Executable Matrix Operations on Matrices of Arbitrary Dimensions

Christian Sternagel and René Thiemann

The Archive of Formal Proofs, 2010.


We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic semirings satisfy the axioms that are required by our matrix theory. Our formalization is part of the CeTA system which contains several termination techniques. The provided theories have been essential to formalize matrix-interpretations and arctic interpretations.


   AFP entry


author = "Christian Sternagel and Ren{\'e} Thiemann",
title = "{E}xecutable {M}atrix {O}perations on {M}atrices of {A}rbitrary {D}imensions",
booktitle = "The Archive of Formal Proofs",
editor = "Gerwin Klein and Tobias Nipkow and Lawrence Paulson",
publisher = "\url{}",
year = 2010,
month = Jun,
note = "Formal proof development"
ISSN = "2150-914x",
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