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Program extraction in exact real arithmetic


The importance of an abstract approach to a computation theory over general data types has been stressed by Tucker in many of his papers. Berger and Seisenberger recently elaborated the idea for extraction out of proofs involving (only) abstract reals. They considered a proof involving coinduction of the proposition that any two reals in [−1, 1] have their average in the same interval, and informally extract a Haskell program from this proof, which works with stream representations of reals. Here we formalize the proof, and machine extract its computational content using the Minlog proof assistant. This required an extension of this system to also take coinduction into account.

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Kenji Miyamoto is supported by the Marie Curie Initial Training Network in Mathematical Logic – MALOA – from Mathematical Logic to Applications, PITN-GA-2009-238381

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

U. Berger (1993) Program extraction from normalization proofs. In: M. Bezem and J. Groote (eds.) Typed Lambda Calculi and Applications. Springer Verlag Lecture Notes in Computer Science 664 91106.

U. Berger (2009) From coinductive proofs to exact real arithmetic. In: E. Grädel and R. Kahle (eds.) Computer Science Logic. Springer Verlag Lecture Notes in Computer Science 5771 132146.

U. Berger , M. Eberl and H. Schwichtenberg (2003) Term rewriting for normalization by evaluation. Information and Computation 183 1942.

U. Berger and M. Seisenberger (2010) Proofs, programs, processes. In: F. Ferreira et al. (eds.) Proceedings CiE 2010. Springer Verlag Lecture Notes Computer Science 6158 3948.

A. Ciaffaglione and P. D. Gianantonio (2006) A certified, corecursive implementation of exact real numbers. Theoretical Computer Science 351 3951.

P. Letouzey (2003) A new extraction for coq. In: H. Geuvers and F. Wiedijk (eds.) Types for Proofs and Programs, Second International Workshop, TYPES 2002. Springer Verlag Lecture Notes in Computer Science 2646 200219.

H. Schwichtenberg (2008) Realizability interpretation of proofs in constructive analysis. Theory of Computing Systems 43 (3) 583602.

J. V. Tucker and J. I. Zucker (1992) Theory of computation over stream algebras, and its applications. In: Havel, I. M. and Koubek, V. (eds.) Mathematical Foundations of Computer Science. Springer Verlag Lecture Notes in Computer Science 629 6280.

E. Wiedmer (1980) Computing with infinite objects. Theoretical Computer Science 10 133155.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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