A Formal Model for Direct-style Asynchronous Observables

Languages like F#, C#, and recently also Scala, provide "Async" programming models which aim to make asynchronous programming easier by avoiding an inversion of control that is inherent in callback-based programming models. This paper presents a novel approach to integrate the Async model with observable streams of the Reactive Extensions model. Reactive Extensions are best-known from the .NET platform, and widely-used implementations of its programming model exist also for Java, Ruby, and other languages. This paper contributes a formalization of the unified "Reactive Async" model in the context of an object-based core calculus. Our formal model captures the essence of the protocol of asynchronous observables using a heap evolution property. We prove a subject reduction theorem; the theorem implies that reduction preserves the heap evolution property. Thus, for well-typed programs our calculus ensures the protocol of asynchronous observables.