Joseph A. Goguen, Grant Malcolm's Algebraic Semantics of Imperative Programs PDF

By Joseph A. Goguen, Grant Malcolm

ISBN-10: 026207172X

ISBN-13: 9780262071727

Algebraic Semantics of crucial courses offers a self-contained and novel "executable" creation to formal reasoning approximately critical courses. The authors' basic target is to enhance programming skill via enhancing instinct approximately what courses suggest and the way they run.The semantics of valuable courses is laid out in a proper, applied notation, the language OBJ; this makes the semantics hugely rigorous but uncomplicated, and gives aid for the mechanical verification of application properties.OBJ used to be designed for algebraic semantics; its declarations introduce symbols for types and features, its statements are equations, and its computations are equational proofs. hence, an OBJ "program" is an equational thought, and each OBJ computation proves a few theorem approximately any such idea. which means an OBJ software used for outlining the semantics of a application already has an actual mathematical that means. furthermore, typical concepts for mechanizing equational reasoning can be utilized for verifying axioms that describe the impact of critical courses on summary machines. those axioms can then be utilized in mechanical proofs of homes of programs.Intended for complicated undergraduates or starting graduate scholars, Algebraic Semantics of significant courses comprises many examples and workouts in software verification, all of which are performed in OBJ.

Show description

Read or Download Algebraic Semantics of Imperative Programs PDF

Best discrete mathematics books

Discrete Mathematics for Computer Science - download pdf or read online

A growing number of desktop scientists from assorted components are utilizing discrete mathematical buildings to provide an explanation for strategies and difficulties. in line with their educating reviews, the authors supply an obtainable textual content that emphasizes the basics of discrete arithmetic and its complex subject matters. this article indicates find out how to show unique rules in transparent mathematical language.

The numerical solution of systems of polynomials arising in by Andrew John Sommese PDF

Written through the founders of the hot and increasing box of numerical algebraic geometry, this is often the 1st booklet that makes use of an algebraic-geometric method of the numerical resolution of polynomial structures and likewise the 1st one to regard numerical tools for locating confident dimensional answer units. The textual content covers the complete conception from equipment constructed for remoted suggestions within the 1980's to the newest study on optimistic dimensional units.

Read e-book online Combinatorial Matrix Theory (Encyclopedia of Mathematics and PDF

The booklet bargains with the various connections among matrices, graphs, diagraphs and bipartite graphs. the fundamental conception of community flows is constructed so that it will receive lifestyles theorems for matrices with prescribed combinatorical houses and to procure quite a few matrix decomposition theorems. different chapters disguise the everlasting of a matrix and Latin squares.

Read e-book online Restricted Orbit Equivalence for Actions of Discrete PDF

This monograph bargains a large investigative instrument in ergodic concept and measurable dynamics. the inducement for this paintings is that one may well degree how comparable dynamical structures are by means of asking how a lot the time constitution of orbits of 1 procedure has to be distorted for it to develop into the opposite. varied regulations at the allowed distortion will result in varied limited orbit equivalence theories.

Additional info for Algebraic Semantics of Imperative Programs

Example text

For example, we could also de c lare vars U V Var : var P : Pgm . Note the difference between "var" the and "Var": as a v ar i ab les in a pro g ramm i ng latter has been declared sort name (it is u sed below to den o te the sort of integer former is an OBJ ke y wor d After this, assu ming the previously declared variables of sort Exp, plus the dec­ language), while the . larations op . : Var Exp -> - op _;_ : Pgm Pgm -> Pgm Pgm . subsort Var Nat < Exp . the fo llowing should work: parse P ; := U X + V .

These can b e avoided by using the att ri bute Copyrighted Material idr : , which Chapter 1 34 introduces only the identity e q u at ion s themselves, without invoking a co m p let ion process . Operations can also be declared idempotent , by u si ng the attribute idem; this is implemented simply by adding the i demp ot en t equation to those available in the relevant module . There is no completion . The following is an integer list obj ect with associative and identity attributes : obj NATL I ST 1 i s sort s Nat L i s t N eL i s t subsort s Nat < N eList < L i s t o p 0 : - > Nat .

In this case, we ad d the new cons t an t x . By Theorem 22, the reduction above serves to check t h at the e qu ati on is satisfi ed by all models of JUTEXPEQ . A ft e r the line "clo s e ," the module JUTEXPEQ i s returned to i ts or igi n al state . OBJ also allows declarations to be added p erma­ nently to a module . This is ach ieved by t he command openr , which stands for open and rem ember All of the declarations m ade between openr and c l o s e are p erma­ nently added to the module, and so w ill be available the next time the module is.

Download PDF sample

Algebraic Semantics of Imperative Programs by Joseph A. Goguen, Grant Malcolm


by Thomas
4.0

Rated 4.66 of 5 – based on 49 votes