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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 (12 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 44 (7 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.
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 44 (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 sound and practical. We have investigated several methods of translating function applications, types and λabstractions. Omitting some type information improves the success rate, but can be unsound, so the interactive prover must verify the proofs. This paper presents experimental data that compares the translations in respect of their success rates for three automatic 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 43 (20 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
Sledgehammer: Judgement Day
 In Giesl and Hähnle [62
"... Abstract. Sledgehammer, a component of the interactive theorem prover Isabelle, finds proofs in higherorder logic by calling the automated provers for firstorder logic E, SPASS and Vampire. This paper is the largest and most detailed empirical evaluation of such a link to date. Our test data cons ..."
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Cited by 38 (4 self)
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Abstract. Sledgehammer, a component of the interactive theorem prover Isabelle, finds proofs in higherorder logic by calling the automated provers for firstorder logic E, SPASS and Vampire. This paper is the largest and most detailed empirical evaluation of such a link to date. Our test data consists of 1240 proof goals arising in 7 diverse Isabelle theories, thus representing typical Isabelle proof obligations. We measure the effectiveness of Sledgehammer and many other parameters such as run time and complexity of proofs. A facility for minimizing the number of facts needed to prove a goal is presented and analyzed.
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 26 (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
Using firstorder theorem provers in the Jahob data structure verification system
 In Byron Cook and Andreas Podelski, editors, Verification, Model Checking, and Abstract Interpretation, LNCS 4349
, 2007
"... Abstract. This paper presents our integration of efficient resolutionbased theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data st ..."
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Cited by 23 (2 self)
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Abstract. This paper presents our integration of efficient resolutionbased theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data structures, including data structures such as hash tables and search trees, without the need for interactive theorem proving or techniques tailored to individual data structures. Our primary technical results include: (1) a translation from higherorder logic to firstorder logic that enables the application of resolutionbased theorem provers and (2) a proof that eliminating type (sort) information in formulas is both sound and complete, even in the presence of a generic equality operator. Moreover, our experimental results show that the elimination of this type information dramatically decreases the time required to prove the resulting formulas. These techniques enabled us to verify complex correctness properties of Java programs such as a mutable set implemented as an imperative linked list, a finite map implemented as a functional ordered tree, a hash table with a mutable array, and a simple library system example that uses these container data structures. Our system verifies (in a matter of minutes) that data structure operations correctly update the finite map, that they preserve data structure invariants (such as ordering of elements, membership in appropriate hash table buckets, or relationships between sets and relations), and that there are no runtime errors such as null dereferences or array out of bounds accesses. 1
MaSh: Machine learning for Sledgehammer
 In Sandrine Blazy, Christine PaulinMohring, and David Pichardie, editors, ITP, volume 7998 of Lecture Notes in Computer Science
, 2013
"... Abstract. Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the relevance filter, heuristically ranks the thousands of facts available and selects a subset, based on syntactic similarity to the current goal. We introduce MaSh, an alternative tha ..."
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Cited by 22 (17 self)
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Abstract. Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the relevance filter, heuristically ranks the thousands of facts available and selects a subset, based on syntactic similarity to the current goal. We introduce MaSh, an alternative that learns from successful proofs. New challenges arose from our "zeroclick" vision: MaSh should integrate seamlessly with the users' workflow, so that they benefit from machine learning without having to install software, set up servers, or guide the learning. The underlying machinery draws on recent research in the context of Mizar and HOL Light, with a number of enhancements. MaSh outperforms the old relevance filter on large formalizations, and a particularly strong filter is obtained by combining the two filters.
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 20 (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, it is necessary to translate higherorder logic formulae to firstorder form. This translation should ideally be both sound and practical. We have implemented three higherorder to firstorder translations, with particular emphasis on the translation of types. Omitting some type information improves the success rate, but can be unsound, so the interactive prover must verify the proofs. In this paper, we will describe our translations and experimental data that compares the three translations in respect of their success rates for various automatic provers. 1