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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.
Extracting Programs from Constructive HOL Proofs via IZF SetTheoretic Semantics
"... Abstract. Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple settheoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, Z ..."
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Abstract. Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple settheoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard settheoretic semantics in such a way that the constructive core of HOL is mapped into IZF. We use the disjunction, numerical existence and term existence properties of IZF to provide a program extraction capability from proofs in the constructive core. We can implement the disjunction and numerical existence properties in two different ways: one modifying Rathjen’s realizability for CZF and the other using a new direct weak normalization result for intensional IZF by Moczyd̷lowski. The latter can also be used for the term existence property. 1
A NORMALIZING INTUITIONISTIC SET THEORY WITH INACCESSIBLE SETS ∗
, 2006
"... Vol. 3 (3:6) 2007, pp. 1–31 ..."
EXTRACTING PROGRAMS FROM CONSTRUCTIVE HOL PROOFS VIA IZF SETTHEORETIC SEMANTICS
, 2007
"... Vol. 4 (3:5) 2008, pp. 1–17 ..."
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.