Locales: A Module System for Mathematical Theories

Ballarin, Clemens

doi:10.1007/s10817-013-9284-7

Cited by 69 publications

(58 citation statements)

References 12 publications

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“…Its logic-based on classical simple type theory-balances expressiveness and automatability. We benefited from many features of the system, including codatatypes [5], Isabelle/jEdit [28], the Isar proof language [27], locales [4], and Sledgehammer [8]. It is perhaps indicative of the maturity of theorem proving technology that most of the issues we encountered were unrelated to Isabelle.…”

Section: Discussion and Related Workmentioning

confidence: 99%

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Formalizing Bachmair and Ganzinger's Ordered Resolution Prover

Schlichtkrull¹,

Blanchette²,

Traytel³

et al. 2018

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Abstract. We present a formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving in Isabelle/HOL, culminating with a refutationally complete first-order prover based on ordered resolution with literal selection. We develop general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. Our work clarifies several of the fine points in the chapter's text, emphasizing the value of formal proofs in the field of automated reasoning.

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Section: Discussion and Related Workmentioning

confidence: 99%

“…We exploit this to keep the development parameterized by a type of atoms a and an abstract type of substitutions s, through Isabelle locales [4] (Abstract _ Substitution.thy). A locale represents a module parameterized by types and terms that satisfy some assumptions.…”

Section: Preliminariesmentioning

confidence: 99%

Formalizing Bachmair and Ganzinger's Ordered Resolution Prover

Schlichtkrull¹,

Blanchette²,

Traytel³

et al. 2018

EasyChair Preprints

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show abstract

“…We first prove structural invariants on arbitrary states (M , N ) reachable from ( , N ), namely: (1) each variable occurs at most once in M ; (2) …”

Section: Is Satisfiable If and Only If M Nmentioning

confidence: 99%

“…The SMT solvers, and one of the superposition provers [56], are built around a SAT solver, resulting in a situation where SAT solvers are employed to prove their own metatheory. -Locales [2,25] parameterize theories over operations and assumptions, encouraging a modular style. They are useful to express hierarchies of concepts and to reduce the number of parameters and assumptions that must be threaded through a formal development.…”

Section: Introductionmentioning

confidence: 99%

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

Blanchette

Fleury

Weidenbach

2016

Automated Reasoning

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We developed a formal framework for conflict-driven clause learning (CDCL) using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL calculus is connected first to a more concrete calculus, then to a SAT solver expressed in a functional programming language, and finally to a SAT solver in an imperative language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants, including the Davis-Putnam-Logemann-Loveland (DPLL) calculus. The imperative program relies on the two-watched-literal data structure and other optimizations found in modern solvers. We used Isabelle's Refinement Framework to automate the most tedious refinement steps. The most noteworthy aspects of our work are the inclusion of rules for forget, restart, and incremental solving and the application of stepwise refinement.

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“…• Locales [Ballarin, 2014] parameterize theories over operations and assumptions, encouraging a modular style of development. They are useful to express hierarchies of related concepts and to reduce the number of parameters and assumptions that must be passed around.…”

Section: Introductionmentioning

confidence: 99%

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

Blanchette

Fleury

Weidenbach

2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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We developed a formal framework for SAT solving using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL (conflictdriven clause learning) calculus is connected to a SAT solver that always terminates with correct answers. The framework offers a convenient way to prove theorems about the SAT solver and experiment with variants of the calculus. Compared with earlier verifications, the main novelties are the inclusion of the CDCL rules for forget, restart, and incremental solving and the use of refinement.

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Locales: A Module System for Mathematical Theories

Cited by 69 publications

References 12 publications

Formalizing Bachmair and Ganzinger's Ordered Resolution Prover

Formalizing Bachmair and Ganzinger's Ordered Resolution Prover

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

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