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
iand returns the
ith entry of the sequence, or
A computable function
f(x, y)that takes in some "state"
xfrom the previous step, as well as some extra input
yat the current step.