Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

Blanchette, Jasmin Christian

doi:10.1145/3293880.3294087

Cited by 28 publications

(20 citation statements)

References 65 publications

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“…The results are summarized in the following table, showing for each prover how many unsatisfiable and satisfiable problems were solved and how many seconds were needed on average by each prover on the problems that were solved by all four: The detailed results of the evaluation are available online, together with instructions for reproducing them. 3 As expected, RP x is not competitive. A prover's performance comes from its calculus, its heuristics, and its indexing data structures.…”

Section: Obtaining Executable Codesupporting

confidence: 64%

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A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness. Methodologically, we apply stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for first-order logic. CCS Concepts • Theory of computation → Logic and verification; Automated reasoning;

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Section: Obtaining Executable Codesupporting

confidence: 64%

“…The present work is part of the IsaFoL (Isabelle Formalization of Logic) project, 1 which aims at developing a library of results about logic and automated reasoning [3]. The Isabelle files are available in the Archive of Formal Proofs [38,39] and in the IsaFoL repository.…”

mentioning

confidence: 99%

A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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“…Jasmin Christian Blanchette recently remarked that the automated reasoning community has largely stood on the sidelines of developments in proof assistants, preferring to 'reflexively turn to "pen and paper" -by which we usually mean L A T E X to define our logics, specify our proof systems, and establish their soundness and completeness' [5]. In a similar vein, we urge logic teachers to become early adopters of proof assistants.…”

Section: Discussionmentioning

confidence: 99%

Isabelle/HOL as a Meta-Language for Teaching Logic

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Villadsen

Blackburn

2020

Electron. Proc. Theor. Comput. Sci.

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Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of classical propositional logic with only two primitive symbols), the second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided sequent calculus that uses our Sequent Calculus Verifier (SeCaV). We describe each formalization in turn, concentrating on how we used them in our teaching, and commenting on features that are interesting or useful from a logic education perspective. In the conclusion, we reflect on the lessons learned and where they might lead us next.

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“…We have not found related work where a miniature proof assistant is developed inside another proof assistant. Overall our approach is related to the IsaFoL -Isabelle Formalization of Logic (https:// bitbucket.org/isafol) project which unites researchers in formalizing logic in Isabelle [1]. Among the formalizations in the project are SAT-solving, first-order resolution, a paraconsistent logic, natural deduction, sequent calculi and more.…”

Section: Discussionmentioning

confidence: 99%

Students' Proof Assistant (SPA)

Schlichtkrull¹,

Villadsen²,

From

2019

Electron. Proc. Theor. Comput. Sci.

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The Students' Proof Assistant (SPA) aims to both teach how to use a proof assistant like Isabelle and also to teach how reliable proof assistants are built. Technically it is a miniature proof assistant inside the Isabelle proof assistant. In addition we conjecture that a good way to teach structured proving is with a concrete prover where the connection between semantics, proof system, and prover is clear. The proofs in Lamport's TLAPS proof assistant have a very similar structure to those in the declarative prover SPA. To illustrate this we compare a proof of Pelletier's problem 43 in TLAPS, Isabelle/Isar and SPA. We also consider Pelletier's problem 34, also known as Andrews's Challenge, where students are encouraged to develop their own justification function and thus obtain a lot of insight into the proof assistant. Although SPA is fully functional we have so far only used it in a few educational scenarios.

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Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

Cited by 28 publications

References 65 publications

A verified prover based on ordered resolution

A verified prover based on ordered resolution

Isabelle/HOL as a Meta-Language for Teaching Logic

Students' Proof Assistant (SPA)

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