Applicative functor
An applicative functor is an abstraction that applies functions within a computational context to context-wrapped values while combining their contexts.
Functional Programming in Scala, Second Edition
An applicative functor is an abstraction that applies effectful functions to effectful arguments while combining their contexts.
- How it is used
- Combines independent effectful values and supplies the effect interface required by generic traversal.
- How deep it goes
- Defines `unit`, `map2`, and `apply`; contrasts monadic dependency and states identity, associativity, and naturality laws.
- Examples
- Uses Option map lookups, fixed and header-driven CSV parsers, validation, and State-based indexing traversals.
- What you can do after
- Build it from scratch by implementing `unit` and `map2` or `apply`, then deriving traversal and higher-arity combinators.
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Learn Haskell by Example
Applicative is a Haskell type class for applying functions in a computational context to values in that context and sequencing the resulting computations.
- How it is used
- Composes fixed sequences of effectful parser actions into structured results.
- How deep it goes
- Defines `pure`, `(<*>)`, and helper operators, then implements an Applicative instance for a custom Parser.
- Examples
- Demonstrates Maybe arithmetic, Hello World parsing, and PNM Header parsing.
- What you can do after
- Build it from scratch, implement and use an Applicative Parser for fixed-format input.
Read how Learn Haskell by Example explains applicative functor →
Related concepts
- monadcontrasts with · A monad is a functional abstraction that encapsulates computational context and provides operations for composing computations while preserving that context.
- applicative applyuses · Applicative apply is an operation that applies a function within an applicative context to a value within a compatible context while combining their effects.
- parseruses · A parser is a software component or algorithm that analyzes input according to a grammar or format to identify its structure, often producing a structured representation or reporting errors.
- associativityused by · Associativity is the property of a binary operation that regrouping its operands does not change the result.
- Validatedimplemented by · Validated is an error-handling data type that represents successful or failed computations and can accumulate errors across combined failures.
- maybe functionuses · The maybe function eliminates a Maybe value by returning a default for Nothing or applying a handler to the contained value.
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