Why does `Bits` depend on `Num`?

Question

I've been coding my own bit-vectors (represented as strict tuples over Word64 values) as an exercise in time and space optimizations and wanted to define instances of the Bits typeclass for them, but then I noticed that the class declaration for Bits is defined as follows:

class Num a => Bits a

To workaround this, I'm defining a fake Num instance as well, made up mostly of error-valued functions as a hack, but this doesn't feel right...

What was the rationale of depending on the Num type-class for bit-wise operations? Wouldn't it make more sense to be able to have Bits instances independen from having to declare a Num instance as well?

Answer 1

Bits depends on Num, because Num provides numeric literals and negation, which are used in the default methods for Bits, like so:

bit :: Int -> a
bit i               = 1 `shiftL` i

testBit           :: a -> Int -> Bool    
x `testBit` i       = (x .&. bit i) /= 0        

If there were no default methods, you could imagine getting away without the Num constraint.