Effective homology of bicomplexes, formalized in Coq
In this paper, we present a complete formalization in the Coq theorem prover of an important
algorithm in computational algebra, namely the calculation of the effective homology of a …
algorithm in computational algebra, namely the calculation of the effective homology of a …
ACL2 verification of simplicial degeneracy programs in the Kenzo system
Abstract Kenzo is a Computer Algebra system devoted to Algebraic Topology, and written in
the Common Lisp programming language. It is a descendant of a previous system called …
the Common Lisp programming language. It is a descendant of a previous system called …
Formalization of a normalization theorem in simplicial topology
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 …
Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the …
Generating certified code from formal proofs: a case study in homological algebra
We apply current theorem proving technology to certified code in the domain of abstract
algebra. More concretely, based on a formal proof of the Basic Perturbation Lemma (a …
algebra. More concretely, based on a formal proof of the Basic Perturbation Lemma (a …
Diagrammatic logic applied to a parameterisation process
C Dominguez, D Duval - Mathematical Structures in Computer …, 2010 - cambridge.org
This paper provides an abstract definition of a class of logics, called diagrammatic logics,
together with a definition of morphisms and 2-morphisms between them. The definition of the …
together with a definition of morphisms and 2-morphisms between them. The definition of the …
Mediated Access to Symbolic Computation Systems
Kenzo is a symbolic computation system devoted to Algebraic Topology. It has been
developed by F. Sergeraert mainly as a research tool. The challenge is now to increase the …
developed by F. Sergeraert mainly as a research tool. The challenge is now to increase the …
Executing in common lisp, proving in ACL2
M Andrés, L Lambán, J Rubio - International Conference on Mathematical …, 2007 - Springer
In this paper, an approach to integrate an already-written Common Lisp program for
algebraic manipulation with ACL2 proofs of properties of that program is presented. We …
algebraic manipulation with ACL2 proofs of properties of that program is presented. We …
Computing in coq with infinite algebraic data structures
Computational content encoded into constructive type theory proofs can be used to make
computing experiments over concrete data structures. In this paper, we explore this …
computing experiments over concrete data structures. In this paper, we explore this …
A parameterization process: from a functorial point of view
C Dominguez, D Duval - International Journal of Foundations of …, 2012 - World Scientific
The parameterization process used in the symbolic computation systems Kenzo and EAT is
studied here as a general construction in a categorical framework. This parameterization …
studied here as a general construction in a categorical framework. This parameterization …
[PDF][PDF] Modeling inheritance as coercion in the Kenzo system
In this paper the analysis of the data structures used in a symbolic computation system,
called Kenzo, is undertaken. We deal with the specification of the inheritance relationship …
called Kenzo, is undertaken. We deal with the specification of the inheritance relationship …