We present a model of jazz improvisation where short-term decision making by each performer is modeled as a function from contexts to music. Contexts can be shared, such as an agreed-upon chord progression, or they can also be private - a current state for each musician. We formalize this model in Haskell to generate potentially infinitely long jazz improvisations, and we have also used the same model in Python to support real-time human-computer interaction through jazz.