On Rewriting Rules in Mizar

Korniłowicz, Artur

doi:10.1007/s10817-012-9261-6

Cited by 30 publications

(21 citation statements)

References 8 publications

(6 reference statements)

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“…Its main modules are: -SCANNER and PARSER doing lexical analysis, checking validity of the article against the MIZAR grammar and creating parse-tree of a given article, [7,8]; -ANALYZER doing type-checking, identification and disambiguation of used symbols, resolving hidden arguments; -REASONER controlling the structure of reasonings; -PRECHECKER transforming entry inferences into their disjunctive normal form and processing Skolem constants (constants generated by basing on existential premises); -EQUALIZER computing the congruence closure of the universe of discourse collected from the given inference, [19]; -UNIFIER performing unification.…”

Section: About Mizarmentioning

confidence: 99%

Definitional Expansions in Mizar

Korniłowicz

2015

J Autom Reasoning

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The MIZAR VERIFIER uses definitional expansions for controlling proof structures. In this paper we propose another use of definitional expansions-enriching verified inferences by expansions of definitions of formulae included in the inferences and increasing the number of premises accessible by CHECKER. This introduces more knowledge to the reasoning, which helps to draw more conclusions. Some statistics about influence of such expansions on the MIZAR MATHEMATICAL LIBRARY are presented.

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Section: About Mizarmentioning

confidence: 99%

Definitional Expansions in Mizar

Korniłowicz

2015

J Autom Reasoning

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“…it also provides syntactic constructions to launch specialized algorithms for processing particular mechanisms (e.g. term identifications, term reductions [7], flexary connectives [8]) increasing computational power of VERIFIER (e.g. equational calculus [9], [10]).…”

Section: Introductionmentioning

confidence: 99%

Introducing Euclidean Relations to Mizar

Naumowicz

Korniłowicz

2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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Abstract-In this paper we present the methodology of implementing a new enhancement of the Mizar proof checker based on enabling special processing of Euclidean predicates, i.e. binary predicates which fulfill a specific variant of transitivity postulated by Euclid. Typically, every proof step in formal mathematical reasoning is associated with a formula to be proved and a list of references used to justify the formula. With the proposed enhancement, the Euclidean property of given relations can be registered during their definition, and so the verification of some proof steps related to these relations can be automated to avoid explicit referencing.

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“…Computer assisted proof development frameworks can check of the proofs scripts created in this way, according to the opinion of some proof writers, is extremely difficult or (i) the visualization of proof scripts in HTML format is being improved [27], (ii) the new Mizar language constructions [16,17,19] that stem from informal deductions are implemented into new versions of MML [10], respecting the license requirements [1], (iii) there are experiments with strengthening the Mizar inference checker by implementing selected computer algebra capabilities in order to reduce user input and shorten MML texts [21], (iv) methods of rebuilding the reasoning structure to extract lemmas have been developed [23].…”

Section: Introductionmentioning

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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On Rewriting Rules in Mizar

Abstract: This paper presents some tentative experiments in using a special case of rewriting rules in Mizar

Cited by 30 publications

References 8 publications

Definitional Expansions in Mizar

Definitional Expansions in Mizar

Introducing Euclidean Relations to Mizar

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

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