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» From Coinductive Proofs to Exact Real Arithmetic
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CIE
2005
Springer
13 years 11 months ago
Formalising Exact Arithmetic in Type Theory
In this work we focus on a formalisation of the algorithms of lazy exact arithmetic `a la Potts and Edalat [1]. We choose the constructive type theory as our formal verification t...
Milad Niqui
MST
2007
168views more  MST 2007»
13 years 5 months ago
Productivity of Edalat-Potts Exact Arithmetic in Constructive Type Theory
In this work we focus on a formalisation of the algorithms of lazy exact arithmetic `a la Edalat–Potts in type theory. We choose the constructive type theory extended with coind...
Milad Niqui
DIAGRAMS
2010
Springer
13 years 5 months ago
Heterogeneous Reasoning in Real Arithmetic
Abstract. Diagrams often complement sentential proofs in mathematics. However, diagrams are rarely used as standalone reasoning tools. Thus we propose to integrate diagrammatic rea...
Matej Urbas, Mateja Jamnik
MICS
2007
100views more  MICS 2007»
13 years 5 months ago
A New Method for Real Root Isolation of Univariate Polynomials
A new algorithm for real root isolation of univariate polynomials is proposed, which is mainly based on exact interval arithmetic and bisection method. Although exact interval arit...
Ting Zhang, Bican Xia
ENTCS
2008
91views more  ENTCS 2008»
13 years 5 months ago
Implementing Real Numbers With RZ
RZ is a tool which translates axiomatizations of mathematical structures to program specifications using the realizability interpretation of logic. This helps programmers correctl...
Andrej Bauer, Iztok Kavkler