Computing in Coq with Infinite Algebraic Data Structures

Domínguez, César; Rubio, Julio

doi:10.1007/978-3-642-14128-7_18

Cited by 2 publications

(2 citation statements)

References 19 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We finish this section with a comparison between the ACL2 formalisation of the cone construction and the Coq formalisation of the same result [19]. As we explained in the Introduction, the gap between the ACL2 formalisation and the Kenzo code is much smaller than the one between Coq and Kenzo.…”

Section: A Comparison With Other Approachesmentioning

confidence: 93%

Modelling algebraic structures and morphisms in ACL2

Heras

Martín-Mateos

Pascual

2015

AAECC

View full text Add to dashboard Cite

In this paper, we present how algebraic structures and morphisms can be modelled in the ACL2 theorem prover. Namely, we illustrate a methodology for implementing a set of tools that facilitates the formalisations related to algebraic structuresas a result, an algebraic hierarchy ranging from setoids to vector spaces has been developed. The resultant tools can be used to simplify the development of generic theories about algebraic structures. In particular, the benefits of using the tools presented in this paper, compared to a from-scratch approach, are especially relevant when working with complex mathematical structures; for example, the structures employed in Algebraic Topology. This work shows that ACL2 can be a suitable tool for formalising algebraic concepts coming, for instance, from computer algebra systems.

show abstract

Section: A Comparison With Other Approachesmentioning

confidence: 93%

Modelling algebraic structures and morphisms in ACL2

Heras

Martín-Mateos

Pascual

2015

AAECC

View full text Add to dashboard Cite

show abstract

“…This is the reason why a project to apply formal methods to the study of Kenzo as a software system was launched some years ago [6,12]. Eventually, this research line arrived to the formalization of some parts of Algebraic Topology and Homological Algebra by using proof assistants as Isabelle/HOL [2,3] or Coq [7]. A different approach to using Coq to implement in constructive type theory some features of Kenzo can be found in [4].…”

Section: Introductionmentioning

confidence: 97%

Formalization of a normalization theorem in simplicial topology

Lambán

Martín-Mateos

Rubio

et al. 2012

Ann Math Artif Intell

Self Cite

View full text Add to dashboard Cite

In this paper we present a complete formalization of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. Even if the Normalization Theorem is usually stated as a higher-order result (with a Category Theory flavor) we manage to give a first-order proof of it. To this aim it is instrumental the introduction of an algebraic data structure called simplicial polynomial. As a demonstration of the validity of our techniques we developed a formal proof in the ACL2 theorem prover. This work is dedicated to our colleague and friend Mirian Andrés. She started this research but passed away at the age of only 29 due to a car accident. Mirian, the best friend for your friends, we do not forget you.

show abstract

Computing in Coq with Infinite Algebraic Data Structures

Cited by 2 publications

References 19 publications

Modelling algebraic structures and morphisms in ACL2

Modelling algebraic structures and morphisms in ACL2

Formalization of a normalization theorem in simplicial topology

Contact Info

Product

Resources

About