Interleaving Strategies

Rewrite strategies are used to specify how mathematical exercises are solved in interactive learning environments, and to provide feedback to students solving such exercises. We have developed a generic strategy language with which we can specify rewrite strategies in many (mathematical) domains. Although our strategy language is quite powerful, it lacks an essential component for specifying strategies, namely the interleaving of two strategies. Often students have to perform multiple subtasks, but the order in which these tasks are performed is irrelevant, and steps of solutions may be interleaved. We show the need for combinators that support interleaving by means of several examples. We extend our strategy language with different combinators for interleaving, define the semantics of the extension, and show how the interleaving combinators are implemented in the parsing framework we use for recognizing student behavior and providing hints.