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A function is a mapping from one set, called a domain, to another set, called the codomain. A function associates every element in the domain with exactly one element in the codomain. In Scala, both domain and codomain are types.
val square : Int => Int = x => x * x
| package matryoshka { | |
| trait Interpret[T[_[_]]] { | |
| type ^[Outer[_], Inner[_]] = Outer[T[Inner]] | |
| trait Transform[F[_], G[_]] { | |
| /** Bottom-up transforms. */ | |
| type GAlgebraicM[W[_], M[_]] = F[W ^ G] => M[G ^ G] | |
| type AlgebraicM[M[_]] = F ^ G => M[G ^ G] // GAlgebraicM[Id, M] | |
| type GAlgebraic[W[_]] = F[W ^ G] => G ^ G // GAlgebraicM[W, Id] | |
| type Algebraic = F ^ G => G ^ G // GAlgebraicM[Id, Id] |
Tageless Final interpreters are an alternative to the traditional Algebraic Data Type (and generalized ADT) based implementation of the interpreter pattern. This document presents the Tageless Final approach with Scala, and shows how Dotty with it's recently added implicits functions makes the approach even more appealing. All examples are direct translations of their Haskell version presented in the Typed Tagless Final Interpreters: Lecture Notes (section 2).
The interpreter pattern has recently received a lot of attention in the Scala community. A lot of efforts have been invested in trying to address the biggest shortcomings of ADT/GADT based solutions: extensibility. One can first look at cats' Inject typeclass for an implementation of [Data Type à la Carte](http://www.cs.ru.nl/~W.Swierstra/Publications/DataTypesA
When defining complex functions in pointfree style, I often find myself switching to pointful style. Sometimes, I even convert to ANF and annotate the types to understand the steps.
After completing the function definition, I often convert back to pointfree style for conciseness. End of the story: To understand it again a couple of weeks later, I start expanding to annotated pointful again.
The small 10-lines library at the end of this post allows to define pointfree functions with intermediate type annotations.
Credits: Agda and EqReasoning for syntactical inspiration.
| // @flow | |
| declare module 'react-relay' { | |
| declare export type RecordState = 'EXISTENT' | 'NONEXISTENT' | 'UNKNOWN'; | |
| declare export type onCompleted = (response: ?Object, errors: ?Array<PayloadError>) => void | |
| declare export type onError = (error: Error) => void | |
| declare export type CommitOptions = { | |
| onCompleted: onCompleted, |
