= Solution
Clamp a nonpositive count to zero. Taking restricts the domain of present indices; dropping translates that domain:
``
take' :: Int -> List a -> List a
take' count (List f) = List query
where
k = max 0 count
query i
| i < 0 || i >= k = Nothing
| otherwise = f i
drop' :: Int -> List a -> List a
drop' count (List f) = List query
where
k = max 0 count
query i
| i < 0 || i > maxBound - k = Nothing
| otherwise = f (i+k)
length' :: List a -> Int
length' (List f) = countFrom 0
where
countFrom i = case f i of
Nothing -> i
Just _ -> countFrom (i+1)
``
For finite length $m$, the first two operations give lengths $\min(k,m)$ and $\max(m-k,0)$, respectively. The length loop reaches the first absent index, namely $m$, so it terminates for a total finite representation. It does not terminate on an infinite represented <sequence>. There is no assumption that an arbitrary stored query <function> takes constant time.
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