Mizar

Trybulec, Andrzej

doi:10.1007/11542384_4

Cited by 10 publications

(8 citation statements)

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“…T HE Mizar system [1], [2], [3] is a computer proofassistant system used for encoding formal mathematical data (definitions and theorems) and verifying mathematical proofs. The system comprises a dedicated formal computer language -the Mizar language, a collection of command-line tools including the VERIFIER and a repository of formal texts -Mizar Mathematical Library (MML) that have been written in the Mizar language and machine-verified for their logical correctness by the VERIFIER.…”

Section: Introductionmentioning

confidence: 99%

“…It is designed to write declarative-style documents both readable for humans and effectively processed by computers. 1 The feature-rich language enables producing rigorous and semantically unambiguous texts. Apart from rules for writing traditional mathematical items (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…As far as binary predicates are concerned, which is directly related to the topic of this paper, the current version of the Mizar system supports registering reflexivity, irreflexivity, symmetry, asymmetry and connectedness. The transitivity 1 The legibility of proofs is a subject of ongoing research [4], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

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Introducing Euclidean Relations to Mizar

Naumowicz

Korniłowicz

2017

Annals of 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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Introducing Euclidean Relations to Mizar

Naumowicz

Korniłowicz

2017

Annals of Computer Science and Information Systems

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“…It has motivated systems like STUDENT [2], Mathematical Vernacular [3], Mizar [4], OMEGA [5], Isar [6], Vip [7], Theorema [8], MathLang [9], Naproche [10], and FMathL [11]. These systems permit user interaction in a notation that resembles English more than logical symbolisms do.…”

Section: Introductionmentioning

confidence: 99%

Translating between Language and Logic: What Is Easy and What Is Difficult

Ranta

2011

Lecture Notes in Computer Science

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Abstract. Natural language interfaces make formal systems accessible in informal language. They have a potential to make systems like theorem provers more widely used by students, mathematicians, and engineers who are not experts in logic. This paper shows that simple but still useful interfaces are easy to build with available technology. They are moreover easy to adapt to different formalisms and natural languages. The language can be made reasonably nice and stylistically varied. However, a fully general translation between logic and natural language also poses difficult, even unsolvable problems. This paper investigates what can be realistically expected and what problems are hard.

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“…Other interfaces similar in spirit to ours include Alcor [6], which extends the Mizar system [24] with knowledge management services such as searching and authoring assistance, and Plato [11], which uses TeXmacs as authoring tool for the Omega system [21]. The architecture is somewhat similar to ours, with a middleware component mediating between prover and interface.…”

Section: Discussionmentioning

confidence: 99%

A Framework for Interactive Proof

Aspinall

Lüth²,

Winterstein

Towards Mechanized Mathematical Assistants

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Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their life-cycle: creation, maintenance and exploitation. The framework connects together different kinds of component, exchanging messages using a common communication infrastructure and protocol called PGIP. The main channel connects provers to displays. Provers are the back-end interactive proof engines and displays are components for interacting with the user, allowing browsing or editing of proofs. At the core of the framework is a broker middleware component which manages proof-in-progress and mediates between components.

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Mizar

Cited by 10 publications

References 0 publications

Introducing Euclidean Relations to Mizar

Introducing Euclidean Relations to Mizar

Translating between Language and Logic: What Is Easy and What Is Difficult

A Framework for Interactive Proof

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