Dataflow execution models are used to build highly scalable parallel systems. A programming model that targets parallel dataflow exe- cution must answer the following question: How can parallelism between two dependent nodes in a dataflow graph be exploited? This is difficult when the dataflow language or programming model is implemented by a monad, as is common in the functional community, since expressing dependence between nodes by a monadic bind suggests sequential execution. Even in monadic constructs that explicitly separate state from computation, problems arise due to the need to reason about opaquely defined state. Specifically, when abstractions of the chosen programming model do not enable adequate reasoning about state, it is difficult to detect parallelism between composed stateful computations. In this paper, we propose a programming model that enables the composition of stateful computations and still exposes opportunities for parallelization. We also introduce smap, a higher-order function that can exploit parallelism in stateful computations. In addition to a formalization in the language of category theory, we present an implementation of our programming model and smap in Haskell. We show that basic concepts from functional reactive programming can be built on top of our programming model with little effort. We compare these implementations to a state-of-the-art approach using monad-par and LVars to expose parallelism explicitly and reach the same level of performance, showing that our programming model successfully extracts parallelism that is present in an algorithm. Further evaluation shows that smap is expressive enough to implement parallel reductions and our programming model resolves short-comings of the stream-based programming model for current state-of-the-art big data processing systems.