A Declarative Language for the Coq Proof Assistant

Corbineau, Pierre

doi:10.1007/978-3-540-68103-8_5

Cited by 39 publications

(27 citation statements)

References 13 publications

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“…It is an open question whether the same results can be achieved for more complex declarative languages whose statements could alter partial proof terms in a non structural way. Our understanding is that this is the case at least for the proof language presented in [4].…”

Section: Discussionmentioning

confidence: 96%

Declarative Representation of Proof Terms

Coen

2009

J Autom Reasoning

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Abstract. We present a declarative language inspired by the pseudonatural language used in Matita for the explanation of proof terms. We show how to compile the language to proof terms and how to automatically generate declarative scripts from proof terms. Then we investigate the relationship between the two translations, identifying the amount of proof structure preserved by compilation and re-generation of declarative scripts.

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Section: Discussionmentioning

confidence: 96%

Declarative Representation of Proof Terms

Coen

2009

J Autom Reasoning

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“…The result of this work was the environment Mizar Mode for HOL enabling writing proofs in a Mizar declarative way [24]. The similar solutions were implemented in other procedural proof assistants, e.g., Declare [25], Isar language for Isabelle [18], Mizar-light for HOL Light [26], miz3 for HOL Light [27], [28]. However, the similarity between these environments and Mizar system generally is limited to a few rules that are similar to the rules of the S. Jaśkowski natural deduction style [29], responsible for the universal quantifier introduction, the thesis indication, the implication elimination, the introduction of the reasoning by cases.…”

Section: Mizar and Corresponding Object Logicmentioning

confidence: 99%

Progress in the Independent Certiﬁcation of Mizar Mathematical Library in Isabelle

Kaliszyk

Pąk

2017

Annals of Computer Science and Information Systems

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Abstract-The Mizar Mathematical Library is one of the largest collections of machine understandable formal proofs encompassing many areas of today mathematics including results from algebra, analysis, topology, and lattice theory. The Mizar system has so far been the only tool able to completely process, certify, and make use of these developments. In this paper, we present the progress in the development of an independent certification mechanism of Mizar proofs based on the Isabelle logical framework. The approach allows rechecking the Mizar formal proofs based on a more succinct and more precisely specified formal infrastructure. Additionally, it necessitates a full formal specification of the mechanisms that ensure the correctness of the defined objects, in particular, the proofs that such mechanisms are correct. The development already covers an important part of the Mizar library foundations. We improve the mechanism for defining Mizar structures and show that it permits simpler validation of proof developments involving such objects. To demonstrate this, we perform a complete translation of the Mizar net of basic algebraic structures including their attributes and certify all the corresponding proofs in Isabelle.

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“…Since each step of the reasoning can have at most one premise located in the preceding step, intuitions related to the 3rd MIL problem can be expressed as follows: a step where at least some of the information it requires is available in the directly preceding step is more comprehensive than a step in which all information is far away in the proof. This interpretation has a lot in common with the construction then implemented in Mizar, Isabelle/Isar and other systems where the proof style inspired by Mizar is implemented: Declare [25], Mizar Mode for HOL [15], Mizar-light for HOL-light [29], MMode for Coq [6], declarative proof language (DPL) for Coq [4]. The construction then indicates that a fact derived directly before should be used in the current step as (part of) its justification.…”

Section: Formulation Of Behaghel's Law Determinantsmentioning

confidence: 99%

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

Pąk

2015

J Autom Reasoning

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Proof development in proof assistants such as HOL, Coq, Mizar, etc. is an activity where authors usually produce proofs by typing out proof scripts or system tactics. Quite frequently, however, authors also have to read existing proof scripts, either to imitate smart proof pieces, or to refactor fragments of reasoning to make some theorem stronger, more easily applicable and so on. Therefore, it is important to develop techniques to improve legibility of proofs, since it directly affects productivity of script writers. To analyze the legibility of natural deduction proofs, we investigate proof graphs that represent the flow of information in given reasoning. Our analysis of the information flow leads to methods of improving proof readability based on Behaghel's First Law, which states that in legible text relevant pieces of information must occur close to each other. The presented method maximizes the number of close connections between premises and steps that use these steps as justification. In this paper we show that our optimization method is NP-hard.

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A Declarative Language for the Coq Proof Assistant

Cited by 39 publications

References 13 publications

Declarative Representation of Proof Terms

Declarative Representation of Proof Terms

Progress in the Independent Certiﬁcation of Mizar Mathematical Library in Isabelle

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

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