Titlebook: Intelligent Computer Mathematics; MKM, Calculemus, DML Jacques Carette,David Aspinall,Wolfgang Windsteige Conference proceedings 2013 Sprin

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The Formalization of Syntax-Based Mathematical Algorithms Using Quotation and Evaluationaningful way. A formalization of such an algorithm should include a specification of its computational behavior, a specification of its mathematical meaning, and a mechanism for applying the algorithm to actual expressions. Achieving these goals requires the ability to integrate reasoning about the

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Certification of Bounds of Non-linear Functions: The Templates Methodrtificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales’ proof of Kepler’s conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis

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A Universal Machine for Biform Theory Graphsze deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time.

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Mathematical Practice, Crowdsourcing, and Social MachinesMathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated

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Automated Reasoning Service for ,he service uses several automated reasoning systems combined with several premise selection methods trained on previous . proofs, to attack a new conjecture that uses the concepts defined in the . library. The public online incarnation of the service runs on a 48-CPU server, currently employing in p

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Understanding Branch Cuts of Expressionss involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the single-valued counterparts, the common approach to encoding multi-valued functions in computer algebra systems. While the defini

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Formal Mathematics on Display: A Wiki for Flyspeckproof assistant. The functions implemented in . include in-browser editing, strong AI/ATP proof advice, verification, and HTML rendering. The HTML rendering contains hyperlinks and provides on-demand explanation of the proof state for each proof step. In the present paper we show the prototype . Wik

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Determining Points on Handwritten Mathematical Symbolsor the writing not to follow simple baselines. In order to understand the scale and relative positioning of individual characters, it is necessary to identify the location of certain expected features. These are typically identified by particular points in the symbols, for example, the baseline of a

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Capturing Hiproofs in HOL Lightditional structure can be used to abstract away from details, or to label particular portions to explain their purpose..In this paper we present two complementary methods for capturing hiproofs in HOL Light, along with a tool to produce web-based visualisations. The first method uses ., by modifying