Illustration.  DL has been successfully applied to a great number of discontinuous dependencies, both of the overt and of the covert type. The non-deterministic operations have been used to model particle shift and complement alternation constructions.  The deterministic operations of sort 1 (single split point) are used in the analysis of non-peripheral extraction, discontinuous idioms, gapping and ellipsis, quantifier scope construal, reflexivisation, pied-piping and the Dutch cross- serial dependencies, among others.