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Section: Scientific Foundations

Relational paradigm

For any source code analysis or transformation, after fact extraction comes elaboration, aggregation or other further analyses of these facts. For fact analysis, we base our entire research on the simple formal concept of a “relation”.

There are at least three lines of research that have explored the use of relations. First, in SQL, n-ary relations are used as basic data type and queries can be formulated to operate on them. SQL is widely used in database applications and a vast literature on query optimization is available. There are, however, some problems with SQL in the applications we envisage: (a) Representing facts about programs requires storing program fragments (e.g., tree-structured data) and that is not easy given the limited built-in datatypes of SQL; (b) SQL does not provide transitive closures, which are essential for computing many forms of derived information; (c) More generally, SQL does not provide fixed-point computations that help to solve sets of equations. Second, in Prolog, Horn clauses can be used to represent relational facts and inference rules for deriving new facts. Although the basic paradigm of Prolog is purely declarative, actual Prolog implementations add imperative features that increase the efficiency of Prolog programs but hide the declarative nature of the language. Extensions of Prolog with recursion have resulted in Datalog in many variations [AHV95]. In F(p)–L a Prolog database and a special-purpose language are used to represent and query program facts.

Third, in SETL, the basic data type was the set. Since relations can easily be represented as sets of tuples, relation-based computations can, in principle, be expressed in SETL. However, SETL as a language was very complicated and has not survived. However, work on programming with sets, bags and lists has continued well into the 90's and has found a renewed interested with the revival of Lisp dialects in 2008 and 2009.

We have already mentioned the relational program representation by Linton. In Rigi, a tuple format (RSF) is introduced to represent untyped relations and a language (RCL) to manipulate them. Relational algebra is used in GROK, Crocopat and Relation Partition Algebra (RPA) to represent basic facts about software systems and to query them. In GUPRO graphs are used to represent programs and to query them. Relations have also been proposed for software manufacture, software knowledge management, and program slicing. Sometimes, set constraints are used for program analysis and type inference. More recently, we have carried out promising experiments in which the relational approach is applied to problems in software analysis and feature analysis. Typed relations can be used to decouple extraction, analysis and visualization of source code artifacts. These experiments confirm the relevance and viability of the relational approach to software analysis, and also indicate a certain urgency of the research direction of this team.



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