## Figures from this paper

## 46 Citations

A Model of Mizar Concepts - Unification

- Computer ScienceFormaliz. Math.
- 2010

The theory presented is an abstraction from the existing implementation of the Mizar system and is devoted to the formalization of Mizar expressions, including standarized constructor signature, arity-rich signatures, and the unification of Mizr expressions.

Towards the Construction of a Model of Mizar Concepts

- Computer ScienceFormaliz. Math.
- 2008

Towards the Construction of a Model of Mizar Concepts The aim of this paper is to develop a formal theory of Mizar linguistic concepts following the ideas from [14] and [13]. The theory here…

On Semilattice Structure of Mizar Types

- Mathematics
- 2004

One can verify that every poset which is Mizar-widening-like is also Noetherian and upperbounded and has l.u.b.’s. One can verify that every sup-semilattice which is Noetherian is also…

Solving Two Problems in General Topology Via Types

- Computer ScienceTYPES
- 2004

It is shown, based on two problems in general topology, how typed objects can be used instead of untyped text to better represent mathematical content understandable both for human and computer checker.

Mizar's Soft Type System

- Computer ScienceTPHOLs
- 2007

This paper will interpret Mizar types as soft types, by translating Mizar's type judgments into sequents of untyped first order predicate logic, and prove that the Mizar type system is correct with respect to this translation in the sense that each derivable type judgment translates to a provable sequent.

Presentation and Manipulation of Mizar Properties in an Isabelle Object Logic

- Computer ScienceCICM
- 2017

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 Mathematical Library in OMDoc Format

- Computer Science
- 2007

This paper presents an experiment of using the Mizar system to transform the Mizr library into the OMDoc format (Open Mathematical Documents), an XML-based representation format for mathematical knowledge that is geared towards making formula structure and context dependencies explicit.

Trends in Contemporary Computer Science

- Mathematics
- 2014

Formal characterization of ADL in terms of Mizar attributes and clusters is given, obtaining also the characterization of the class of generalized almost distributive lattices.

Formalizing Foundations of Mathematics

- Computer Science
- 2002

This work represents three of the most important foundations Isabelle/HOL, Mizar, and ZFC set theory as well as relations between them and provides the starting point of a systematic study of formalized foundations in order to compare, relate, and integrate them.

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