## A Comparison of Mizar and Isar (2002)

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Venue: | J. Automated Reasoning |

Citations: | 8 - 0 self |

### BibTeX

@ARTICLE{Wenzel02acomparison,

author = {Markus Wenzel and Freek Wiedijk},

title = {A Comparison of Mizar and Isar},

journal = {J. Automated Reasoning},

year = {2002},

volume = {29},

pages = {389--411}

}

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### Abstract

Abstract. The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a Mizar mode on top of a tactical prover, allowing one to combine a mathematical proof language with other styles of proof checking. Currently the only fully developed Mizar mode in this style is the Isar proof language for the Isabelle theorem prover. In fact the Isar language has become the official input language to the Isabelle system, even though many users still use its low-level tactical part only. In this paper we compare Mizar and Isar. A small example, Euclid’s proof of the existence of infinitely many primes, is shown in both systems. We also include slightly higher-level views of formal proof sketches. Moreover a list of differences between Mizar and Isar is presented, highlighting the strengths of both systems from the perspective of end-users. Finally, we point out some key differences of the

### Citations

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Citation Context ... Muzalewski, 1993; Wiedijk, 1999), and the Isar interface by Markus Wenzel from Munich, Germany (Wenzel, 1999; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson and Tobias Nipkow (=-=Paulson, 1994-=-; Nipkow et al., 2002). From the perspective of recipients of formal proof documents, human readers, the proof languages of both systems appear very similar. The key differences (concerning the underl... |

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Citation Context ...ctured proof languages, proof sketches. 1.1. Overview 1. Introduction We compare two systems for formalizing mathematics in the computer: the Mizar system by Andrzej Trybulec from Bia̷lystok, Poland (=-=Rudnicki, 1992-=-; Trybulec, 1993; Muzalewski, 1993; Wiedijk, 1999), and the Isar interface by Markus Wenzel from Munich, Germany (Wenzel, 1999; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson an... |

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(Show Context)
Citation Context ...computer: the Mizar system by Andrzej Trybulec from Bia̷lystok, Poland (Rudnicki, 1992; Trybulec, 1993; Muzalewski, 1993; Wiedijk, 1999), and the Isar interface by Markus Wenzel from Munich, Germany (=-=Wenzel, 1999-=-; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson and Tobias Nipkow (Paulson, 1994; Nipkow et al., 2002). From the perspective of recipients of formal proof documents, human read... |

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Citation Context ... of informal mathematics. Apart from the Mizar and Isar developments, in recent years research into the declarative proof style has resulted in several experimental systems. The ‘Mizar mode for HOL’ (=-=Harrison, 1996-=-) provides an alternative interface for interactive proof composition in HOL (notably HOL Light), transferring useful ideas from the Mizar proof language into the tactical setting of HOL. Harrison int... |

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Citation Context ...ns). The system has been sufficiently developed to conduct some example proofs from classical analysis, covering a few pages of text. It has not been applied any further, though. DECLARE (Syme, 1997; =-=Syme, 1998-=-) is a stand-alone prototype system for ‘declarative’ proof development, which acts like a compiler for formal documents consisting of theory specifications and structured proof outlines. The proof la... |

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Citation Context ...ilar relations). The system has been sufficiently developed to conduct some example proofs from classical analysis, covering a few pages of text. It has not been applied any further, though. DECLARE (=-=Syme, 1997-=-; Syme, 1998) is a stand-alone prototype system for ‘declarative’ proof development, which acts like a compiler for formal documents consisting of theory specifications and structured proof outlines. ... |

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Citation Context ...guages, proof sketches. 1.1. Overview 1. Introduction We compare two systems for formalizing mathematics in the computer: the Mizar system by Andrzej Trybulec from Bia̷lystok, Poland (Rudnicki, 1992; =-=Trybulec, 1993-=-; Muzalewski, 1993; Wiedijk, 1999), and the Isar interface by Markus Wenzel from Munich, Germany (Wenzel, 1999; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson and Tobias Nipkow ... |

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Citation Context ...iew 1. Introduction We compare two systems for formalizing mathematics in the computer: the Mizar system by Andrzej Trybulec from Bia̷lystok, Poland (Rudnicki, 1992; Trybulec, 1993; Muzalewski, 1993; =-=Wiedijk, 1999-=-), and the Isar interface by Markus Wenzel from Munich, Germany (Wenzel, 1999; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson and Tobias Nipkow (Paulson, 1994; Nipkow et al., 20... |

4 |
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Citation Context ...etches. 1.1. Overview 1. Introduction We compare two systems for formalizing mathematics in the computer: the Mizar system by Andrzej Trybulec from Bia̷lystok, Poland (Rudnicki, 1992; Trybulec, 1993; =-=Muzalewski, 1993-=-; Wiedijk, 1999), and the Isar interface by Markus Wenzel from Munich, Germany (Wenzel, 1999; Wenzel, 2002a; Wenzel, 2002b) to the Isabelle system by Larry Paulson and Tobias Nipkow (Paulson, 1994; Ni... |

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