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QArith: Coq formalisation of lazy rational arithmetic
 Types for Proofs and Programs, volume 3085 of LNCS
, 2003
"... Abstract. In this paper we present the Coq formalisation of the QArith library which is an implementation of rational numbers as binary sequences for both lazy and strict computation. We use the representation also known as the SternBrocot representation for rational numbers. This formalisation use ..."
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Cited by 9 (2 self)
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Abstract. In this paper we present the Coq formalisation of the QArith library which is an implementation of rational numbers as binary sequences for both lazy and strict computation. We use the representation also known as the SternBrocot representation for rational numbers. This formalisation uses advanced machinery of the Coq theorem prover and applies recent developments in formalising general recursive functions. This formalisation highlights the rĂ´le of type theory both as a tool to verify handwritten programs and as a tool to generate verified programs. 1
Program Extraction from Large Proof Developments
, 2003
"... It is well known that mathematical proofs often contain (abstract) algorithms, but although these algorithms can be understood by a human, it still takes a lot of time and effort to implement this algorithm on a computer; moreover, one runs the risk of making mistakes in the process. From a fully... ..."
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Cited by 6 (4 self)
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It is well known that mathematical proofs often contain (abstract) algorithms, but although these algorithms can be understood by a human, it still takes a lot of time and effort to implement this algorithm on a computer; moreover, one runs the risk of making mistakes in the process. From a fully...
Admissible Digit Sets and a Modified SternBrocot Representation
, 2004
"... We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a nite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sucient conditions that such a \digit ..."
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We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a nite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sucient conditions that such a \digit set" yields an admissible representation of [0; +1]. Furthermore we establish the productivity and correctness of the homographic algorithm for such \admissible" digit sets. In the second part of the paper we discuss representation of positive real numbers based on the Stern{Brocot tree. We show how we can modify the usual Stern{Brocot representation to yield a ternary admissible digit set.