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Algebraic Semantics of Imperative Programs: (Foundations of Computing)

Algebraic Semantics of Imperative Programs: (Foundations of Computing)


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About the Book

"Algebraic Semantics of Imperative Programmes" presents a self-contained and novel "executable" introduction to formal reasoning about imperative programmes. The authors' primary goal is to improve programming ability by improving intuition about what programmes mean and how they run. The semantics of imperative programmes 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 programme 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 "programme" "is" an equational theory, and every OBJ computation "proves" some theorem about such a theory. This means that an OBJ programme used for defining the semantics of a programme 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 programmes on abstract machines. These axioms can then be used in mechanical proofs of properties of programmes. Intended for advanced undergraduates or beginning graduate students, "Algebraic Semantics of Imperative Programmes" contains many examples and exercises in programme verification, all of which can be done in OBJ.

Table of Contents:
Part 1 Background in general algebra and OBJ: signatures; algebras; terms; variables; equations; rewriting and equational deduction - attributes of operations, denotational semantics for objects, the theorem of constants; importing modules; literature. Part 2 Stores, variables, values, and assignment: stores, variables, and values - OBJ's built-in inequality; assignment. Part 3 Composition and conditionals: sequential composition; conditionals; structural induction. Part 4 Proving programme correctness: example - absolute value; sample - computing the maximum of two values. Part 5 Iteration: invariants - example - greatest common divisor; termination. Part 6 Arrays: some simple examples; exercises; specifications and proofs. Part 7 Procedures: non-recursive procedures - procedures with no parameters, procedures with varparameters, procedures with expparameters; recursive procedures - procedures with no parameters, procedures with varparameters. Part 8 Some comparison with other approaches; summary of the semantics; first order logic and induction; order sorted algebra; OBJ3 syntax; instructors' guide.

About the Author :
Grant Malcolm is Chancellor of University of York and Chairman of NHS England.


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Product Details
  • ISBN-13: 9780262071727
  • Publisher: MIT Press Ltd
  • Publisher Imprint: MIT Press
  • Height: 229 mm
  • No of Pages: 240
  • Spine Width: 27 mm
  • Width: 180 mm
  • ISBN-10: 026207172X
  • Publisher Date: 22 May 1996
  • Binding: Hardback
  • Language: English
  • Series Title: Foundations of Computing
  • Weight: 590 gr


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Algebraic Semantics of Imperative Programs: (Foundations of Computing)
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