  Linear logics have been shown to be able to embed both rewriting-based
approaches and process calculi in a single, declarative framework. In this
paper we are exploring the embedding of double-pushout graph transformations
into quantified linear logic, leading to a Curry-Howard style isomorphism
between graphs and transformations on one hand, formulas and proof terms on the
other. With linear implication representing rules and reachability of graphs,
and the tensor modelling parallel composition of graphs and transformations, we
obtain a language able to encode graph transformation systems and their
computations as well as reason about their properties.
