Discrete Mathematics

Read e-book online Algebraic Semantics of Imperative Programs PDF

By Joseph A. Goguen, Grant Malcolm

ISBN-10: 026207172X

ISBN-13: 9780262071727

Algebraic Semantics of valuable courses provides a self-contained and novel "executable" creation to formal reasoning approximately principal courses. The authors' fundamental aim is to enhance programming skill by way of bettering instinct approximately what courses suggest and the way they run.The semantics of important courses is laid out in a proper, carried out notation, the language OBJ; this makes the semantics hugely rigorous but easy, 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. therefore, an OBJ "program" is an equational conception, and each OBJ computation proves a few theorem approximately the sort of conception. which means an OBJ application used for outlining the semantics of a application already has an actual mathematical that means. additionally, commonplace ideas for mechanizing equational reasoning can be utilized for verifying axioms that describe the impact of crucial courses on summary machines. those axioms can then be utilized in mechanical proofs of homes of programs.Intended for complex undergraduates or starting graduate scholars, Algebraic Semantics of central courses includes many examples and workouts in application 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 Using a Computer Second Edition by John O'Donnell PDF

Discrete arithmetic utilizing a working laptop or computer bargains a brand new, "hands-on" method of instructing Discrete arithmetic. utilizing software program that's freely on hand on Mac, computer and Unix structures, the sensible language Haskell permits scholars to test with mathematical notations and ideas -- a realistic method that gives scholars with rapid suggestions and permits teachers to watch development simply.

Download e-book for iPad: A Long-run Collaboration on Games With Long-run Patient by Drew Fudenberg, David K. Levine

This ebook brings jointly the joint paintings of Drew Fudenberg and David Levine (through 2008) at the heavily attached issues of repeated video games and acceptance results, in addition to comparable papers on extra basic concerns in online game thought and dynamic video games. The unified presentation highlights the habitual issues in their paintings.

Read e-book online Diophantine analysis PDF

It is a pre-1923 old replica that was once curated for caliber. caliber insurance was once performed on every one of those books in an try and eliminate books with imperfections brought via the digitization strategy. even though we now have made top efforts - the books can have occasional blunders that don't abate the analyzing event.

Extra resources for Algebraic Semantics of Imperative Programs

Example text

We might, in fact, view the module STORE as specifying a simple programming language, and we give an example below of a program written in this language. STORE also defines the language's semantics, in that it s p e c ifies how the constructs of the language act upon, or modify, stores (in this case, there is only one construct, the assignment). The beauty of the definition is that the only restriction imposed on the sort Store is that stores associate integer values with program variables, in a way that can be modified by assignments.

Ural number expressions which c o nt ai n quoted identifiers . obj EXP i s pr QIO . sort Exp . subsort Id < Exp . op 0 : - > Exp . op s - : Exp - > Exp [pree 1 J Exp Exp -> Exp [pr ee 5J op - +op - * - : Exp Exp -> Exp [pr ee 3] endo (a) The following mo dule defines a n operation subst : Exp Id Exp -> E xp which takes an exp res si on E 1 , a quoted identifier X an d an exp ress io n E2, an d r e t u r ns the result of replacing all O Ccurrences of X in E2 by E 1 ; i . e . , E 1 is substituted for X in E2 .

E . , they are strings pr efix ed with a quote ( ' ) . ural number expressions which c o nt ai n quoted identifiers . obj EXP i s pr QIO . sort Exp . subsort Id < Exp . op 0 : - > Exp . op s - : Exp - > Exp [pree 1 J Exp Exp -> Exp [pr ee 5J op - +op - * - : Exp Exp -> Exp [pr ee 3] endo (a) The following mo dule defines a n operation subst : Exp Id Exp -> E xp which takes an exp res si on E 1 , a quoted identifier X an d an exp ress io n E2, an d r e t u r ns the result of replacing all O Ccurrences of X in E2 by E 1 ; i .

Download PDF sample

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


by Joseph
4.3

Rated 4.10 of 5 – based on 39 votes