Applications of typed $\lambda$-terms to categorical attributed graph transformations

This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of $\lambda$-terms in a typed $\lambda$-calculus with inductive types. In this paper we present solutions to cope with single pushout construction for the graph structure and the computations functions. As this rewrite system uses inductive types, the expressive power of attribute computations increases and appears to be more efficient than the one based on $\Sigma$-algebras. Some examples showing the interest of our computation approach are described in this paper.