[Haskell-beginners] Pattern matching over functions

[Giacomo Tesio]

Hi Haskellers,

I'm wondering why, given that functions and referential transparency are
first class citizens in haskell, it isn't possible to write a mapping
function this way:

f1 :: a -> b

f2 :: a -> b

f3 :: c -> a -> b

map :: (a -> b) -> T a -> T b
map f1 = anEquivalentOfF1InTCategory
map f2 = anEquivalentOfF2InTCategory
map f3 $ c = anEquivalentOfF3withCInTCategory
map unknown = aGenericMapInTCategory

Is it "just" the implementation complexity of the feature in ghc that
prevents this?
Or is it "conceptually" wrong?

At a first look, I thought that most of complexity here should be related
to function's equality, but than I thought that the function full name
should uniquely map from the category of meanings in the programmer mind to
the category of implementations available to the compiler's.


Giacomo
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