New Developments in Parsing Mizar

Abstract

The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the developer, the richness leads to syntactic complexity, such as dealing with overloading. Recently the Mizar team has been making a fresh approach to the problem of parsing the Mizar language. One aim is to make the language accessible to users and other developers. In this paper we describe these new parsing efforts and some applications thereof, such as large-scale text refactorings, pretty-printing, HTTP parsing services, and normalizations of Mizar texts.

Development of a Flexible Mizar Tokenizer and Parser for Information Retrieval System

“…1. The existing parser used in the proof verification program of the Mizar system first reads an article and converts it into the Weakly Strict Mizar (WS-Mizar) language [4], [5]. In the WS-Mizar language, all terms are fully parenthesized, therefore, there is no ambiguity in operator precedence.…”

Four Decades of Mizar

“…Efficient use of AI/ATP methods was possible via the translation from Mizar logic into TPTP first order logic and dedicated XML format for information interchange. The need for such cooperation forced the developers of Mizar to implement new intermediate dialects of the language carrying more information (and making it more explicit)-weakly strict and more strict Mizar [3]. Also hyperlinked form of an article was reused [11,36].…”

Definitional Expansions in Mizar

“…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.…”