Per the materialist/deterministic 'there is no free will' mental model, yes: the function taking the input stream is pure.

On the per-event basis, this model boils down to a 'function' evaluating each event with multiple outputs and inputs:

Inputs: the stimuli, mental state prior to stimuli

Outputs: your actions and resultant mental state

The output mental state is then the input for the next iteration/evaluation.