Created
July 15, 2019 18:25
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Comonads
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| trait Functor[F[_]] { | |
| def map[A,B](fa: F[A])(f: A => B): F[B] | |
| } | |
| // For lifting pure values into effects and to chain effects | |
| trait Monad[F[_]] extends Functor[F] { | |
| def pure(x: A): F[A] | |
| def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B] | |
| // map can now be defined in terms of pure and flatten so Monad is a functor | |
| } | |
| trait Comonad[F[_]] extends Functor[F] { | |
| def extract(x: F[A]): A | |
| def coflatMap[A, B](fa: F[A])(f: F[A] => B): F[B] | |
| def coflatten[A](fa: F[A]): F[F[A]] | |
| // map can be defined in terms of coflatMap and extract | |
| } | |
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| import cats.Comonad | |
| case class FocusedGrid[A](focus: Tuple2[Int,Int], grid : Vector[Vector[A]]) | |
| implicit val focusedGridComonad = new Comonad[FocussedGrid] { | |
| override def map[A,B](fa: FocusedGrid[A])(f: A => B): FocusedGrid[B] = | |
| FocusedGrid(fa.focus, fa.grid.map(row => row.map(a => f(a)))) | |
| override def coflatten[A](fa: FocusedGrid[A]): FocusedGrid[FocusedGrid[A]] = { | |
| val grid = fa.grid.mapWithIndex((row, ri) => | |
| row.mapWithIndex((col, ci) => | |
| FocussedGrid((ri, ci), fa.grid))) | |
| FocusedGrid(fa.focus, grid) | |
| } | |
| override def coflatMap[A, B](fa: FocusedGrid[A])(f: FocusedGrid[A] => B): FocusedGrid[B] = { | |
| val grid = coflatten(fa).grid.map(_.map(col => f(col))) | |
| FocusedGrid(fa.focus, grid) | |
| } | |
| override def extract[A](fa: FocusedGrid[A]): A = fa.grid(fa.focus._1)(fa.focus._2) | |
| } | |
| // Image Manipulation can be done using FocusedGrid |
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