By T. H. Tse

Established methodologies are a favored and strong device in details structures improvement. many various ones exist, every one using a few versions and so a specification needs to be switched over from one shape to a different throughout the improvement method. to unravel this challenge, Dr. Tse proposes a unifying framework at the back of well known dependent versions. He methods the matter from the viewpoints of algebra and class conception. He not just develops the frameworks but in addition illustrates their sensible and theoretical usefulness. hence, this e-book will offer perception for software program engineers into how methodologies will be formalized, and should open up quite a number purposes and difficulties for theoretical laptop scientists.

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**Extra resources for A Unifying Framework for Structured Analysis and Design Models: An Approach Using Initial Algebra Semantics and Category Theory**

**Sample text**

For example: (/) Commutative law holds for the operations seln and para: se\nE(u, v) = seln^O, u) para£(w, v) = para£(v, u) but it does not hold for the operation sequ. (//) Associative law holds for the operations sequ, seln and para when there is no intermediate process name: 44 Chapter 4 An Initial Algebra Framework sequE(u, v)), w) , sequ^v, ^ ^ ^ £ , v)), H>) = selnE(u, task^Cnull^, seln^v, w))) para^task^null^, para^O, v)), w) = para £ (w, task^null^, para^(v, w))) (///) Furthermore, if we create an error supersort for every sort in our signature, and specify conditional equations, then more complex behavioural rules can also be defined.

2 ALGEBRAS In studying the properties of systems of a complex nature, we often classify the objects under consideration into different types. For example, we may have object types like booleans and integers in computer science, or tasks and events in information systems. We are also interested in the operations which act on these objects and generate other objects. We want to provide an abstract notion of these object types, independent of the objects under study. The formal mechanism for defining these object types and operations is known as a signature (like the key signature in music).

Hence h is an isomorphism or, in order words, A is isomorphic to B. 6 Sample Term in Initial Algebra 48 Chapter 4 An Initial Algebra Framework We shall construct X as a union of X^ for all integers j > 0. We construct X^ by mathematical induction as follows: (a) For any sort s in S, we define X ' ' as the set containing all terms of the form " a " , where each a is a symbol in ZA . , j-l. ; tnY\ where a is a symbol in £ and each t is a term in X ^ such that max{/ } = 7 - 1 . We define x ' " r V 5 5 to be the family of all X^ u ; .