Nondeterminism introduced by race conditions and message reorderings makes parallel and
distributed programming hard. Nevertheless, promising approaches such as LVars and CRDTs address
this problem by introducing a partial order structure on shared state that describes how the state evolves over time. \emph{Monotone} programs that respect the order are deterministic. Datalog-inspired languages incorporate this idea of monotonicity in a first-class way but they are not general-purpose. We would like parallel and distributed languages to be as natural to use as any
functional language, without sacrificing expressivity, and with a formal basis of
study as appealing as the lambda calculus.

This paper presents $\lambda_\vee$, a core language for deterministic parallelism that embodies the ideas above. In $\lambda_\vee$, values may increase over time according to a \emph{streaming order} and all computations are monotone with respect to that order. The streaming order coincides with the approximation order found in Scott semantics and so unifies the foundations of functional programming with the foundations of deterministic distributed computation. The resulting lambda calculus has a computationally adequate model rooted in domain theory. It integrates the compositionality and power of abstraction characteristic of functional programming with the declarative nature of Datalog.