Seventeen Provers Under the Hammer

Desharnais, Martin; Vukmirović, Petar; Blanchette, Jasmin; Wenzel, Makarius

doi:10.4230/lipics.itp.2022.8

Cited by 4 publications

(1 citation statement)

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“…In this case, the untrusted output of these external provers is used to guide the (re)construction of a formal proof. For instance, hammers [14], as well as SMTCoq [15] fall in this category. But interactive provers and automated provers usually do not speak the same logic: most interactive theorem provers implement a flavor of higher-order logic with inductive types, a strict superset of the fragments of first-order logic handled by automated theorem provers.…”

Section: Introductionmentioning

confidence: 99%

Compositional Pre-processing for Automated Reasoning in Dependent Type Theory

Blot

Cousineau

Crance

et al. 2023

Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs

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In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical fragment. This very often prevents users from applying these tactics in other contexts, even similar ones.This paper discusses the design and the implementation of pre-processing operations for automating formal proofs in the Coq proof assistant. It presents the implementation of a wide variety of predictible, atomic goal transformations, which can be composed in various ways to target different backends. A gallery of examples illustrates how it helps to expand significantly the power of automation engines.

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Section: Introductionmentioning

confidence: 99%

Compositional Pre-processing for Automated Reasoning in Dependent Type Theory

Blot

Cousineau

Crance

et al. 2023

Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs

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ALASCA: Reasoning in Quantified Linear Arithmetic

Korovin

Kovács

Reger

et al. 2023

Lecture Notes in Computer Science

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Automated reasoning is routinely used in the rigorous construction and analysis of complex systems. Among different theories, arithmetic stands out as one of the most frequently used and at the same time one of the most challenging in the presence of quantifiers and uninterpreted function symbols. First-order theorem provers perform very well on quantified problems due to the efficient superposition calculus, but support for arithmetic reasoning is limited to heuristic axioms. In this paper, we introduce the $$\textsc {Alasca}$$ A L A S C A calculus that lifts superposition reasoning to the linear arithmetic domain. We show that $$\textsc {Alasca}$$ A L A S C A is both sound and complete with respect to an axiomatisation of linear arithmetic. We implemented and evaluated $$\textsc {Alasca}$$ A L A S C A using the Vampire theorem prover, solving many more challenging problems compared to state-of-the-art reasoners.

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Hammering Floating-Point Arithmetic

Torstensson,

Weber

2023

Lecture Notes in Computer Science

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Sledgehammer, a component of the interactive proof assistant Isabelle/HOL, aims to increase proof automation by automatically discharging proof goals with the help of external provers. Among these provers are a group of satisfiability modulo theories (SMT) solvers with support for the SMT-LIB input language. Despite existing formalizations of IEEE floating-point arithmetic in both Isabelle/HOL and SMT-LIB, Sledgehammer employs an abstract translation of floating-point types and constants, depriving the SMT solvers of the opportunity to make use of their dedicated decision procedures for floating-point arithmetic.We show that, by extending Sledgehammer’s translation from the language of Isabelle/HOL into SMT-LIB with an interpretation of floating-point types and constants, floating-point reasoning in SMT solvers can be made available to Isabelle/HOL. Our main contribution is a description and implementation of such an extension. An evaluation of the extended translation shows a significant increase of Sledgehammer’s success rate on proof goals involving floating-point arithmetic.

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Seventeen Provers Under the Hammer

Cited by 4 publications

References 1 publication

Compositional Pre-processing for Automated Reasoning in Dependent Type Theory

Compositional Pre-processing for Automated Reasoning in Dependent Type Theory

ALASCA: Reasoning in Quantified Linear Arithmetic

Hammering Floating-Point Arithmetic

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