Proof Development with Ωmega: The Irrationality of $$\sqrt 2$$

Siekmann, Jörg H.; Benzmüller, Christoph; Fiedler, Armin; Meier, Andreas; Normann, Immanuel; Pollet, Martin

doi:10.1007/978-94-017-0253-9_11

Cited by 21 publications

(20 citation statements)

References 20 publications

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“…The most notable integrations of automatic provers in proof assistants, either as oracles or with proof reconstruction, are probably Otter in ACL2 [25]; Bliksem and veriT in Coq [2,4]; Gandalf in HOL98 [18]; Z3 in HOL4 [11]; CVC Lite in HOL Light [26]; Vampire in Mizar [35]; Bliksem, EQP, LEO, Otter, PROTEIN, SPASS, TPS, and Waldmeister in ΩMEGA [39]; and Yices in PVS [36]. Of these, only LEO and Yices appear to have been significantly tailored to their host system.…”

Section: Related Workmentioning

confidence: 99%

More SPASS with Isabelle

Blanchette

Popescu

Wand

et al. 2012

Interactive Theorem Proving

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Abstract. 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 clause-selection 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 language-based security.

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Section: Related Workmentioning

confidence: 99%

More SPASS with Isabelle

Blanchette

Popescu

Wand

et al. 2012

Interactive Theorem Proving

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“…An APE includes a proof assistant and an intelligent interface Much research is done in the field of proof assistants, such as Mizar [44], Isabelle, Coq [10], or Ωmega [56], which include libraries of highly interlinked formal proofs and theorems [44,1], the backbone of our environment. Fig.…”

Section: An Environment For Correctness and Understandingmentioning

confidence: 99%

“…Users are usually presented with an extract of the fully formalised proof, but can explore the proof on different levels of abstractions (e.g. see the proof plan data structure PDS [7,22] in Ωmega [4,56] or high-level proofs in [13]), or request the system to print all steps, declarations, and definitions.…”

Section: An Environment For Correctness and Understandingmentioning

confidence: 99%

Formal Proof: Reconciling Correctness and Understanding

Calude

Müller

2009

Lecture Notes in Computer Science

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A good proof is a proof that makes us wiser. Manin [41, p. 209].Abstract. Hilbert's concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness reaches a standard that no pen-and-paper proof can match, but an essential component of mathematics -the insight and understanding -seems to be in short supply. So, what makes a proof understandable? To answer this question we first suggest a list of symptoms of understanding. We then propose a vision of an environment in which users can write and check formal proofs as well as query them with reference to the symptoms of understanding. In this way, the environment reconciles the main features of proof: correctness and understanding.

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“…There have been several attempts to combine interactive theorem provers (which are better at formal modeling than at proving theorems) with a variety of automatic theorem provers (ATPs) [1,7,20,39,42]. One of the most successful such combinations is Sledgehammer [27,34], which interfaces Isabelle/HOL [31] with resolution provers for classical first-order logic.…”

Section: Introductionmentioning

confidence: 99%

Extending Sledgehammer with SMT Solvers

Blanchette

Böhme

Paulson

2011

Lecture Notes in Computer Science

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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.

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Proof Development with Ωmega: The Irrationality of $$\sqrt 2$$

Cited by 21 publications

References 20 publications

More SPASS with Isabelle

More SPASS with Isabelle

Formal Proof: Reconciling Correctness and Understanding

Extending Sledgehammer with SMT Solvers

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