Feature-oriented Programming - FOMDD

FOMDD

Feature Oriented Model Driven Design (FOMDD) combines the ideas of AHEAD with Model Driven Design (MDD) (a.k.a. Model-Driven Architecture (MDA)). AHEAD functions capture the lockstep update of program artifacts when a feature is added to a program. But there are other functional relationships among program artifacts that express derivations. For example, the relationship between a grammar g_f and its parser source s_f is defined by a compiler-compiler tool, e.g., javacc. Similarly, the relationship between Java source s_f and its bytecode b_f is defined by the javac compiler. A commuting diagram expresses these relationships. Objects are program representations, downward arrows are derivations, and horizontal arrows are deltas. The figure to the right shows the commuting diagram for program p₃ = i•j•h = .

A fundamental property of a commuting diagram is that all paths between two objects are equivalent. For example, one way to derive the bytecode b₃ of parser p₃ (lower right object in the above figure) from grammar g_f of parser f (upper left object) is to derive the bytecode b_f and refine to b₃, while another way refines g_f to g₃, and then derive b₃:

b_i • b_j • javac • javacc = javac • javacc • g_i • g_j

There are possible paths to derive the bytecode b₃ of parser p₃ from the grammar g_f of parser f. Each path represents a metaprogram whose execution synthesizes the target object (b₃) from the starting object (g_f). There is a potential optimization: traversing each arrow of a commuting diagram has a cost. The cheapest (i.e., shortest) path between two objects in a commuting diagram is a geodesic, which represents the most efficient metaprogram that produces the target object from a given object.

Note: A “cost metric” need not be a monetary value; cost may be measured in production time, peak or total memory requirements, some informal metric like “ease of explanation”, or a combination of the above (e.g., multi-objective optimization). The idea of a geodesic is quite general, and should be understood and appreciated from this more general context.

Note: It is possible for there to be m starting objects and n ending objects in a geodesic; when m=1 and n>1, this is the Directed Steiner Tree Problem, which is NP-hard.

Commuting diagrams are important for at least two reasons: (1) there is the possibility of optimizing the synthesis of artifacts (e.g., geodesics) and (2) they specify different ways of constructing a target object from a starting object. A path through a diagram corresponds to a tool chain: for an FOMDD model to be consistent, it should be proven (or demonstrated through testing) that all tool chains that map one object to another in fact yield equivalent results. (If different paths/tool chains yield different results, then either there is a bug in one or more of the tools or the FOMDD model is wrong).

Note: the above ideas were inspired by category theory.