FOSD metamodels

Feature-oriented software development (FOSD) is a general paradigm for software generation, where a model of a product line is a tuple of 0-ary and 1-ary functions (program transformations). This page discusses a more abstract concept of models of product lines of product lines (PL**2) called metamodels, and product lines of product lines of product lines called meta-metamodels (PL**3), and further abstract concepts.

Metamodels
A metamodel is a model whose instances are models. A GenVoca model of a product line is a tuple whose components are features (0-ary or 1-ary functions). An extension (a.k.a. delta or refinement) of a model is a "meta-feature", which is a tuple of deltas that can modify an existing product line by modifying existing features and adding new features. As a simple example, consider GenVoca model M that contains three features a-c:


 * $$M = [ a, b, c ]$$

Suppose meta-model MM contains three meta-features AAA-CCC, each of which is a tuple with a single non-identity feature:



\begin{align} MM & = [ AAA, BBB, CCC ] \\ & = [ [a,0,0], [0,b,0], [0,0,c] ] \end{align} $$

where 0 is the null feature. Model M is constructed by adding the meta-features of MM, where + is the composition operation (see FOSD).



\begin{align} M & = AAA + BBB + CCC & \text{expression} \\ & = [a,0,0]+[0,b,0]+[0,0,c] & \text{substitution} \\ & = [a+0+0, 0+b+0, 0+0+c] & \text{composition} \\ & = [a,b,c] & \text{simplification where } 0+x=x+0=x \end{align} $$

MM models a product line of product lines (PL**2). That is, different MM expressions correspond to GenVoca models of different product lines..