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.

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**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.

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

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