How to tell if a list is infinite?

Question

Is there a way to tell if a list in Haskell is infinite? The reason is that I don\'t want to apply functions such as length to infinite lists.

Answer 1

The Halting Problem was first proved unsolvable by assuming a Halting Oracle existed, then writing a function that did the opposite of what that oracle said would happen. Let's reproduce that here:

isInfinite :: [a] -> Bool
isInfinite ls = {- Magic! -}

Now, we want to make a list impossibleList that does the opposite of what isInfinite says it should. So, if impossibleList is infinite, it is actually [], and if it isn't infinite, it is something : impossibleList.

-- using a string here so you can watch it explode in ghci
impossibleList :: [String]
impossibleList =
    case isInfinite impossibleList of
        True -> []
        False -> "loop!" : impossibleList

Try this out yourself in ghci with isInfinite = const True and isInfinite = const False.