Isabelle Import Infrastructure for the Mizar Mathematical Library

  title={Isabelle Import Infrastructure for the Mizar Mathematical Library},
  author={C. Kaliszyk and Karol Pak},
We present an infrastructure that allows importing an initial part of the Mizar Mathematical Library into the Isabelle/Mizar object logic. For this, we first combine the syntactic information provided by the Mizar parser with the syntactic one originating from the Mizar verifier. The proof outlines are then imported by an Isabelle package, that translates particular Mizar directives to appropriate Isabelle meta-logic constructions. This includes processing of definitions, notations, typing… 
3 Citations
Declarative Proof Translation
This paper proposes efficient algorithms for declarative proof outline translation and demonstrates the practicality of these algorithms by automatically translating the proof outlines in 200 articles from the Mizar Mathematical Library to the Isabelle/Isar proof style.
Syntactic-Semantic Form of Mizar Articles
This paper proposes a new XML-based format which combines both syntactic and semantic data and is intended to facilitate various applications of the Mizar library requiring fullest possible information to be retrieved from the formalization files.
An Experiment on Mizar Adjectives with Extra Visible Arguments
  • Adam Naumowicz
  • Mathematics
    2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
  • 2020
This paper presents the extended processing of adjectives with visible arguments in the Mizar system by presenting the results of a case study based on refactoring selected Mizar Mathematical Library theories.


Presentation and Manipulation of Mizar Properties in an Isabelle Object Logic
This paper discusses various elements of the Mizar language and the possible ways how these can be represented in the Isabelle framework in order to allow a suitable way of working in typed set theory.
Towards a Mizar environment for Isabelle: foundations and language
It is shown how Isabelle types can be used to differentiate between the syntactic categories of the Mizar language, such as sets and Mizar types including modes and attributes, and how they interact with the basic constructs of the Tarski-Grothendieck set theory.
Progress in the independent certification of mizar mathematical library in isabelle
  • C. Kaliszyk, Karol Pak
  • Computer Science, Mathematics
    2017 Federated Conference on Computer Science and Information Systems (FedCSIS)
  • 2017
This paper improves the mechanism for defining Mizar structures and shows that it permits simpler validation of proof developments involving such objects and performs a complete translation of the Mizar net of basic algebraic structures including their attributes and certify all the corresponding proofs in Isabelle.
Accessing the Mizar Library with a Weakly Strict Mizar Parser
The main result of the work described here is the implementation of an independent parser of the Weakly Strict Mizar language (WS-Mizar) along with a formal specification of its grammar and a program simulating an existing Mizar utility but using the new parser.
A Comparison of Mizar and Isar
A list of differences between Mizar and Isar is presented, highlighting the strengths of both systems from the perspective of end-users, and some key differences of the internal mechanisms of structured proof processing in either system are pointed out.
The Isabelle Framework
Isabelle, which is available from , is a generic framework for interactive theorem proving. The Isabelle/Puremeta-logic allows the formalization of the syntax and inference
The Mizar Mathematical Library in OMDoc: Translation and Applications
This paper presents a translation of the Mizar library into the OMDoc format (Open Mathematical Documents), an XML-based representation format for mathematical knowledge, and exemplifies interoperability by indexing the translated library in the MathWebSearch engine, which provides an “applicable theorem search” service (almost) out of the box.
MPTP 0.2: Design, Implementation, and Initial Experiments
  • J. Urban
  • Computer Science
    Journal of Automated Reasoning
  • 2006
The second version of the Mizar Problems for Theorem Proving (MPTP) system is described and it is shown that on the nonarithmetical problems, countersatisfiability is no longer detected by the ATP systems, suggesting that the ‘Mizar deconstruction’ done by MPTP is in this case already complete.
Importing HOL into Isabelle/HOL
The importer works by replaying proofs within Isabelle/HOL that have been recorded in HOL 4 or HOL-light and is therefore completely safe and facilitates a true integration of imported theorem and theorems that are already available in Isabelle /HOL.
Presenting and Explaining Mizar