Download Refinement Calculus: A Systematic Introduction by Ralph-Johan Back PDF

By Ralph-Johan Back

ISBN-10: 0387984178

ISBN-13: 9780387984179

ISBN-10: 1461216745

ISBN-13: 9781461216742

Much present learn in computing device technology is worried with questions: is a software right? and the way will we increase an accurate application holding correctness? This latter query is called the refinement of courses and the aim of this ebook is to contemplate those questions in a proper atmosphere. in truth, correctness seems to be a unique case of refinement and so the focal point is on refinement. even supposing an inexpensive history wisdom is believed from arithmetic and CS, the publication is a self-contained advent compatible for graduate scholars and researchers coming to this topic for the 1st time. there are many workouts supplied of various levels of challenge.

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9, is also a refinement and thus a correct implementation of the specification. Moreover, any choice that cuts down on the number of alternatives will also be a refinement of the specification. An example is x := 0 n x := 1 n ... n x := 9 ~ x:= 3 n x := 7 . This explains the central importance of the notion of refinement in analyzing contracts: it captures and generalizes the notion of implementing a specification. In some situations we need to consider an infinite number of alternatives. For instance, to set x to any nonnegative value, we can use the following specification: n {x := n I n ~ O} .

This explains the central importance of the notion of refinement in analyzing contracts: it captures and generalizes the notion of implementing a specification. In some situations we need to consider an infinite number of alternatives. For instance, to set x to any nonnegative value, we can use the following specification: n {x := n I n ~ O} . Here one of the statements x : = n is chosen from the infinite set of possible statements. As an executable statement, this construct would be difficult to implement in its full generality (in the sense that any possibility could be chosen in practice).

2_________________________________ Posets, Lattices, and Categories This chapter introduces the central mathematical structures that are needed to formalize the refinement calculus: partially ordered sets (posets), lattices, and categories. We identify the basic properties of posets and lattices, and use them for a classification of lattices. We also show how to construct new lattices out of old ones as Cartesian products and function spaces. We study structure-preserving mappings (homomorphisms) on lattices.

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