Functor
A functor is an abstraction that maps values or objects while preserving the structure and relationships of their surrounding context.
The Joy of JavaScript
A functor is a structure or abstraction that provides a mapping operation over contained values while preserving the surrounding structure.
- How it is used
- Uses map to compose transformations over contained values, including validation flows that skip work after failure.
- How deep it goes
- Defines map through identity and composition rules, then implements a reusable mixin; defers extensive algebraic theory.
- Examples
- Demonstrates array mapping, an Id transformation pipeline, and Success/Failure branches that run or skip mapped functions.
- What you can do after
- Build it from scratch with an Id-style container and map mixin, then apply the contract to conditional validation.
Learn Haskell by Example
Functor is the Haskell type class for types whose parameterized values support structure-preserving mapping over their contents.
- How it is used
- Uses fmap to transform values inside CSV results, IO actions, parsers, and random generators without discarding their contexts.
- How deep it goes
- Defines Functor through fmap and kinds, then implements a Parser instance; functor laws are not detailed.
- Examples
- Demonstrates CSV Either mapping, command-line IO [String] conversion, Parser MagicNumber construction, and a RandomIO Functor exercise.
- What you can do after
- Apply it via fmap, <$> and <$ to change contained results while preserving list, Maybe, Either, IO, or Parser structure.
Functional Programming in Scala, Second Edition
A functor is an abstraction that provides a map operation for transforming values inside a computational structure while preserving that structure.
- How it is used
- Generalizes map across type constructors to factor duplicated transformations into reusable combinators.
- How deep it goes
- Defines the Scala interface, derives distribute and codistribute, and justifies identity and composition laws through structural preservation.
- Examples
- Uses List, Option, Gen, Parser, Par, generic unzip, and codistribute to demonstrate map’s shared shape.
- What you can do after
- Apply it to derive structure-preserving transformations and generic combinators from map alone.
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Functional Design and Architecture: Examples in Haskell
A functor is an abstraction that supports mapping a function over a value while preserving the structure of its context.
- How it is used
- Generalizes structure-preserving mapping into reusable functional operations for lists, optional values, and domain models.
- How deep it goes
- Defines fmap, demonstrates lists and nested Maybe values, and constructs a custom instance for a domain-specific algebraic type.
- Examples
- Uses name-length lists, nested Maybe values, integer-to-string mapping, and a SandwichConstructor continuation instance.
- What you can do after
- Build a Functor instance for a parameterized type and apply fmap across ordinary, nested, and domain-specific structures.
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Functional Programming in JavaScript
An abstract container or computational context that supports mapping a function over its contents while preserving its structure.
- How it is used
- Uses containers to transform values while reducing scattered null checks and caller-managed error-handling complexity.
- How deep it goes
- Explains fmap operationally and demonstrates immutable chaining, while deliberately stopping short of category theory.
- Examples
- Demonstrates Wrapper, arithmetic with plus3, identity extraction, logging, chained fmap calls, and Array map and filter signatures.
- What you can do after
- Build it from scratch with a Wrapper class, wrap values, map transformations, and chain immutable computations.
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Fabulous Adventures in Data Structures and Algorithms
A functor is a mapping between categories that preserves their objects, morphisms, and composition.
- How it is used
- Uses composable abstractions to connect category theory with programming-language design and generic interfaces.
- How deep it goes
- Defines categories, morphisms, variance, and endofunctors, then stops short of deeper category-theoretic development.
- Examples
- Uses a three-object category, a C# integer-to-string function, and a diagram of dashed mapping arrows.
- What you can do after
- Evaluate type relationships and generic interfaces using covariance, contravariance, and preserved morphisms.
Read how Fabulous Adventures in Data Structures and Algorithms explains functor →
Related concepts
- monadincludes · A monad is a functional abstraction that encapsulates computational context and provides operations for composing computations while preserving that context.
- data transformationuses · A data transformation is an operation or function that maps input data or its representation to modified data or a different representation.
- optionincludes · An option type is a type that explicitly represents either a value of a specified type or the absence of a value.
- listincludes · A list is an ordered collection of elements arranged in a sequence.
- traverseincludes · Traverse is an operation that maps an effectful function across a traversable structure and collects the results within an applicative context.
- Genimplemented by · Gen is a QuickCheck type representing a computation that generates randomized values of a specified type.
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