Verification of the redecoration algorithm for triangular matrices

Authors:
Ralph Matthes;Martin Strecker
Affiliations:
C. N. R. S. et Université Paul Sabatier-Toulouse III, Institut de Recherche en Informatique de Toulouse, Toulouse Cedex 9;C. N. R. S. et Université Paul Sabatier-Toulouse III, Institut de Recherche en Informatique de Toulouse, Toulouse Cedex 9
Venue:
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Year:
2007

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Abstract

Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. Redecoration of triangular matrices has a succinct implementation in this representation, thus giving the challenge of proving it correct. This has been achieved within Coq, using also induction with measures. An axiomatic approach allowed a verification in the Isabelle theorem prover, giving insights about the differences of both systems.