[Haskell-cafe] Client-extensible heterogeneous types (Duck-typed variadic functions?)

[Jacek Generowicz]

Using Brandon's code as a starting point (as it's far neater than  
mine), let's try asking some questions about fractions (I've included  
the whole program at the end).

     questions = [ addition 1 2, addition (1%2) (1%3) ]

This works, but the the fractions are shown as "1 % 2" and to make it  
presentable to non-Haskellers, we have to change that to "1/2".

In order to do this, I tried to replace show with my own version which  
I call view (in type class View). At this point I get

../arithmetic/hackBrandon.hs:63:23:
     Ambiguous type variable `t' in the constraints:
       `Num t'
         arising from the literal `1'
                      at ../arithmetic/hackBrandon.hs:63:23
       `View t'
         arising from a use of `addition'
                      at ../arithmetic/hackBrandon.hs:63:14-25
       `Read t'
         arising from a use of `addition'
                      at ../arithmetic/hackBrandon.hs:63:14-25
     Probable fix: add a type signature that fixes these type  
variable(s)


My problem is that I don't see where I could add a type signature, but  
still keep

    addition :: a -> a -> Question

polymorphic.

  ======= Here's the code demonstrating the problem =====


{-# LANGUAGE NoMonomorphismRestriction #-}
import System.IO (hFlush, stdout)
import Data.Ratio

data Result = Correct | Improve String | Huh String | Incorrect String
               deriving Show

data Question = Question { ask    :: String
                          , answer :: String
                          , check  :: String -> Result }

bool2result True  = Correct
bool2result False = Incorrect ""

readCheckBy :: (Read a) => (a -> Bool) -> String -> Result
readCheckBy pred str =
  case reads str of [(val,"")] -> bool2result (pred val)
                    _ -> Huh ""

readCheck :: (Read a, Eq a) => a -> String -> Result
readCheck v s = readCheckBy (==v) s

-- customized show

class View a where
     view :: a -> String

instance View Int where
     view = show

instance (Integral n) => View (Ratio n) where
     view = show

-- helpers

value val prompt = Question prompt (view val) (readCheck val)

infix2 op symbol a b = value (op a b) (unwords [view a, symbol, view b])

addParam :: (View a) => (funTy -> String -> qty) -> (a -> funTy) ->  
String -> (a -> qty)
addParam qmakr fun string v = qmakr (fun v) (string++" "++view v)

prefix1 = addParam value
prefix2 = addParam prefix1
prefix3 = addParam prefix2

-- question 'types'

addition       = infix2 (+) "+"

questions = [ addition 1 2
             , addition (1%2) (1%3)
             ]

test :: Question -> IO ()
test q = do
  putStr $ ask q ++ " = "
  hFlush stdout
  reply <- getLine
  putStrLn $ show $ check q reply

main = mapM_ test questions