Enumerator programs appear quite often in even an elementary computer science textbook without a formal definition. It does not seem to fit the standard definition of a computable function (through mu recursion, Turing machines or lambda calculus), which takes a single input and a single output.
What's a standard literature definition of an enumerator program? I would imagine either:
A computable function that takes in an additional input
i
and returns thei
th entry of the sequence, orA computable function
f(x, y)
that takes in some "state"x
from the previous step, as well as some extra inputy
at the current step.