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Neutral element

As explained in Learn Haskell by Example

A neutral element is a value that leaves another value unchanged when combined with an operation.

A neutral element leaves another value unchanged when combined with an operation. For a Monoid, mempty satisfies mappend mempty a == a and mappend a mempty == a. section 7.3.1

In practical Haskell code, the neutral element depends on the operation:

  • Csv uses an empty value with no header and no columns. section 7.3.1

Combining a list with mempty

[1,2,3] <> mempty <> [4,5,6] produces [1,2,3,4,5,6], because mempty contributes no elements.

How Learn Haskell by Example covers it

How deep it goes
Defines identity laws and applies them to lists, strings, and Csv values without formal proof.
Examples
Demonstrates [], empty strings, and an empty Csv as neutral elements for append operations.
What it assumes
Assumes an associative combining operation and connects that operation to Semigroup before adding mempty.
What you can do after
Apply via Haskell's Monoid class by defining mempty for a chosen combining operation.
How it connects
Connects neutral elements with Monoid, Semigroup, associative operations, mappend, and mconcat.
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Learn Haskell by Example. The section links point to the parts of the book it draws on.