If we have two functions, f1 and f2 then we can chain them togehter (f1(f2 x)).
But even better, we can create an operator that combines the two functions into one, f = f1 . f2.
This operator (.) is called the function composition operator. All of the ideas from "normal functions"
can be applied to monadic functions.
So if there is a function composition operator for normal functions, there is also one for
monadic functions.
The monadic function composition operation is formally called Kleisli composition (pronounced: klai-slee).
The operator is called a Kleisli Arrow.
In Haskell, it is written as <=<. It is a monadic equivalent of ..
It too is an infix operator that two different functions.
f =<< x -- x is passed into f
g <=< f =<< x -- x is passed through f then g
The Kleisli Category is a mathematical space where all monadic functions belong. Instead of having a Function Category with regular functions and function composition, we instead have monadic functions and the Kleisli Arrow.
- A monadic function is the "object" in the Kleisli Category
- The Kleisli composition operator
<=<is the "arrow" that connects together monadic functions (the "objects") in the Kleisli Category
The Kleisli composition has the following definition:
(m >=> n) x =
do
y <- m x
n y
here m and n are two monadic functions.
The net result of (m >=> n) is a brand new
single monadic function that performs the effects of both m and n with m's effect sequenced before n.