How to create a string representation of a function in Haskell. How to print a function in a fancy way?

Question

My goal is to be able to represent boolean expressions as strings, for example "True or False is True". In order to make it possible I first made some boolean predicates:

and' :: Bool -> Bool -> Bool
and' p q = p && q

or' :: Bool -> Bool -> Bool
or' p q = p || q

-- ... same for nor, nand, xor, imply and equivalent

equ' :: Bool -> Bool -> Bool
equ' p q = p == q

After that, I decided to make a function that maps functions to strings. I relied on the pattern matching feature of Haskell, but my trick didn't work.

-- representation function, a.k. "show" for functions
repr :: (Bool -> Bool -> Bool) -> [Char]
repr and'  = "and"
repr or'   = "or"
repr nand' = "nand"
repr nor'  = "nor"
repr xor'  = "xor'"
repr impl' = "implies"
repr equ'  = "equivalent to"
repr other = error "No representation for the given predicate"

GHC thinks that function name is a parameter name and considers only the first definition as a general case. For the remaining lines, GHC raises a warning that the "pattern match is redundant". This is an example of running repr function:

*LogicH99> repr equ'
"and"

Expected "equivalent to"

Is it possible to print a function in a fancy way in Haskell?

Answer 1

For functions in general, no there isn't. But for functions of type Bool -> Bool -> Bool, there's so few possibilities that it's practical to just exhaustively enumerate all inputs, by doing something like this:

repr f = case (f False False, f False True, f True False, f True True) of
    (False, False, False, True) -> "and"
    (False, True, True, True) -> "or"
    -- ...
    (True, False, False, True) -> "equivalent to"
    _ -> error "No representation for the given predicate"