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.

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**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 .

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

by Joseph

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