Is it necessary to convert all inputs to lambdas in Haskell?
I implemented map function only converting f to \f.
And it occurs error during runtime(attached below).
map_ xs = \f -> case xs of
[] -> []
y:ys -> (f y):(map f ys)
map_ square [3, 4]
ERROR - Type error in application
*** Expression : map_ square [3,4]
*** Term : [3,4]
*** Type : [c]
*** Does not match : a -> b
Is it necessary to convert all inputs to lambdas in Haskell?
No. Indeed lambdas usually only appear in fancy higher-level abstractions.
From
case xs of
[] -> ...
y:ys -> ...
the compiler infers that xs's type is a list. From
map_ xs = ...
the compiler infers that list is the first argument to map_.
But in your call to map_, you've put the function as the first argument; the list as second. The standard type for map in the Prelude is
map :: (a -> b) -> [a] -> [b]
IOW function first, list second.
So which do you intend?
map_ is simply a different name. Whereas with map _ you would express that the first argument is completely ignored. Indeed there's also a syntactic shorthand for flipping around arguments, but it requires abuse of infix-section notation: (`map` xs) f
f x = ... and f = \x -> ... are (mostly) equivalent. For "multiple" arguments, you peel them off in the same order; f x y = ... and f x = \y -> ... and f = \x -> \y -> ... all (mostly) equivalent. (I say "mostly", because it's not worth getting into the subtle differences here... and because I can't give an accurate explanation of said differences.)