maxBits :: (Bits a, Bounded a) => a -> Int maxBits x = bitSize m where m = maxBound _ = x == mNote the last line. It constrains x and m to be of the same type. More generally, it could be done for example thus:

sameType :: a -> a -> () sameType = undefined maxBits :: (Bits a, Bounded a) => a -> Int maxBits x = bitSize m where m = maxBound _ = sameType x mWith the maxBits we can do the following, which was what I was after.

toBits :: (Bounded a, Bits a) => a -> [Bool] toBits x = [testBit x i | i <- [0 .. maxBits x - 1]] ofBits :: Bits a => [Bool] -> a ofBits bits = foldr f 0 bits where f True n = shiftL n 1 + 1 f False n = shiftL n 1 propWord8Bits :: Int -> Bool propWord8Bits x = y == ofBits (toBits y) where y :: Word8 y = fromIntegral (x `mod` 256) propWord16Bits :: Int -> Bool propWord16Bits x = y == ofBits (toBits y) where y :: Word16 y = fromIntegral (x `mod` 256) propWord32Bits :: Int -> Bool propWord32Bits x = y == ofBits (toBits y) where y :: Word16 y = fromIntegral (x `mod` 256)However, from the theoretical viewpoint, I am rather uncertain I understand the picture completely. Suppose there are uninhabited types:

data A data BLet's give them some properties:

class TShow a where showType :: stringBut this is rejected by the compiler as showType does not mention a... Is there a way around? Yes. For example:

data Shown a = Shown String class TShow a where showType :: Shown a instance TShow A where showType = Shown "A" instance TShow B where showType = Shown "B"But when we want to write a function tshow that accepts a type as an argument, we have to either use showType and pass that argument in the return type (yes, lovely Haskell permits passing information through the return type), or make believe the type is inhabited, but to do it well we need to constrain the type of showType, which is tricky:

tshow :: TShow a => a -> String tshow a = s where shown = showType Shown s = shown constrain :: a -> Shown a -> () constrain = undefined _ = constrain a shownThen, we can use tshow like this:

tshow (undefined :: A)Does it makes sense? Hm, not really. Passing the type through the return type makes more sense:

let (Shown x) = (showType :: Shown A) in xis a better design.. So something like this should do instead:

data MaxBits a = MaxBits Int maxBits :: (Bits a, Bounded a) => MaxBits a maxBits = r m where m = maxBound r :: Bits a => a -> MaxBits a r m = MaxBits (bitSize m)I am still having this cognitive difficulty coaxing GHC to type expressions like maxBits. It does not seem natural. Maybe I am missing something beautiful right under my nose?

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