We present Aleatora, an early-stage framework for building compositions from lazy, effectful streams. Aleatora’s streams, which may be combined by sequential, parallel, or functional composition, are well-suited to expressing interactive and aleatoric musical compositions. Aleatora includes a networking module which aids in writing compositions for the Internet of Sounds using network data sources such as OSC, external APIs, and Internet sound repositories (e.g. Freesound). This paper describes the design and implementation of Aleatora and demonstrates how it can facilitate weaving external input sources, such as network streams, into compositions.