Built-in Treatment of an Axiomatic Floating-Point Theory for SMT Solvers

10 pages•Published: August 19, 2013

Sylvain Conchon, Guillaume Melquiond, Cody Roux and Mohamed Iguernelala

Abstract

The treatment of the axiomatic theory of floating-point numbers is
out of reach of current SMT solvers, especially when it comes to
automatic reasoning on approximation errors. In this paper, we
describe a dedicated procedure for such a theory, which provides an
interface akin to the instantiation mechanism of an SMT solver.
This procedure is based on the approach of the Gappa tool: it
performs saturation of consequences of the axioms, in order to
refine bounds on expressions. In addition to the original approach,
bounds are further refined by a constraint solver for linear
arithmetic. Combined with the natural support for equalities
provided by SMT solvers, our approach improves the treatment of
goals coming from deductive verification of numeric programs. We
have implemented it in the Alt-Ergo SMT solver.

Keyphrases: axiomatic theory, floating point, real arithmetic, simplex, smt

In: Pascal Fontaine and Amit Goel (editors). SMT 2012. 10th International Workshop on Satisfiability Modulo Theories, vol 20, pages 12-21.

Links:	https://easychair.org/publications/paper/KH27
	https://doi.org/10.29007/wh99

BibTeX entry

@inproceedings{SMT2012:Built_Treatment_Axiomatic_Floating,
  author    = {Sylvain Conchon and Guillaume Melquiond and Cody Roux and Mohamed Iguernelala},
  title     = {Built-in Treatment of an Axiomatic Floating-Point Theory for SMT Solvers},
  booktitle = {SMT 2012. 10th International Workshop on Satisfiability Modulo Theories},
  editor    = {Pascal Fontaine and Amit Goel},
  series    = {EPiC Series in Computing},
  volume    = {20},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/KH27},
  doi       = {10.29007/wh99},
  pages     = {12-21},
  year      = {2013}}

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