Type sig of `($)`

Programming
1

Understanding the ($) Operator in Haskell

The ($) operator is a type of function composition in Haskell, also known as the apply operator. It is defined as follows:

($) :: (a -> b) -> a -> b
f $ a = f a

This is nearly identical to the official definition, except that the official definition uses a sophisticated type TYPE:

($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
f $ x =  f x

The TYPE type is a type-level computation, which allows programs to be written at the type-level. It is necessary in the ($) operator definition because it allows functions to be applied at the type-level, allowing for more efficient computation.

2

The ($) operator in Haskell is a type of function composition, also known as the apply operator. It is defined as follows:

($) :: (a -> b) -> a -> b
f $ a = f a

The official definition of ($) uses a sophisticated type TYPE. Here is the official definition:

($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
f $ x = f x

The TYPE type is a type-level computation that allows programs to be written at the type level. It is necessary in the definition of ($) because it allows functions to be applied at the type level, enabling more efficient computation.