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47
2001b, ‘The CADE17 ATP System Competition
 Journal of Automated Reasoning
"... Abstract. The results of the IJCAR ATP System Competition are presented. ..."
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Abstract. The results of the IJCAR ATP System Competition are presented.
Encoding monomorphic and polymorphic types
, 2012
"... Abstract. Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings ..."
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Cited by 27 (14 self)
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Abstract. Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of “cover”. The new encodings are implemented, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes. 1
MaSh: Machine Learning for Sledgehammer
"... 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 ..."
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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. 1
MetiTarski: Past and Future
"... Abstract. A brief overview is presented of MetiTarski [4], an automatic theorem prover for realvalued special functions: ln, exp, sin, cos, etc. MetiTarski operates through a unique interaction between decision procedures and resolution theorem proving. Its history is briefly outlined, along with c ..."
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Abstract. A brief overview is presented of MetiTarski [4], an automatic theorem prover for realvalued special functions: ln, exp, sin, cos, etc. MetiTarski operates through a unique interaction between decision procedures and resolution theorem proving. Its history is briefly outlined, along with current projects. A simple collision avoidance example is presented. 1
HALO: Haskell to Logic through Denotational Semantics
"... Even welltyped programs can go wrong, by encountering a patternmatch failure, or simply returning the wrong answer. An increasinglypopular response is to allow programmers to write contracts that express semantic properties, such as crashfreedom or some useful postcondition. We study the static ..."
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Even welltyped programs can go wrong, by encountering a patternmatch failure, or simply returning the wrong answer. An increasinglypopular response is to allow programmers to write contracts that express semantic properties, such as crashfreedom or some useful postcondition. We study the static verification of such contracts. Our main contribution is a novel translation to firstorder logic of both Haskell programs, and contracts written in Haskell, all justified by denotational semantics. This translation enables us to prove that functions satisfy their contracts using an offtheshelf firstorder logic theorem prover. 1.
Automatic Proof and Disproof in Isabelle/HOL
, 2011
"... Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation. Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the c ..."
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Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation. Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the counterexample generator Quickcheck uses the ML compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT. Together with the Isar structured proof format and a new asynchronous user interface, these tools have radically transformed the Isabelle user experience. This paper provides an overview of the main automatic proof and disproof tools.
Quantifier instantiation techniques for finite model finding in SMT
 Proceedings of the 24th International Conference on Automated Deduction (Lake Placid, NY, USA), 2013, LNCS 7898
"... Abstract. SMTbased applications increasingly rely on SMT solvers being able to deal with quantified formulas. Current work shows that for formulas with quantifiers over uninterpreted sorts countermodels can be obtained by integrating a finite model finding capability into the architecture of a mo ..."
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Abstract. SMTbased applications increasingly rely on SMT solvers being able to deal with quantified formulas. Current work shows that for formulas with quantifiers over uninterpreted sorts countermodels can be obtained by integrating a finite model finding capability into the architecture of a modern SMT solver. We examine various strategies for ondemand quantifier instantiation in this setting. Here, completeness can be achieved by considering all ground instances over the finite domain of each quantifier. However, exhaustive instantiation quickly becomes unfeasible with larger domain sizes. We propose instantiation strategies to identify and consider only a selection of ground instances that suffices to determine the satisfiability of the input formula. We also examine heuristic quantifier instantiation techniques such as Ematching for the purpose of accelerating the search. We give experimental evidence that our approach is practical for use in industrial applications and is competitive with other approaches. 1
More SPASS with Isabelle  Superposition with hard sorts and configurable simplification
, 2012
"... Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types ..."
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Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clauseselection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a case study featuring a formalization of languagebased security.
Finding conflicting instances of quantified formulas in SMT
 In Formal Methods in ComputerAided Design (FMCAD
"... (SMT) solvers have been used successfully in a variety of applications including verification, automated theorem proving, and synthesis. While such solvers are highly adept at handling ground constraints in several decidable background theories, they primarily rely on heuristic quantifier instantiat ..."
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(SMT) solvers have been used successfully in a variety of applications including verification, automated theorem proving, and synthesis. While such solvers are highly adept at handling ground constraints in several decidable background theories, they primarily rely on heuristic quantifier instantiation methods such as Ematching to process quantified formulas. The success of these methods is often hindered by an overproduction of instantiations which makes ground level reasoning difficult. We introduce a new technique that alleviates this shortcoming by first discovering instantiations that are in conflict with the current state of the solver. The solver only resorts to traditional heuristic methods when such instantiations cannot be found, thus decreasing its dependence upon Ematching. Our experimental results show that our technique significantly reduces the number of instantiations required by an SMT solver to answer “unsatisfiable ” for several benchmark libraries, and consequently leads to improvements over stateoftheart implementations. I.