  Probabilistic pushdown automata (pPDA) are a standard operational model for
programming languages involving discrete random choices and recursive
procedures. Temporal properties are useful for specifying the chronological
order of events during program execution. Existing approaches for model
checking pPDA against temporal properties have focused mostly on
$\omega$-regular and LTL properties. In this paper, we give decidability and
complexity results for the model checking problem of pPDA against
$\omega$-visibly pushdown languages that can be described by specification
logics such as CaRet. These logical formulae allow specifying properties that
explicitly take the structured computations arising from procedural programs
into account. For example, CaRet is able to match procedure calls with their
corresponding future returns, and thus allows to express fundamental program
properties such as total and partial correctness.
