AXIOM: the scientific computation system
AXIOM: the scientific computation system
Algorithms for computer algebra
Algorithms for computer algebra
A constructive algebraic hierarchy in Coq
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Journal of Functional Programming
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Zenon: an extensible automated theorem prover producing checkable proofs
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Proceedings of the 7th Workshop on Programming Languages and Analysis for Security
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In this paper we present a FoCaL formalization for quotient structures which are common in mathematics. We first present a framework for stating invariant properties of the data manipulated by running programs. A notion of equivalence relation is then encoded for the FoCaL library. It is implemented through projections functions, this enables us to provide canonical representations which are commonly used in Computer Algebra but seldom formally described. We further provide a FoCaL formalization for the code used inside the library for modular arithmetic through the certification of quotient groups and quotient rings which are involved in the model. We finally instantiate our framework to provide a trusted replacement of the existing FoCaL library.