Categories for Software Engineering by José L. Fiadeiro

By José L. Fiadeiro

Demonstrates how classification concept can be utilized for formal software program improvement. The mathematical toolbox for the software program Engineering within the new age of advanced interactive platforms.

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For every i is said to be true in A, written A N ^ , if and only if A N^,-0 at every state /. We also write A Nxc& for a collection of propositions 0 meaning that each proposition of

for a collection A of sequences meaning that is true in every XEA. Finally, for every set

is a consequence of <&, denoted

We are going to show that this synchronous flavour is captured through the notion of specification morphism (interpretation between theories) as a mathematical model of the relationship between systems and their components. An interpretation between theories is typically defined as a mapping between their signatures that preserves theorems. Notice, once again, the idea of structure preservation presiding to the definition of morphisms. The structure being preserved in this case is given by the properties of the processes involved as captured through the theorems of the specifications.

Specifications have a "social life" that results from the need to adapt features. Feature adaptation [86] typically comes about when the class is inherited. To be consistent with [86], the notion of morphism that can capture such structural aspects of class specifications has to account for the following operations: • Rename a feature. e. without a chosen implementation). • Redefine a feature, changing the original signature, preconditions or postconditions. • Add conditions to the invariant. There are other circumstances in which features can be changed, like assigning an implementation to a feature that so far was "deferred".

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