Truth Tables from Anonymous Functions in Haskell

Question

I'm trying to generate a truth table for a given boolean expression. I could do this with creating a new Datatype BoolExpr, but I want to do it with an anonymous function. It's supposed to work like this:

> tTable (\x y -> not (x || y))
output:
F F | T
F T | F
T F | F
T T | F

My approach:

tbl p = [(uncurry p) tuple | tuple <- allval]
        where allval=[(x,y) | x <- [False,True], y <- [False,True]]

This works, but only for 2 Arguments. I want to do it for any number of Arguments. So I figured I would make a function that takes the Arguments from a List:

argsFromList f []     = f
argsFromList f (x:xs) = argsFromList (f x) xs

This does not work:

 Occurs check: cannot construct the infinite type: t = t1 -> t
   Expected type: t -> [t1] -> t1 -> t
   Inferred type: (t1 -> t) -> [t1] -> t1 -> t
 In the expression: argsFromList (f x) xs

I don't understand what the problem is here. I would be very grateful if anyone could point me into the right direction or post a link that does.

Answer 1

If you want to build a truth table for boolean functions with an arbitrary number of arguments, you're creating a function that must work for multiple types, so you'll have to use type classes:

{-# LANGUAGE FlexibleInstances #-}

class TruthTable a where
  truthTable :: a -> [([Bool], Bool)]

instance TruthTable Bool where
  truthTable b = [([], b)]

instance TruthTable a => TruthTable (Bool -> a) where
  truthTable f = [ (True  : inps, out) | (inps, out) <- truthTable (f True)] ++ 
                 [ (False : inps, out) | (inps, out) <- truthTable (f False)]

For example:

*Main> mapM_ print $ truthTable (&&)
([True,True],True)
([True,False],False)
([False,True],False)
([False,False],False)