A constraint language for algebraic term based on rewriting theory

A key feature of Model Driven Engineering is the ability to define meta-models, but also constraints that have to be satisfied by their instances. Constraints are expressed in OCL (Object Constraint Language), which became a standard. OCL Constraints offer the possibility to capture properties which cannot be easily encoded in the meta-model. In the programming language community, instead of meta-models, we generally use grammars or algebraic signatures to define the syntax of the programs or abstract syntax trees (AST) we consider. But unfortunately, even when considering rich formalisms such as many-sorted signatures with subtyping or dependent types, they are not expressive enough to encode in a simple way some subsets of terms we want to consider. For instance arithmetic expressions which have at most two levels of plus operator, this includes a, a+b, (a+b)+(b+c), but not a+(b+(c+d)) for instance. There is a need for a constraint language dedicated to tree based data structures such as terms and AST. In this paper we present both a language to express constraints on trees, and a compilation scheme that shows how to translate constraints into an executable formalism based on term rewriting and strategies