GDA is written in C, checkout its API documentation.
C API Gda documentation
C API Gdaui documenation, for GTK+ 3.0 widgets.
GDA has GObject Introspection support, so Vala Bindings are automatically generated.
GDA has GObject Introspection support, Vala Bindings and Vala Bindings Documentation
GDA provides a set of GTK+ widgets you can use in your application, Vala Bindings and Vala Bindings Documentation