In particular, you can search compact infinite spaces by only considering a finite number of steps: "What is going on here is that computable functionals are continuous, which amounts to saying that finite amounts of the output depend only on finite amounts of the input. But the Cantor space is compact, and in analysis and topology there is a theorem that says that continuous functions defined on a compact space are uniformly continuous. In this context, this amounts to the existence of a single `n` such that for all inputs it is enough to look at depth `n` to get the answer (which in this case is always finite, because it is an integer). I’ll explain all this in another post. Here I will illustrate this by running the program in some examples."
In particular, you can search compact infinite spaces by only considering a finite number of steps: "What is going on here is that computable functionals are continuous, which amounts to saying that finite amounts of the output depend only on finite amounts of the input. But the Cantor space is compact, and in analysis and topology there is a theorem that says that continuous functions defined on a compact space are uniformly continuous. In this context, this amounts to the existence of a single `n` such that for all inputs it is enough to look at depth `n` to get the answer (which in this case is always finite, because it is an integer). I’ll explain all this in another post. Here I will illustrate this by running the program in some examples."
This is the follow-up post mentioned in the quote: http://math.andrej.com/2008/11/21/a-haskell-monad-for-infini...