Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the ?Formalizing 100 Theorems? challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
Kaliszyk, C., Rabe, F.: A survey of languages for formalizing mathematics. ... Megill, N., Wheeler, D.A.: Metamath: A Computer Language for Mathematical Proofs (2019). http://us.metamath.org/downloads/metamath.pdf 14.
Describes the use of computer programs to check several proofs in the foundations of mathematics.
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Megill, N., Wheeler, D.A.: Metamath: A Computer Language for Mathematical Proofs. LULU Press, Morrisville (2019) 11. Paulson, L.C.: Set theory for verification: I. From foundations to functions. J. Autom. Reason.
One of the world's leading mathematicians explores the enigmas, paradoxes, and random qualities that exist within the field of mathematics and discusses his ground-breaking discovery of the Omega number, a complex representation of ...
The first part of the book provides easy-to-read informal discussion of abstract mathematics and computers for general audiences.
For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Metamath: A computer language for pure mathematics. ... Journal of Computer and Systems Sciences, 17:348–375, 1978. ... A mechanically checked proof of the correctness of the kernel of the AMD5 K 86 floating-point division program.
For 4K resolution rendering speed is capped to 10 fps for WebCL whereas to 25fps for OpenCL. Interesting results provided measurements of ... Kaeli, D.R., Mistry, P., Schaa, D., Zhang, D.P.: Heterogeneous Computing with OpenCL 2.0.
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.