Monoid
A monoid is an algebraic structure consisting of a set with an associative binary operation and an identity element.
Functional Programming in Scala, Second Edition
A Monoid is an algebraic structure with an associative binary operation and an identity element.
- How it is used
- Enables generic folds, compositional calculations, and parallel aggregation over foldable data.
- How deep it goes
- Defines operations and laws, implements list folds and products, and stops short of broader algebraic structures.
- Examples
- Uses strings, lists, integers, booleans, options, endofunctions, and a fused count-and-sum mean calculation.
- What you can do after
- Build it from scratch by defining lawful instances and generic combineAll, foldMap, and product operations.
Read how Functional Programming in Scala, Second Edition explains Monoid →
Learn Haskell by Example
Monoid is a Haskell type class extending Semigroup with a neutral element and operations for combining collections of values.
- How it is used
- Generalizes CSV appending so optional input and collections of values can be combined with a shared interface.
- How deep it goes
- Defines Monoid operations and laws, demonstrates built-in instances, and implements a Csv instance without proving laws formally.
- Examples
- Demonstrates list and String concatenation, `mconcat`, numeric Sum/Product wrappers, and CSV table appending.
- What you can do after
- Apply it via Haskell type class instances to combine lists, strings, and CSV values using `(<>)`, `mempty`, and `mconcat`.
Clojure: The Essential Reference
An algebraic monoid is a set equipped with an associative binary operation and an identity element.
- How it is used
- Adapts reducing functions for fold operations that need an initial value without accepting one as a separate argument.
- How deep it goes
- Defines identity and associativity, then details arity, contracts, return behavior, and common constructor errors.
- Examples
- Demonstrates string concatenation, map merging, numeric addition, and composed reducer transformations.
- What you can do after
- Apply r/monoid to build fold combiners with correct zero-argument initialization and two-argument reduction.
Related concepts
- Semigroupkind of · A semigroup is a set equipped with an associative binary operation.
- foldMapused by · foldMap transforms the elements of a data structure and combines the results using the operations of a monoid, discarding the original structure.
- identity elementhas part · An element that, under a specified binary operation, leaves every element in the operation’s domain unchanged when combined with it.
- reduction operationuses · A reduction operation combines multiple input values or partial results according to a combining rule to produce fewer results, often a single aggregate.
- completingcontrasts with · completing is a Clojure function that adapts a binary reducing function with completion behavior for use as a transducer reducing function.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.