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Program extraction in exact real arithmetic†

Published online by Cambridge University Press:  10 November 2014

KENJI MIYAMOTO  and
HELMUT SCHWICHTENBERG
KENJI MIYAMOTO
Affiliation:
Mathematisches Institut, LMU, Theresienstr. 39, D-80333 München, Germany Email: miyamoto@math.lmu.de, schwicht@math.lmu.de
HELMUT SCHWICHTENBERG
Affiliation:
Mathematisches Institut, LMU, Theresienstr. 39, D-80333 München, Germany Email: miyamoto@math.lmu.de, schwicht@math.lmu.de
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Abstract

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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Footnotes

†

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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