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A LargeScale Experiment in Executing Extracted Programs
"... It is a wellknown fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction can generate the corresponding programs automatically. Previous work has focused on the difficulties in obtaining a program ..."
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It is a wellknown fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction can generate the corresponding programs automatically. Previous work has focused on the difficulties in obtaining a program from a formalization of the Fundamental Theorem of Algebra inside the Coq proof assistant. In theory, this program allows one to compute approximations of roots of polynomials. However, as we show in this work, there is currently a big gap between theory and practice. We study the complexity of the extracted program and analyze the reasons of its inefficiency, showing that this is a direct consequence of the approach used throughout the formalization.
A LargeScale Experiment in Executing Extracted Programs
"... 1 Introduction Several approaches can be used for certifying software. A first one, perhaps the most natural, is to start with an handwritten program and then inspect it formally in a suitable logical system, like Hoare logic. But there exists an alternative approach where one needs not write the pr ..."
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1 Introduction Several approaches can be used for certifying software. A first one, perhaps the most natural, is to start with an handwritten program and then inspect it formally in a suitable logical system, like Hoare logic. But there exists an alternative approach where one needs not write the program, but rather obtains it automatically from a mathematical proof. This automatic transformation of proofs into correctbyconstruction programs is called (program) extraction.