Il 15/08/2018 23:06, Stefan Chacko ha scritto:
3. Why do we use clinches in such definitions. I concluded you need clinches if a function is not associative
such as (a-b)+c . (Int->Int)->Int->Int
But also if a higher order function needs more than one argument. (a->b)->c .
Can you please explain it ?
funXYZ :: Int -> Int -> Int -> Int funXYZ x y z = (x - y) + z if you rewrite in pure lamdda-calculus, without any syntax-sugars it became fun_XYZ :: (Int -> (Int -> (Int -> Int))) fun_XYZ = \x -> \y -> \z -> (x - y) + z so fun_XYZ is a function `\x -> ...` that accepts x, and return a function, that accepts a parameter y, and return a function, etc... You can also rewrite as: funX_YZ :: Int -> (Int -> (Int -> Int)) funX_YZ x = \y -> \z -> (x - y) + z or funXY_Z :: Int -> Int -> (Int -> Int) funXY_Z x y = \z -> (x - y) + z and finally again in the original funXYZ_ :: Int -> Int -> Int -> Int funXYZ_ x y z = (x - y) + z I used different names only for clarity, but they are the same exact function in Haskell. In lambda-calculus the form \x y z -> (x - y) + z is syntax sugar for \x -> \y -> \z -> (x - y) + z On the contrary (as Francesco said) (Int -> Int) -> Int -> Int is a completely different type respect Int -> Int -> Int -> Int In particular a function like gHX :: (Int -> Int) -> Int -> Int gHX h x = h x has 2 parameters, and not 3. The first parameter has type (Int -> Int), the second type Int, and then it returns an Int. Equivalent forms are: g_HX :: (Int -> (Int -> Int)) g_HX = \h -> \x -> h x gH_X :: (Int -> Int) -> (Int -> Int) gH_X h = \x -> h x gHX :: (Int -> Int) -> Int -> Int gHX_ h x = h x IMHO it is similar to logic: intuitively it seems easy and natural, but if you reflect too much, it is not easy anymore... but after you internalize some rules, it is easy and natural again. Regards, Massimo