Andrea Simone Costa jfet97

Introduction to Yoneda and Coyoneda

Yoneda (and its duel Coyoneda) is well known in the Category Theory field and has been ported over to functional languages such as Haskell. Each have their uses - sometimes in similar scenarios, also in very different ways.

This will be a newbie's explanation of the concept, using Haskell to illustrate, without any Category Theory.

From what I've read, the Yonedas are not 'daily-drivers' (not used everyday), but rather can be pulled out when the time is right.

Uses: Both Yoneda's can be used to help speed up a program where there are many fmap with long lists or big trees involved. Coyoneda can be used if you want to create an 'interface' and build up calculations, then pass those calculations to an 'executor' to run them.

Purity and pure FP

purity is a syntactical property of programs, more precisely defined as referential transparency: replacing an expression for its bound value doesn't change meaning (precise definition)
side effects are things that break referential transparency (precise definition)
There's no direct connection between the concepts of IO, State and so on, and side effects. Traditionally, these things are side effectful (break referential transparency), but you can have abstractions that are pure (don't break ref.trans.)
Due to the above, the term purely functional programming is not an oxymoron, it makes perfect sense.
In haskell style pure FP, type constructors and algebras are used to represent "things that would otherwise traditionally be side effects (break ref.trans.)". We call these F[_]s effects or computational contexts for brevity. You can see for yourself how this cannot be a precise definition (especially because they could also have kind higher than * -> *, even though most famous a

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	mapped types syntax and intro

	https://www.typescriptlang.org/play?#code/C4TwDgpgBA8gRgKygXigbwFBW1AZge3wC4oBnYAJwEsA7AcwBosc4BDCkmgVwFs4IKGAL4YMoSFACSAEwg1gVUAB4AKgD4U6ZtgDaAaSi0oAawgh8uKCoC6JFfuvDR46AGVWPaKhlyFy+AhqGAD0wTgAegD8omLg0AAKFPg8VKRUuCCqGqiYOFD6hjQmZhZWtlAAFACUKBqJyakQqg5BIrES9SlpuFQQ0pqdqemZAUGhEdEYsgDGADbs0NP4NORQFGDTJIPdvdKiSyvAeFzAXBReaxsAdGwU1SFheU-PUFGiuCdnEFfAABZyFQqADdWLMasgNLkcCDZtooOM3kIqkA

	a tweet that prompted the idea for the talk

	https://twitter.com/kentcdodds/status/1608187990215655424

	but since this isn't possible with satisfies (it doesn't participate in inference, in an example like that it only provides contextual types) the answer was to use a function with a reverse mapped type