Using Abstract Stobjs in ACL2 to Compute Matrix Normal Forms
Authors: 
Laureano Lambán, Francisco J. Martín-Mateos, Julio Rubio, José-Luis Ruiz-ReinaAuthors Info & Claims
Laureano Lambán, Francisco J. Martín-Mateos, Julio Rubio, José-Luis Ruiz-ReinaAuthors Info & ClaimsPages 354 - 370
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.
References
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Sep 2017
549 pages
© Springer International Publishing AG 2017.
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Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 26 September 2017
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