## A Comparison of the Mathematical Proof Languages Mizar and Isar (2002)

Venue: | Journal of Automated Reasoning |

Citations: | 9 - 3 self |

### BibTeX

@ARTICLE{Wenzel02acomparison,

author = {Markus Wenzel and Freek Wiedijk},

title = {A Comparison of the Mathematical Proof Languages Mizar and Isar},

journal = {Journal of Automated Reasoning},

year = {2002},

volume = {29},

pages = {2002}

}

### OpenURL

### 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 di#ers 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 o#cial input language to the Isabelle system, even though many users still use its low-level tactical part only.

### Citations

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(Show Context)
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, both proof languages appear very similar. The key differences (concerning the underlying concepts a... |

83 | An overview of the Mizar project
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(Show Context)
Citation Context ... proof sketches. 1.1. Overview 1. Introduction We compare the proof languages of 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... |

81 | Isar — a generic interpretative approach to readable formal proof documents
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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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28 |
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(Show Context)
Citation Context ...d in several experimental systems that focus on accessible representations of formal proofs themselves, rather than just proof checking as exercised for several decades now. 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... |

23 |
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(Show Context)
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; Sy-=-me, 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. ... |

10 |
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(Show Context)
Citation Context ... 1.1. Overview 1. Introduction We compare the proof languages of 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 ...hree main principles, namely ‘first-order decomposition and enrichment’, ‘second-order schema application’, and ‘appeals to automation’. DECLARE has been advertised as ‘three tactic theo=-=rem proving’ (Syme, 1999).-=- The system draws from the general experience of the HOL family (and Harrison’s Mizar mode), but renounces established principles like full reduction to basic logical principles inside. DECLARE has ... |

5 |
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Citation Context ...compare the proof languages of 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 ... systems are restricted to primitive inferences in pure logic, where users may occasionally specify their own set of rules, but advanced proof procedures are unavailable. The teaching tool ProveEasy (=-=Burstall, 1998)-=- provides an interactive editor for primitive natural-deduction proof texts presented in a strictly backward manner. The underlying structure is oriented towards the well-established λ-calculus view ... |

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2 |
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(Show Context)
Citation Context .... Introduction We compare the proof languages of 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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