First-Order Sketch Conditions and Constraints -- A Category Independent Approach

Abstract: Generalizing different variants of "graph conditions and constraints" as well as "universal constraints" and "negative universal constraints" in the Diagram Predicate Framework (DPF), we introduce for arbitrary categories $\mathbf{Cxt}$ and "statement" functors $\mathtt{Stm}:\mathbf{Cxt}\to\mathbf{Set}$ general first-order sketch conditions and constraints. Sketches are used in DPF to formalize different kinds of diagrammatic software models. We discuss the use of sketch constraints for describing the syntactic structure of sketches. We outline the use of sketch constraints to deduce knowledge implicitly given in a sketch as well as procedures to deduce sketch constraints from given sketch constraints. We use the simple but paradigmatic modeling formalism "Category Theory" as running example.