@MISC{Berger_fromcoinductive, author = {Ulrich Berger}, title = {From coinductive proofs to exact real arithmetic}, year = {} }

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Abstract

Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic. 1

...ork on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits [1, 2] or linear fractional transformations =-=[3]-=-) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, but there are two important differences. Th...

...duction. 1 Introduction Most of the recent work on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits =-=[1, 2]-=- or linear fractional transformations [3]) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, bu...

...duction. 1 Introduction Most of the recent work on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits =-=[1, 2]-=- or linear fractional transformations [3]) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, bu...