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24
Encoding Monomorphic and Polymorphic Types
"... Abstract. Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonot ..."
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Abstract. Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonotonic types must generally be encoded. We extend this work to rank1 polymorphism and show how to eliminate even more clutter. We also 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
Hybrid contract checking via symbolic simplification
 In: Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation
, 2012
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Monotonicity or how to encode polymorphic types safely and efficiently
"... Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are either bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonoton ..."
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Cited by 3 (3 self)
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Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are either bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonotonic types must generally be encoded. We extend this work to rank1 polymorphism and show how to eliminate even more clutter by also erasing most occurrences of nonmonotonic types, without sacrificing soundness or completeness. The new encodings are implemented in the Sledgehammer tool for Isabelle/HOL. Our evaluation finds them considerably superior to previous schemes.
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.
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.
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.
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
LEOII and Satallax on the Sledgehammer Test Bench
, 2012
"... Sledgehammer is a tool that harnesses external firstorder automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEOII and Satallax, the two most prominent higherorder ATPs, improving its performance on higherorder problems. To ex ..."
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Sledgehammer is a tool that harnesses external firstorder automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEOII and Satallax, the two most prominent higherorder ATPs, improving its performance on higherorder problems. To explore their usefulness, these ATPs are measured against firstorder ATPs and builtin Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library. Sledgehammer provides an ideal test bench for individual features of LEOII and Satallax, revealing areas for improvements.
A Shallow Embedding of Resolution and Superposition Proofs into the λΠCalculus Modulo
 PXTP
, 2013
"... The λΠcalculus modulo is a proof language that has been proposed as a proof standard for (re)checking and interoperability. Resolution and superposition are proofsearch methods that are used in stateoftheart firstorder automated theorem provers. We provide a shallow embedding of resolution an ..."
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The λΠcalculus modulo is a proof language that has been proposed as a proof standard for (re)checking and interoperability. Resolution and superposition are proofsearch methods that are used in stateoftheart firstorder automated theorem provers. We provide a shallow embedding of resolution and superposition proofs in the λΠcalculus modulo, thus offering a way to check these proofs in a trusted setting, and to combine them with other proofs. We implement this embedding as a backend of the prover iProver Modulo.