Mathematics in Computer Science

, Volume 5, Issue 4, pp 437–467 | Cite as

A Validated Real Function Calculus

  • Pieter Collins
  • Milad Niqui
  • Nathalie Revol
Open Access


We present a framework for validated numerical computations with real functions. The framework is based on a formalisation of abstract data types for basic floating-point arithmetic, interval arithmetic and function models based on Banach algebra. As a concrete instantiation, we develop an elementary smooth function calculus approximated by sparse polynomial models. We demonstrate formal verification applied to validated calculus by a formalisation of basic arithmetic operations in a theorem prover. The ultimate aim is to develop a formalism powerful enough for reachability analysis of nonlinear hybrid systems.


Interval arithmetic Floating point Function calculus 

Mathematics Subject Classification (2010)




Helpful discussions with Mioara Joldeş and Rolland Zumkeller are acknowledged. The second author was supported by a VENI Grant from The Netherlands Organisation for Scientific Research (NWO).

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Maastricht UniversityMaastrichtThe Netherlands
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  3. 3.INRIA, LIP (UMR 5668 CNRS, ENS de Lyon, INRIA, UCBL)Université de LyonLyonFrance

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