FOSD program cubes

In <a href="/facts/Feature-oriented_software_development/Ilc1y1nA">feature-oriented software development</a>, feature-oriented software development program cubes (FOSD program cubes) are n-dimensional arrays of functions (program transformations) that represent n-dimensional product lines. A program is a composition of features: a base program is augmented with increments in program functionality, called features, to produce a complex program. A <a href="/facts/Software_product_line/I6SIMRb7">software product line</a> (SPL) is a family of related programs. A typical product line has F0 as a base program, and F1..Fn as features that could be added to F0. Different compositions of features yield different programs.
Let + denote the feature composition operation. A program P in SPL might have the following expression:

P = F8 + F4 + F2 + F1 + F0
That is, P extends program F0 with features F1, F2, F4, and F8 in this order.
We can recast P in terms of a projection and contraction of a 1-dimensional array.
Let Fi = [F0 .. Fn] denote the array of features used by a product line. A projection of Fi eliminates
unneeded features, yielding a shorter array (call it) Gi. A contraction of Gi sums each Gi in a specific order, to yield a scalar expression. The expression for P becomes:

P
        =
        
          ∑
          
            i
            =
            (
            0
            ,
            1
            ,
            2
            ,
            4
            ,
            8
            )
          
        
        
          
            F
          
          
            i
          
        
      
    
    {\displaystyle P=\sum _{i=(0,1,2,4,8)}\mathbf {F} _{i}}

where the index values accomplish projection and summation is array contraction. This idea 
generalizes to n-dimensional arrays that model multi-dimensional product lines.

FOSD program cubes open-in-new

FOSD program cubes