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Chapters: Metamath. Source: Wikipedia. Pages: 135. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Metamath is a computer-assisted proof checker. It has no specific logic embedded and can simply be regarded as a device...
Chapters: Metamath. Source: Wikipedia. Pages: 135. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Metamath is a computer-assisted proof checker. It has no specific logic embedded and can simply be regarded as a device to apply inference rules to formulas. Simplicity is the master concept in the design of Metamath: the language of Metamath, employed to state the definitions, axioms, inference rules and theorems is only composed of a handful of keywords and all the proofs are checked using one simple algorithm based on the substitution of variables (with optional provisos for what variables must remain distinct after a substitution is made). This "substitution" is just the simple replacement of a variable with an expression and not the proper substitution described in works on predicate calculus. Metamath has been used to develop set.mm, a human-readable database containing about 8000 (As of March 2008) fully formal proofs of mathematical theorems built upon ZFC set theory. Those proofs may be browsed on the internet using an interface called Metamath Proof Explorer. New theorems are added to set.mm daily; a table of the most recent proofs is maintained. Contributions are welcome. Help and information can be received either by asking Megill himself or by consulting a wiki, where some FAQs are located. Metamath's simplicity philosophy has good and bad consequences. Unlike the Mizar system and other proof assistants, which tend to imitate the informal proofs normally used by mathematicians by automating (and hiding) the most technical parts, proofs developed using Metamath are fully detailed; this entails that every step can be verified by the readers even if the mathematical field the theorem belongs to is not known to them (though actual development of theorems and proofs normally requires...More: http://booksllc.net/?id=6023946
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