FOSD Origami

Feature-oriented programming or ''feature-oriented software development (FOSD)'' is a general paradigm for program synthesis in software product lines. The feature-oriented programming page is recommended, it explains how an FOSD model of a domain is a tuple of 0-ary functions (called values) and a set of 1-ary (unary) functions called features. This page discusses multidimensional generalizations of FOSD models, which are important for compact specifications of complex programs.

Origami

A fundamental generalization of metamodels is ''origami''. The essential idea is that a program's design need not be represented by a single expression; multiple expressions can be used. This involves the use of multiple orthogonal GenVoca models.

:: Example: Let T be a tool model, which has features P (parse), H (harvest),D (doclet), and J (translate to Java). P is a value and the rest are unary-functions. A tool T1 that parses a file written in a Java dialect language and translates it to pure Java is modeled by: T1 = J•P. And a javadoc-like tool T2 parses a file in a Java dialect, harvests comments, and translates harvested comments into an HTML page is: T2 = D•H•P. So tools T1 and T2 are among the products of the product line of T.

:: A language model L describes a family (product line) of Java dialects. It includes the features: B (Java 1.4), G (generics), S (State machines). B is a value, and the rest are unary functions. So a dialect of Java L1 that has generics (i.e., Java 1.5) is: L1 = G•B. And a dialect of Java L2 that has language support for state machines is: L2 = S•B. So dialects L1 and L2 are among the products of the product line of L.

:: To describe a javadoc like tool (E) for the dialect of Java with state machines requires two expressions: one that defines the tool functionality for E (using the T model) and its Java dialect (using the L model):

E = D•H•P -- tool equation
E = S•B -- language equation

:: Models L and T are orthogonal GenVoca models: one expresses the feature-based structure of the E tool, and the other the feature-based structure of its input language. Note that models T and L really are ''abstract'' in the following sense: the implementation of any feature of T really depends on the tool's dialect (expressed by L), and (symmetrically) the implementation of any feature of L really depends on the tool's functionality (expressed by T). So the only way one could implement E is by knowing both T and L equations.

Let U= ₁,U₂,...,U_nbe a GenVoca model of n features, and
W= ₁,...W_mbe a GenVoca model of m features. The relationship
between two orthogonal models U and W is a matrix UW, called an
''Origami matrix'', where each
row corresponds to a feature in U and each column corresponds to
a feature in W. Entry UW_ij is a function that implements the
''combination'' of features U_i and W_j.

: Note: UW is the tensor product of U and W (i.e., UW=U×W).

$UW = U \times W = \begin UW_ & UW_ & \cdots & UW_ \\ \vdots & \vdots & \ddots & \vdots \\ UW_ & UW_ & \cdots & UW_ \end$

:: Example. Recall models T= ,H,D,Jand L= ,G,S The Origami matrix TL is:

$TL = T \times L = \begin PB & PG & PS \\ HB & HG & HS \\ DB & DG & DS \\ JB & JG & JS \end$

:: where PB is a value that implements a parser for Java, PG is a unary-function that extends a Java parser to parse generics, and PS is a unary-function that extends a Java parser to parse state machine specifications. HB is a unary-function that implements a harvester of comments on Java code. HG is a unary-function that implements a harvester of comments on generic code, and HS is a unary-function that implements a harvester of comments on state machine specifications, and so on.

To see how multiple equations are used to synthesize a program, again consider
models U and W. A program F is described by two equations, one per model. We can
write an equation for F in two different ways: referencing features by name or
by their index position, such as:

$F = U_1 \cdot U_2 \cdot U_4 = \sum_ U_i$—U expression of F

$F = W_1 \cdot W_3 = \sum_ W_i$—W expression of F

The UW model defines how models U and W are implemented. Synthesizing program F involves projecting UW of unneeded columns and rows, and aggregating (a.k.a. tensor contraction):

$F = UW_ \cdot UW_ \cdot ... \cdot UW_ = \sum_ \sum_ UW_ = \sum_ \sum_ UW_$

A fundamental property of origami matrices, called ''orthogonality'', is that the order in which dimensions are contracted does not matter. In the above equation, summing across the U dimension (index i) first or the W dimension (index j) first does not matter. Of course, orthogonality is a property that must be verified. Efficient (linear) algorithms have been developed to verify that origami matrices (or tensors/n-dimensional arrays) are orthogonal. The significance of orthogonality is one of view consistency. Aggregating (contracting) along a particular dimension offers a 'view' of a program. Different views should be consistent: if one repairs the program's code in one view (or proves properties about a program in one view), the correctness of those repairs or properties should hold in all views.

In general, a product of a product line may be represented by n expressions, from n ''orthogonal'' and ''abstract'' GenVoca models G₁ ... G_n. The Origami matrix (or cube or tensor) is an n-dimensional array A:

$A = G_1 \times ... \times G_n = \prod_^n G_k$

A product H of this product line is formed by eliminating unnecessary rows, columns, etc.
from A, and aggregating (contracting) the n-cube into a scalar:

$H = \sum_ \sum_ ... \sum_ G_$

:: Example. Recall program E and model T= ,H,D,J E=D•H•P=T₂•T₁•T₀. Similarly, E's representation in model L= ,G,Sis E=S•B=L₂•L₀. Synthesizing E given Origami model TL is evaluating the following expression: $E = \sum_ \sum_ TL_ = \sum_ \sum_ TL_$.

Applications

There are several of product line applications developed using Origami. Among them include:

* tp://ftp.cs.utexas.edu/pub/predator/Origami.pdf AHEAD Tool Suite and Extensible Java Preprocessors* tp://ftp.cs.utexas.edu/pub/predator/ECOOP2005.pdf Expression Problem or the Extensibility Problem* tp://ftp.cs.utexas.edu/pub/predator/OrigamiMDSC.pdf Refinements and Multi-Dimensional Separation of Concerns
More applications to be supplied.

See also

* Feature-oriented programming
* FOSD metamodels

References

{{DEFAULTSORT:Fosd Origami
Programming paradigms