[Haskell-beginners] pattern matching on function names or algebraic type data constructors

[Michael Peternell]

I think the deeper meaning of the error message is that functions are not part of the Eq type class. So you cannot really compare functions. Think about it: 2 functions are the same (mathematically) if they have the same signature and if they return the same value for each legal input. This is computationally not decidable. We could compare function identity, but that would be in contrast to the "referential transparency principle" of Haskell. I'm wondering why the code even compiles though.

Code example:

Prelude> (const 4) == (const 5)

<interactive>:5:11:
    No instance for (Eq (b0 -> a0))
      arising from a use of `=='
    Possible fix: add an instance declaration for (Eq (b0 -> a0))
    In the expression: (const 4) == (const 5)
    In an equation for `it': it = (const 4) == (const 5)

-Michael

Am 23.06.2013 um 11:34 schrieb TP <paratribulations at free.fr>:

> Hi,
> 
> I ask myself if there is a way to make the following code work.
> I would like to pattern match on function names:
> 
> -----------
> f :: Float -> Int
> f x = 1
> 
> g :: Float -> Int
> g x = 2
> 
> pat :: (Float -> Int) -> Bool
> pat t = case t of
>        f -> True
>        g -> False
> 
> main = do
> 
> print $ pat f
> print $ pat g
> -----------
> 
> I don't understand the output:
> 
> -----------
> $ runghc test_pattern_match_on_function_2.hs 
> 
> test_pattern_match_on_function_2.hs:8:9: Warning:
>    Pattern match(es) are overlapped
>    In a case alternative: g -> ...
> True
> True
> -----------
> 
> What is the reason for this message?
> 
> Now, I want to do it on data constructors in a GADT (which are functions if 
> I am right):
> -----------
> {-# LANGUAGE GADTs #-}
> 
> data Foobar where
>    Mult :: Float -> Foobar
>    Plus :: Float -> Foobar
> 
> pat :: (Float -> Foobar) -> Bool
> pat t = case t of
>        Mult -> True
>        Plus -> False
> 
> main = do
> 
> print $ pat Mult
> print $ pat Plus
> -----------
> 
> I obtain:
> 
> -----------
> $ runghc test_pattern_match_on_function.hs 
> 
> test_pattern_match_on_function.hs:9:9:
>    Constructor `Mult' should have 1 argument, but has been given none
>    In the pattern: Mult
>    In a case alternative: Mult -> True
>    In the expression:
>      case t of {
>        Mult -> True
>        Plus -> False }
> 
> test_pattern_match_on_function.hs:9:9:
>    Couldn't match expected type `Float -> Foobar'
>                with actual type `Foobar'
>    In the pattern: Mult
>    In a case alternative: Mult -> True
>    In the expression:
>      case t of {
>        Mult -> True
>        Plus -> False }
> -----------
> 
> Why does it not work? If Mult and Plus are functions, then I should not need 
> to put their arguments in pattern matching.
> 
> Thanks in advance,
> 
> TP
> 
> 
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