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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
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