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Using Abstract Stobjs in ACL2 to Compute Matrix Normal Forms

  • Laureano Lambán
  • Francisco J. Martín-MateosEmail author
  • Julio Rubio
  • José-Luis Ruiz-Reina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10499)

Abstract

We present here an application of abstract single threaded objects (abstract stobjs) in the ACL2 theorem prover, to define a formally verified algorithm that given a matrix with elements in the ring of integers, computes an equivalent matrix in column echelon form. Abstract stobjs allow us to define a sound logical interface between matrices defined as lists of lists, convenient for reasoning but inefficient, and matrices represented as unidimensional stobjs arrays, which implement accesses and (destructive) updates in constant time. Also, by means of the abstract stobjs mechanism, we use a more convenient logical representation of the transformation matrix, as a sequence of elemental transformations. Although we describe here a particular normalization algorithm, we think this approach could be useful to obtain formally verified and efficient executable implementations of a number of matrix normal form algorithms.

Keywords

Matrices ACL2 Abstract stobjs Matrix normal forms 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Laureano Lambán
    • 1
  • Francisco J. Martín-Mateos
    • 2
    Email author
  • Julio Rubio
    • 1
  • José-Luis Ruiz-Reina
    • 2
  1. 1.Department of Mathematics and ComputationUniversity of La RiojaLogroñoSpain
  2. 2.Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevilleSpain

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