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.
A metamodel is a model whose instances are models.[1] 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 whichis 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&expression\\ &=[a,0,0]+[0,b,0]+[0,0,c]&substitution\\ &=[a+0+0,0+b+0,0+0+c]&composition\ &=[a,b,c]&simplificationwhere0+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..