interactive proof assistants and proofproducing reasoners. 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 19 (5 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. 1
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.
SourceLevel Proof Reconstruction for Interactive Theorem Proving
"... Abstract. Interactive proof assistants should verify the proofs they receive from automatic theorem provers. Normally this proof reconstruction takes place internally, forming part of the integration between the two tools. We have implemented sourcelevel proof reconstruction: resolution proofs are ..."
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Cited by 17 (2 self)
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Abstract. Interactive proof assistants should verify the proofs they receive from automatic theorem provers. Normally this proof reconstruction takes place internally, forming part of the integration between the two tools. We have implemented sourcelevel proof reconstruction: resolution proofs are automatically translated to Isabelle proof scripts. Users can insert this text into their proof development or (if they wish) examine it manually. Each step of a proof is justified by calling Hurd’s Metis prover, which we have ported to Isabelle. A recurrent issue in this project is the treatment of Isabelle’s axiomatic type classes. 1
Zenon: an Extensible Automated Theorem Prover Producing Checkable Proofs
"... Abstract. We present Zenon, an automated theorem prover for first order classical logic (with equality), based on the tableau method. Zenon is intended to be the dedicated prover of the Focal environment, an objectoriented algebraic specification and proof system, which is able to produce OCaml code ..."
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Cited by 16 (4 self)
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Abstract. We present Zenon, an automated theorem prover for first order classical logic (with equality), based on the tableau method. Zenon is intended to be the dedicated prover of the Focal environment, an objectoriented algebraic specification and proof system, which is able to produce OCaml code for execution and Coq code for certification. Zenon can directly generate Coq proofs (proof scripts or proof terms), which can be reinserted in the Coq specifications produced by Focal. Zenon can also be extended, which makes specific (and possibly local) automation possible in Focal. 1
Nivelle. Automated proof construction in type theory using resolution
 Special Issue Mechanizing and Automating Mathematics: In honour of N.G. de Bruijn
, 2002
"... Abstract. We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. − A clausification procedure in type theory, equipped with a correctness proof, all encoded using higherorder primitive recursion. − A novel representation of clauses ..."
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Cited by 16 (0 self)
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Abstract. We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. − A clausification procedure in type theory, equipped with a correctness proof, all encoded using higherorder primitive recursion. − A novel representation of clauses in minimal logic such that the λrepresentation of resolution steps is linear in the size of the premisses. − A translation of resolution proofs into lambda terms, yielding a verification procedure for those proofs. − The power of resolution theorem provers becomes available in interactive proof construction systems based on type theory. 1.