Section: New Results
Integration of formal methods in programming languages
Formal islands and Tom
Participants : Emilie Balland, Paul Brauner, Horatiu Cirstea, Yves Guiraud, Pierre-Etienne Moreau, Claudia Tavares.
In [1] we have proposed a framework which makes possible the integration of formally defined constructs into an existing language. The Tom system is an instance of this principle: terms, first-order signatures, rewrite rules, strategies and matching constructs are integrated into Java and C for instance. The high level programming features provided by this approach are presented in [64] . The Tom system is documented in [28] . A general overview of the research problem raised by this approach are presented in [63] .
One interest of Tom is to make the compilation process independent of the considered data-structure. Given any existing data-structure, using a formal anchor definition, it becomes possible to match and to apply transformation rules on the considered data-structures. During the internship of Nicolas Henry, we have developed a mapping to connect data-strucre generated by the Eclipse Modeling Framework to the Tom framework. The long-term goal of this project is to provide constructs to describe transformations of models, ion an expressive and safe way.
Tom is also a natural choice for querying and transforming structured data and in particular XML documents. In [23] we presented an extension of Tom that makes available all the Tom features into a syntax adapted to XML document manipulation. This extension can be in fact easily adapted to accommodate any other structured data provided that a tree representation can be obtained out of it.
We are currently working on the definition of a new type system for Tom along with the associated type inference and checking algorithms [27] . This type system allows to declare polymorphic first-order signatures along subtyping and (in)equations, which will eventually extend the expressivity of the Tom language by allowing the encoding of BNF grammar. Moreover, it provides a strictly defined semantics to Tom 's “star variables” which modelize matched sublists of associative functions symbols.
Extension of pattern-matching
Participants : Emilie Balland, Horatiu Cirstea, Claude Kirchner, Pierre-Etienne Moreau.
Graphs are omnipresent in program analysis. The implementation of static analysers require the representation of control-flow and data-flow graphs for instance. As Tom can only manipulate tree structures, we proposed an extension to deal with graph structures as shown in [10] and [38] , [37] . The main idea is to use paths to represent cycles and shared parts. This leads to an original and clean way for representing, matching and transforming graphs in a rewrite-based environment.
Negation is intrinsic to human thinking and most of the time when searching for something, we base our patterns on both positive and negative conditions. In [14] we present the notion of anti-terms, i.e. terms that may contain complement symbols. We present algorithms for solving anti-pattern matching problems in the syntactic case as well as modulo an arbitrary equational theory E, and we study the specific and practically very useful case of associativity, possibly with a unity (AU). To this end, based on the syntacticness of associativity, we present a rule-based associative matching algorithm, and we extend it to AU. This algorithm is then used to solve AU antipattern matching problems. AU anti-patterns are implemented in the Tom language and we show some examples of their usage.
