Algebraic Semantics of Imperative Programs By Joseph A. Goguen, Grant Malcolm
1996 | 228 Pages | ISBN: 026207172X | DJVU | 2 MB
Algebraic Semantics of Imperative Programs presents a self-contained and novel "executable" introduction to formal reasoning about imperative programs. The authors' primary goal is to improve programming ability by improving intuition about what programs mean and how they run.The semantics of imperative programs is specified in a formal, implemented notation, the language OBJ; this makes the semantics highly rigorous yet simple, and provides support for the mechanical verification of program properties.OBJ was designed for algebraic semantics; its declarations introduce symbols for sorts and functions, its statements are equations, and its computations are equational proofs. Thus, an OBJ "program" is an equational theory, and every OBJ computation proves some theorem about such a theory. This means that an OBJ program used for defining the semantics of a program already has a precise mathematical meaning. Moreover, standard techniques for mechanizing equational reasoning can be used for verifying axioms that describe the effect of imperative programs on abstract machines. These axioms can then be used in mechanical proofs of properties of programs.Intended for advanced undergraduates or beginning graduate students, Algebraic Semantics of Imperative Programs contains many examples and exercises in program verification, all of which can be done in OBJ.

Algebraic Specifications in Software Engineering: An Introduction By Ivo Van Horebeek; Johan Lewi
2011 | 350 Pages | ISBN: 364275032X | DJVU | 3 MB
"I prefer to view formal methods as tools. the use of which might be helpful." E. W. Dijkstra Algebraic specifications are about to be accepted by industry. Many projects in which algebraic specifications have been used as a design tool have been carried out. What prevents algebraic specifications from breaking through is the absence of introductory descriptions and tools supporting the construction of algebraic specifications. On the one hand. interest from industry will stimulate people to make introductions and tools. whereas on the other hand the existence of introductions and tools will stimulate industry to use algebraic specifications. This book should be seen as a contribution towards creating this virtuous circle. The book will be of interest to software designers and programmers. It can also be used as material for an introductory course on algebraic specifications and software engineering at undergraduate or graduate level. Nowadays. there is general agreement that in large software projects appropriate specifications are a must in order to obtain quality software. Informal specifications alone are certainly not appropriate because they are incomplete. inconsistent. inaccurate and ambiguous and they rapidly become bulky and therefore useless. The only way to overcome this problem is to use formal specifications. An important remark here is that a specification formalism (language) alone is not sufficient. What is also needed is a design method to write specifications in that formalism.

Ribet K Current Trends in Arithmetical Algebraic Geometry | 20.31 MB
N/A | 294 Pages

Title: Current Trends in Arithmetical Algebraic Geometry
Author: Kenneth A. Ribet, Editor
Year: N/A

Noise Oscillators and Algebraic Randomness M Planat 2004 | 2.73 MB
N/A | 416 Pages

Title: N/A
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The Center and Focus Problem - Algebraic Solutions and Hypotheses
pdf | 9.43 MB | English | Isbn:‎ B09C5ZJ14N | Author: M.N. Pop | Year: 2021

Algebraic Geometry 1: From Algebraic Varieties to Schemes By Kenji Ueno
1999 | 168 Pages | ISBN: 0821808621 | PDF | 20 MB
This is the first of three volumes on algebraic geometry. Most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an introduction to the theory, which should overcome any such impediment to learning this rich subject.

English | 2021 | ISBN: 1032017252 | 227 pages | True PDF | 9.43 MB
The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback)
This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades.

Algebraic Number Theory Serge Lang 1994
pdf | 22.2 MB | English | Isbn:978-1461269229 | Author: Serge Lang | Year: 1994

A Course In Computational Algebraic Number Theory
pdf | 50.2 MB | English | Isbn:978-3642081422 | Author: Henri Cohen | Year: 2010