Visibly Pushdown Expression Effects for XML Stream Processing

We define an effect system, based upon visibly pushdown languages (VPLs), for a programming language that processes streams of tokens with parenthesis-like matching, as found in XML documents or s-expressions. The effect analysis ensures that programs read and write words in which tokens match, despite the fact that tokens are read and written individually. In particular, the novel treatment of input provides a compositional description of the behaviour of programs with lookahead. We introduce visibly pushdown expressions (VPEs), corresponding to the class of VPLs, as the effects. VPEs generalize regular expression types by incorporating intersection, unmatched tokens, and overlapped concatenation (used in the analysis of operations with lookahead). Hosoya, Vouillon, and Pierce’s decision procedure for language inclusion between regular expression types, via a translation to non-deterministic tree automata, does not apply to VPEs. Instead we obtain a decision procedure via a translation of VPEs to Alur and Madhusudan’s monadic second order logic with matching relation MSOμ.