A formal approach to the specification and transformation of constraints in MDE

This paper introduces a formal approach to constraint-aware model transformation which supports specifying constraints in the definition of transformation rules. These constraints are used to control which structure to create in the target model and which constraints to add to the created structure. The proposed approach is classified under heterogeneous, graph-based and out-place model transformations; and illustrated by applying it to a language translation. It is based on the Diagram Predicate Framework which provides a formalisation of (meta)modelling based on category theory and graph transformation. In particular, the proposed approach uses non-deleting transformation rules that are specified by a joined modelling language which is defined by relating the source and target languages. The relation between source and target languages is formalised by morphisms from their corresponding modelling formalisms into a joined modelling formalism. Furthermore, the application of transformation rules is formalised as a pushout construction and the final target model is obtained by a pullback construction.