NDLI: Invariants for the FoCaL language

Content Provider	Springer Nature Link
Author	Rioboo, Renaud
Copyright Year	2009
Abstract	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.
Ending Page	296
Page Count	24
Starting Page	273
File Format	PDF
ISSN	10122443
e-ISSN	15737470
Journal	Annals of Mathematics and Artificial Intelligence
Issue Number	3-4
Volume Number	56
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-07-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Specification and verification (program logics, model checking, etc.) Mathematics Data invariants Statistical Physics, Dynamical Systems and Complexity Specification and verification Theorem proving Abstract data types; algebraic specification Computer Science Artificial Intelligence (incl. Robotics) FoCaLize Theorem proving (deduction, resolution, etc.) Algebraic specifications Effective mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Automated verification of refinement laws

Labelled splitting

Solving quantified verification conditions using satisfiability modulo theories

Formalizing complex plane geometry

Formalization of a normalization theorem in simplicial topology

Strong order equivalence

Automated Flaw Detection in Algebraic Specifications

Automated generation of machine verifiable and readable proofs: A case study of Tarski’s geometry

Inductive proof search modulo

Invariants for the FoCaL language

Similar Documents

Automated verification of refinement laws

Labelled splitting

Solving quantified verification conditions using satisfiability modulo theories

Formalizing complex plane geometry

Formalization of a normalization theorem in simplicial topology

Strong order equivalence

Automated Flaw Detection in Algebraic Specifications

Automated generation of machine verifiable and readable proofs: A case study of Tarski’s geometry

Inductive proof search modulo

Invariants for the FoCaL language