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Sum-Ĭlassical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses.
#Texmacs presentation software
The mega system is at the core of several related and well-integrated research projects of the mega research group, whose aim is to develop system support for the working mathematician and formal software engineer, in particular it supports proof development at a human oriented level of abstraction. The shift from search based methods to more abstract planning techniques how- ever opened up a new paradigm for mathematical reasoning on a computer and several systems of the new kind now employ a mix of interactive tactic based, search based as well as proof planning based techniques. But in spite of many successful attempts to prove even open mathematical problems auto- matically, their use in everyday mathematical practice is still limited. Classical automated theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces - often in the range of several billion clauses. The work by Milner and others on LCF (28) spawned a research community on tactical theorem proving, which again modest with respect to automa- tion, showed that nevertheless important sequences of deduction could be encapsulated into a tactic and then invoked by the mathematically trained user. International cooperation resulted in creating a database which includes more than 7000 definitions of mathematical concepts and more than 42000 theorems. Since 1989, the most important activity in the Mizar project has been the development of a database for mathematics.
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Roughly at the same time in 1973, the Mizar project2 started as an attempt to reconstruct mathematics based on computers. de Bruijn1 - more modest in its aims with respect to automation - showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proof-checked by a computer.
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While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. The year 2004 marked the fiftieth birthday of the first computer generated proof of a mathematical theorem: "the sum of two even numbers is again an even number" (with Martin Davis' implementation of Presburger Arithmetic in 1954). For instance, it remains complicated to simply put a mathematical text on the web (in a non-graphical format), because the "web-standard" MathML for mathematics is still poorly supported. Moreover, different tools use different data formats, which are often not very compatible. At any rate, it is not straightforward to combine several tools, like including graphics or computer algebra output in a paper. Several of these tools, and in particular T E X/L A T E X, are quite user unfriendly.
#Texmacs presentation pdf
For instance, mathematical texts are usually written with T E X/L A T E X, computations are done with numerical computation software or computer algebra systems, and presentations are done using Power Point or directly from a Pdf file.
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2 Importance of the problem Currently, in the fields of mathematics, physics and computer science, people use different tools for each task. A major challenge is to pro-vide a similar software for scientists, with more specific support for things like mathematical formulas, complex computations, presentations from a laptop and so on. 1 Statement of the problem Ordinary users have the choice between several office suits, like Microsoft Office, Open Office, or Star Office, for common desktop tasks, like text editing, drawing pictures or data administration.