Comparing revisions for page Functors and friends

  == Headline ==

Lecture "Functors and friends" as part of [[Course:Lambdas in Koblenz]]

== Description ==

List processing with [[map function|maps]] and [[fold function|folds]] is generalized to designated classes of types. In particular, we look at data types that can be thought of as modeling containers, and we treat them in a way similar to lists. This is possible, for example, for [[maybe type]]s and [[rose tree]]s. To this end, we leverage the notions of [[functor]] and [[foldable type]]. The corresponding type classes rely on [[higher-kinded polymorphism]]. We exercise maps and folds also in a non-trivial example of [[bidirectional transformation]]. In passing, we also engage in the more general notion of [[applicative functor]]s and the yet more general notion of [[monad]]s. Applicative functors allow for functorial computations to be sequenced (unlike plain functors), but don't allow using results from prior computations in the definition of subsequent ones (unlike monads).

== Concepts ==

* Basic concepts (They are captured as type classes.)
** [[Functor]]
** [[Foldable type|Fold]]
* Data types used for illustration
** [[Rose tree]]
** [[Maybe type]]
* Other concepts at play
** [[Higher-kinded polymorphism]]
** [[Bidirectional transformation]]
* Advanced concepts (They are captued as type classes, too.)
** [[Applicative functor]]
** [[Monad]]
*** Specific monads
**** The [[State monad]]
**** The [[Maybe monad]]
**** The [[Writer monad]]

== Languages ==

* [[Language:Haskell]]

== Features ==

* [[Feature:Total]]
* [[Feature:Cut]]

== Contributions ==

* [[Contribution:haskellTree]]: Bidirectional transformations
* [[Contribution:haskellLogging]]: Logging changes
* [[Contribution:haskellWriter]]: Logging changes monadically


== Metadata ==

* [[memberOf::Course:Lambdas in Koblenz]]
* [[dependsOn::Script:Type-class_polymorphism]]