Results 11  20
of
27
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 ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
(Show Context)
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.
Combinations of theories and the BernaysSchönfinkelRamsey class
 4th International Verification Workshop  VERIFY’07, Bremen
, 2007
"... Abstract. The BernaysSchönfinkelRamsey (BSR) class of formulas is the class of formulas that, when written in prenex normal form, have an ∃ ∗ ∀ ∗ quantifier prefix and do not contain any function symbols. This class is decidable. We show here that BSR theories can furthermore be combined with a ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
Abstract. The BernaysSchönfinkelRamsey (BSR) class of formulas is the class of formulas that, when written in prenex normal form, have an ∃ ∗ ∀ ∗ quantifier prefix and do not contain any function symbols. This class is decidable. We show here that BSR theories can furthermore be combined with another disjoint decidable theory, so that we obtain a decision procedure for quantifierfree formulas in the combination of the BSR theory and another decidable theory. The classical NelsonOppen combination scheme requires theories to be stablyinfinite, ensuring that, if a model is found for both theories in the combination, models agree on cardinalities and a global model can be built. We show that combinations with BSR theories can be much more permissive, even though BSR theories are not always stablyinfinite. We state that it is possible to describe exactly all the (finite or infinite) cardinalities of the models of a given BSR theory. For the other theory, it is thus only required to be able to decide if there exists a model of a given cardinality. With this result, it is notably possible to use some set operators, operators on relations, orders — any operator that can be expressed by a set of BSR formulas — together with the usual objects of SMT solvers, notably integers, reals, uninterpreted symbols, enumerated types. 1
Verifying SAT and SMT in Coq for a fully automated decision procedure
 PSATTT'11: INTERNATIONAL WORKSHOP ON PROOFSEARCH IN AXIOMATIC THEORIES AND TYPE THEORIES
, 2011
"... Enjoying the power of SAT and SMT solvers in the Coq proof assistant without compromising soundness requires more than a yes/no answer from them. SAT and SMT solvers should also return a proof witness that can be checked by an external tool. We propose a fully certified checker for such witnesses w ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Enjoying the power of SAT and SMT solvers in the Coq proof assistant without compromising soundness requires more than a yes/no answer from them. SAT and SMT solvers should also return a proof witness that can be checked by an external tool. We propose a fully certified checker for such witnesses written in Coq. It can currently check witnesses from the SAT solvers ZChaff and MiniSat and from the SMT solver VeriT. Experiments highlight the efficiency of this checker. On top of it, new reflexive Coq tactics have been built that can decide a subset of Coq’s logic by calling external provers and carefully checking their answers.
versat: A Verified Modern SAT Solver
"... Abstract. This paper presents versat, a formally verified SAT solver incorporating the essential features of modern SAT solvers, including clause learning, watched literals, optimized conflict analysis, nonchronological backtracking, and decision heuristics. Unlike previous related work on SATs ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents versat, a formally verified SAT solver incorporating the essential features of modern SAT solvers, including clause learning, watched literals, optimized conflict analysis, nonchronological backtracking, and decision heuristics. Unlike previous related work on SATsolver verification, our implementation uses efficient lowlevel data structures like mutable C arrays for clauses and other solver state, and machine integers for literals. The implementation and proofs are written in GURU, a verifiedprogramming language. We compare versat to a stateoftheart SAT solver that produces certified “unsat ” answers. We also show through an empirical evaluation that versat can solve SAT problems on the modern scale. 1
Using Yices as an automated solver in Isabelle/HOL
 In Automated Formal Methods’08
, 2008
"... We describe our integration of the Yices SMT solver into the Isabelle theorem prover. This integration allows users to take advantage of the powerful SMT solving techniques within the interactive theorem proving environment of Isabelle, considerably increasing the automation level for a significant ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We describe our integration of the Yices SMT solver into the Isabelle theorem prover. This integration allows users to take advantage of the powerful SMT solving techniques within the interactive theorem proving environment of Isabelle, considerably increasing the automation level for a significant subset of Isabelle/HOL. 1.
Proof reconstruction for firstorder logic and settheoretical constructions
 Sixth International Workshop on Automated Verification of Critical Systems (AVOCS ’06) – Preliminary Proceedings
, 2006
"... Proof reconstruction is a technique that combines an interactive theorem prover and an automatic one in a sound way, so that users benefit from the expressiveness of the first tool and the automation of the latter. We present an implementation of proof reconstruction for firstorder logic and setth ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Proof reconstruction is a technique that combines an interactive theorem prover and an automatic one in a sound way, so that users benefit from the expressiveness of the first tool and the automation of the latter. We present an implementation of proof reconstruction for firstorder logic and settheoretical constructions between the interactive theorem prover Isabelle and the automatic SMT prover haRVey. 1
An interpretation of isabelle/hol in hol light
 In Furbach and Shankar [20
"... Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabe ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light. 1
On setdriven combination of logics and verifiers
, 2009
"... Abstract. We explore the problem of automated reasoning about the nondisjoint combination of logics that share set variables and operations. We prove a general combination theorem, and apply it to show the decidability for the quantifierfree combination of formulas in WS2S, twovarible logic with c ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We explore the problem of automated reasoning about the nondisjoint combination of logics that share set variables and operations. We prove a general combination theorem, and apply it to show the decidability for the quantifierfree combination of formulas in WS2S, twovarible logic with counting, and Boolean Algebra with Presburger Arithmetic. Furthermore, we present an overapproximating algorithm that uses such combined logics to synthesize universally quantified invariants of infinitestate systems. The algorithm simultaneously synthesizes loop invariants of interest, and infers the relationships between sets to exchange the information between logics. We have implemented this algorithm and used it to prove detailed correctness properties of operations of linked data structure implementations. 1
A NelsonOppen based Proof System using Theory Specific Proof Systems
, 2011
"... SMT solvers are nowadays pervasive in verification tools. When the verification is about a critical system, the result of the SMT solver is also critical and cannot be trusted. The SMTLIB 2.0 is a standard interface for SMT solvers but does not specify the output of the getproof command. We presen ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
SMT solvers are nowadays pervasive in verification tools. When the verification is about a critical system, the result of the SMT solver is also critical and cannot be trusted. The SMTLIB 2.0 is a standard interface for SMT solvers but does not specify the output of the getproof command. We present a proof system that is geared towards SMT solvers and follows their conceptually modular architecture. Our proof system makes a clear distinction between propositional and theory reasoning. Moreover, individual theories provide specific proof systems that are combined using the NelsonOppen proof scheme. We propose specific proof systems for linear real arithmetic (LRA) and uninterpreted functions (EUF) and discuss proof generation and proof checking. We have evaluated the cost of generating proofs in our proof system. Our experiments on benchmarks taken from the SMTLIB library show that the simple mechanisms used in our approach suffice for a large majority of the selected benchmarks.
Noname manuscript No. (will be inserted by the editor) Extending Sledgehammer with SMT Solvers
"... the date of receipt and acceptance should be inserted later Abstract Sledgehammer is a component of Isabelle/HOL that employs resolutionbased firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is succe ..."
Abstract
 Add to MetaCart
the date of receipt and acceptance should be inserted later Abstract Sledgehammer is a component of Isabelle/HOL that employs resolutionbased 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. The ATPs and SMT solvers nicely complement each other, and Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs ’ reach. 1