The OpenTheory Standard Theory Library

Hurd, Joe

doi:10.1007/978-3-642-20398-5_14

Cited by 44 publications

(48 citation statements)

References 23 publications

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“…Note that, Harrison's formalisation lives within the HOL Light theorem prover, but the rest of our work lives within the HOL4 theorem prover [7]. To bridge this gap, we transported our extension of Harrison's development from HOL Light into HOL4 using the OpenTheory toolchain [3]. OpenTheory replays the primitive inferences from one prover inside another.…”

Section: Methodsmentioning

confidence: 99%

Steps towards Verified Implementations of HOL Light

Myreen

Owens

Kumar

2013

Interactive Theorem Proving

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Abstract. This short paper describes our plans and progress towards construction of verified ML implementations of HOL Light: the first formally proved soundness result for an LCF-style prover. Building on Harrison's formalisation of the HOL Light logic and our previous work on proof-producing synthesis of ML, we have produced verified implementations of each of HOL Light's kernel functions. What remains is extending Harrison's soundness proof and proving that ML's module system provides the required abstraction for soundness of the kernel to relate to the entire theorem prover. The proofs described in this paper involve the HOL Light and HOL4 theorem provers and the OpenTheory toolchain.

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Section: Methodsmentioning

confidence: 99%

Steps towards Verified Implementations of HOL Light

Myreen

Owens

Kumar

2013

Interactive Theorem Proving

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“…Previous work has established connections between different provers at the level of their internal logics [1,[12][13][14][15]39]. These enable results proved in one system to be made available in another, but they do not provide usable source definitions.…”

Section: Introductionmentioning

confidence: 99%

Lem

Mulligan

Owens

Gray

et al. 2014

Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming

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Recent years have seen remarkable successes in rigorous engineering: using mathematically rigorous semantic models (not just idealised calculi) of real-world processors, programming languages, protocols, and security mechanisms, for testing, proof, analysis, and design. Building these models is challenging, requiring experimentation, dialogue with vendors or standards bodies, and validation; their scale adds engineering issues akin to those of programming to the task of writing clear and usable mathematics. But language and tool support for specification is lacking. Proof assistants can be used but bring their own difficulties, and a model produced in one, perhaps requiring many person-years effort and maintained over an extended period, cannot be used by those familiar with another.We introduce Lem, a language for engineering reusable largescale semantic models. The Lem design takes inspiration both from functional programming languages and from proof assistants, and Lem definitions are translatable into OCaml for testing, Coq, HOL4, and Isabelle/HOL for proof, and LaTeX and HTML for presentation. This requires a delicate balance of expressiveness, careful library design, and implementation of transformations -akin to compilation, but subject to the constraint of producing usable and human-readable code for each target. Lem's effectiveness is demonstrated by its use in practice.

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“…A similar approach is done with SMTCoq [2] for the type-theory based proof assistant Coq. Other approaches exist: for example, the OpenTheory project [13] attempts to provide a framework where various HOL theorem provers can share proofs.…”

Section: Introductionmentioning

confidence: 99%

Foundational Proof Certificates in First-Order Logic

Chihani

Miller

Renaud

2013

Automated Deduction – CADE-24

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We present the design philosophy of a proof checker based on a notion of foundational proof certificates. At the heart of this design is a semantics of proof evidence that arises from recent advances in the theory of proofs for classical and intuitionistic logic. That semantics is then performed by a (higher-order) logic program: successful performance means that a formal proof of a theorem has been found. We describe how the λProlog programming language provides several features that help guarantee such a soundness claim. Some of these features (such as strong typing, abstract datatypes, and higher-order programming) were features of the ML programming language when it was first proposed as a proof checker for LCF. Other features of λProlog (such as support for bindings, substitution, and backtracking search) turn out to be equally important for describing and checking the proof evidence encoded in proof certificates. Since trusting our proof checker requires trusting a programming language implementation, we discuss various avenues for enhancing one's trust of such a checker.

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The OpenTheory Standard Theory Library

Cited by 44 publications

References 23 publications

Steps towards Verified Implementations of HOL Light

Steps towards Verified Implementations of HOL Light

Lem

Foundational Proof Certificates in First-Order Logic

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