Type problems

gistfile1.hs

numberwang :: (Floating a) => a -> a -> String                                                                                                                                                                                                 
numberwang x y                                                                                                                                                                                                                                 
  | x / y ^ 2 <= 18.5 = "a"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 25.0 = "b"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 30.0 = "c"                                                                                                                                                                                                                    
  | otherwise = "d"    

-- gives

Prelude> :l baby
[1 of 1] Compiling Main             ( baby.hs, interpreted )

baby.hs:14:15:
    Could not deduce (Ord a) arising from a use of `<='
    from the context (Floating a)
      bound by the type signature for
                 numberwang :: Floating a => a -> a -> String
      at baby.hs:12:15-46
    Possible fix:
      add (Ord a) to the context of
        the type signature for numberwang :: Floating a => a -> a -> String
    In the expression: x / y ^ 2 <= 18.5
    In a stmt of a pattern guard for
                   an equation for `numberwang':
      x / y ^ 2 <= 18.5
    In an equation for `numberwang':
        numberwang x y
          | x / y ^ 2 <= 18.5 = "a"
          | x / y ^ 2 <= 25.0 = "b"
          | x / y ^ 2 <= 30.0 = "c"
          | otherwise = "d"
Failed, modules loaded: none.

-- I can understand this, I think; Floating doesn't conform to Ord. Which seems weird, but ok. Let's try Float?

numberwang :: (Float a) => a -> a -> String                                                                                                                                                                                                    
numberwang x y                                                                                                                                                                                                                                 
  | x / y ^ 2 <= 18.5 = "a"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 25.0 = "b"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 30.0 = "c"                                                                                                                                                                                                                    
  | otherwise = "d"      

-- Gives:

Prelude> :l baby
[1 of 1] Compiling Main             ( baby.hs, interpreted )

baby.hs:12:13:
    `Float' is applied to too many type arguments
    In the type signature for `bmiTell':
      bmiTell :: Float a => a -> a -> String
Failed, modules loaded: none.

-- I don't understand this error at all.

-- Magically, this works. What's the difference?

numberwang :: (RealFloat a) => a -> a -> String                                                                                                                                                                                                
numberwang x y                                                                                                                                                                                                                                 
  | x / y ^ 2 <= 18.5 = "a"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 25.0 = "b"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 30.0 = "c"                                                                                                                                                                                                                    
  | otherwise = "d"    

Ah! I can't use types as constraints. So I can fix it like this:

numberwang :: (Ord a) => (Fractional a) => a -> a -> String                                                                                                                                                                                    
numberwang x y                                                                                                                                                                                                                                 
  | x / y ^ 2 <= 18.5 = "a"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 25.0 = "b"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 30.0 = "c"                                                                                                                                                                                                                    
  | otherwise = "d"       

Or like this:

numberwang :: Float -> Float -> String                                                                                                                                                                                                         
numberwang x y                                                                                                                                                                                                                                 
  | x / y ^ 2 <= 18.5 = "a"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 25.0 = "b"                                                                                                                                                                                                                    
  | x / y ^ 2 <= 30.0 = "c"                                                                                                                                                                                                                    
  | otherwise = "d"   

You can collapse multiple typeclass constraints together like so:

numberwang :: (Ord a, Fractional a) => a -> a -> String