klequis / zz-haskell-notebook

Notes from learning Haskell

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identity element #76

Open klequis opened 2 years ago

klequis commented 2 years ago

Identity Element

identity and identity element are not the same thing.
identity element is often shortened to 'identity' when context makes it clear.
aka: neutral element.

In math: Is an element of a set that when applied in a binary operation, leaves unchanged every element in the set.

Zero (0) is the identity element for addition.

A = {1,2,3} Apply +0 to each element of A to produce B B = {1,2,3}

source: https://en.wikipedia.org/wiki/Identity_element

Left & Right Identity in Haskell

Right identity: x <> mempty = x
Left identity: mempty <> x = x
where
- mempty is the identity element.
- left and right refer to the location of the identity element

Example: Lists

mappend is ++
identity is []

-- left
[]  ++ [1,2,3] = [1,2,3]

-- right
[1,2,3] ++ [] = [1,2,3]