lastLE cleanup

Remember lastLE? Back when we were trying to determine how many digits/bits it takes to represent a non-negative Integer, we used it to avoid copying a prefix of a list just to grab the value at its end.

lastLE :: Integer -> [Integer] -> Maybe (Integer, Int)

lastLE n xs =
    let lastLE' xs prevVal prevIndex
           | head xs <= n = lastLE' (tail xs) (head xs) (prevIndex + 1)
           | otherwise    = if prevIndex < 0 then Nothing
                                             else Just (prevVal, prevIndex)
    in lastLE' xs (-1) (-1)

It still bugs me. First, the mixed guards and if/else are less than idiomatic Haskell:

lastLE n xs =
    let lastLE' xs prevVal prevIndex
           | head xs <= n  = lastLE' (tail xs) (head xs) (prevIndex + 1)
           | prevIndex < 0 = Nothing
           | otherwise     = Just (prevVal, prevIndex)
    in lastLE' xs (-1) (-1)

Second, the head and tail are clumsy:

lastLE n xs =
    let lastLE' (x:xs) prevVal prevIndex
           | x <= n        = lastLE' xs x (prevIndex + 1)
           | prevIndex < 0 = Nothing
           | otherwise     = Just (prevVal, prevIndex)
    in lastLE' xs (-1) (-1)

Third, that accumulator should be strict, so pretend there's a ! in front of prevIndex in that let.

I think I'd rather see Nothing as the otherwise case.

lastLE n xs =
    let lastLE' (x:xs) prevVal !prevIndex
           | x <= n         = lastLE' xs x (prevIndex + 1)
           | prevIndex >= 0 = Just (prevVal, prevIndex)
           | otherwise      = Nothing
    in lastLE' xs (-1) (-1)

Come to think of it, we can be consistent in our use of pairs:

lastLE n xs =
    let lastLE' (x:xs) !prev@(val, index)
           | x <= n         = lastLE' xs (x, index + 1)
           | prevIndex >= 0 = Just prev
           | otherwise      = Nothing
    in lastLE' xs (-1, -1)

Now, one more thing. Can I get rid of the magic numbers there, the -1s? The -1 as initial index needs to be there to get the correct position in the list of powers of the base. The initial val will never be used. If the whole pair is strict, though, we couldn't pass in ⊥ ("bottom", the undefined value, which is undefined in Haskell). Perhaps

lastLE n xs =
    let lastLE' (x:xs) prev@(val, !index)
           | x <= n     = lastLE' xs (x, index + 1)
           | index >= 0 = Just prev
           | otherwise  = Nothing
    in lastLE' xs (undefined, -1)

would be the way to go. Hey! We never even use that value here--it's used in the caller--so we can write

lastLE n xs =
    let lastLE' (x:xs) prev@(_, !index)
           | x <= n     = lastLE' xs (x, index + 1)
           | index >= 0 = Just prev
           | otherwise  = Nothing
    in lastLE' xs (undefined, -1)

and it should work (sure enough, it does), as well as expressing explicitly that we don't use it. Well, that's one magic number down, at least.

Small things...

Good grief... I've let this go for a month. (UPDATE: No, I haven't. It helps to read the dates carefully.)

An option in pattern matching that I wasn't fully aware of: you can use _ when you don't care about what is there, and have no need to refer to it. I guess I did use it on the ByteString readInteger that returns Maybe(Integer, ByteString):

process line = case map B.readInteger (B.words line) of
               [Just (m, _), Just (n, _)] -> numXs m n
               _                          -> -1

But I didn't realize that I could use it in

ysInRange m n d
    | nVal == n = nPos - mPos + 1
    | otherwise = nPos - mPos
    where (_,    mPos) = findFirst' m
          (nVal, nPos) = findFirst' n
          findFirst' x = case findFirst (Ge x, Any) (dDigitYTree d) of
                             Just (Max i, Max j) -> (i, j)
                             Nothing             -> (tenToThe d, numNDigitYs d)

because we need only check for an exact match at the high end.