A Comparison of Mizar and Isar

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A Comparison of Mizar and Isar (2002)

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by Markus Wenzel , Freek Wiedijk

Venue:	J. Automated Reasoning
Citations:	9 - 0 self

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@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

Keyphrases

mizar mode mathematical proof checker mizar many respect small example higher-level view input language mathematical proof language official input language current system isabelle theorem prover low-level tactical part isar proof language proof assistant isabelle system formal proof sketch isar language proof checking john harrison many prime many user key difference andrzej trybulec tactical prover proof input language

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