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We develop a formal proof of the ML type inference algorithm, within the Coq proof assistant. We are much concerned with methodology and reusability of such a mechanization. This proof is also necessary to hope the certiication of a complete ML compiler in the future. In this paper we present the Coq formalization of the typing system and its inference… (More)

We describe here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation. A real number is represented as a sequence of nite B-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the… (More)

a r t i c l e i n f o a b s t r a c t Keywords: Complex floating point arithmetic Error-free transformations Accurate summation Accurate dot product Accurate polynomial evaluation Horner's scheme High precision Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on methods… (More)

— Error-free transformation is a concept that makes it possible to compute accurate results within a floating point arithmetic. Up to now, it has only be studied for real floating point arithmetic. In this short note, we recall the known error-free transformations for real arithmetic and we propose some new error-free transformations for complex floating… (More)

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