Counterpart of #31. Also introduces Coyoneda f a, and Density f a.
Similar optimizations as #27:
Coyoneda
```Dhall
let Either = ./Either/Type
in let Coyoneda = ./Coyoneda/Type
in let emap = ./Either/functor Text
in let fmap = (./Coyoneda/functor (Either Text)).map
in let plusOne = λ(i : Natural) → i + 1
in let plusTwo = λ(i : Natural) → i + 2
in let foo =
λ(y : Coyoneda (Either Text) Natural)
→ fmap Natural Natural plusOne (fmap Natural Natural plusTwo y)
in let bar = ./Coyoneda/lift (Either Text) Natural
in λ(e : Either Text Natural)
→ ./Coyoneda/lower (Either Text) emap Natural (foo (bar e))
```
```Dhall
∀(e : < Left : Text | Right : Natural >) → < Right : Natural | Left : Text >
```
```Dhall
λ(e : < Left : Text | Right : Natural >)
→ merge
{ Left =
λ(x : Text) → < Left = x | Right : Natural >
, Right =
λ(y : Natural) → < Right = (y + 2) + 1 | Left : Text >
}
e
```
Density
```Dhall
let NonEmptyList = ./NonEmptyList/Type
in let Density = ./Density/Type
in let applicative = ./NonEmptyList/applicative
in let fmap = (./Density/functor NonEmptyList).map
in let plusOne = λ(i : Natural) → i + 1
in let plusTwo = λ(i : Natural) → i + 2
in let foo =
λ(y : Density NonEmptyList Natural)
→ fmap Natural Natural plusOne (fmap Natural Natural plusTwo y)
in let bar = ./Density/lift NonEmptyList ./NonEmptyList/comonad Natural
in λ(e : NonEmptyList Natural)
→ ./Density/lower NonEmptyList applicative Natural (foo (bar e))
```
```Dhall
∀(e : { head : Natural, tail : List Natural })
→ { head : Natural, tail : List Natural }
```
```Dhall
λ(e : { head : Natural, tail : List Natural })
→ { head =
(e.head + 2) + 1
, tail =
List/fold
Natural
e.tail
(List Natural)
(λ(x : Natural) → λ(y : List Natural) → [ (x + 2) + 1 ] # y)
([] : List Natural)
}
```
Counterpart of #31. Also introduces
Coyoneda f a, andDensity f a.Similar optimizations as #27:
Coyoneda
```Dhall let Either = ./Either/Type in let Coyoneda = ./Coyoneda/Type in let emap = ./Either/functor Text in let fmap = (./Coyoneda/functor (Either Text)).map in let plusOne = λ(i : Natural) → i + 1 in let plusTwo = λ(i : Natural) → i + 2 in let foo = λ(y : Coyoneda (Either Text) Natural) → fmap Natural Natural plusOne (fmap Natural Natural plusTwo y) in let bar = ./Coyoneda/lift (Either Text) Natural in λ(e : Either Text Natural) → ./Coyoneda/lower (Either Text) emap Natural (foo (bar e)) ``` ```Dhall ∀(e : < Left : Text | Right : Natural >) → < Right : Natural | Left : Text > ``` ```Dhall λ(e : < Left : Text | Right : Natural >) → merge { Left = λ(x : Text) → < Left = x | Right : Natural > , Right = λ(y : Natural) → < Right = (y + 2) + 1 | Left : Text > } e ```Density
```Dhall let NonEmptyList = ./NonEmptyList/Type in let Density = ./Density/Type in let applicative = ./NonEmptyList/applicative in let fmap = (./Density/functor NonEmptyList).map in let plusOne = λ(i : Natural) → i + 1 in let plusTwo = λ(i : Natural) → i + 2 in let foo = λ(y : Density NonEmptyList Natural) → fmap Natural Natural plusOne (fmap Natural Natural plusTwo y) in let bar = ./Density/lift NonEmptyList ./NonEmptyList/comonad Natural in λ(e : NonEmptyList Natural) → ./Density/lower NonEmptyList applicative Natural (foo (bar e)) ``` ```Dhall ∀(e : { head : Natural, tail : List Natural }) → { head : Natural, tail : List Natural } ``` ```Dhall λ(e : { head : Natural, tail : List Natural }) → { head = (e.head + 2) + 1 , tail = List/fold Natural e.tail (List Natural) (λ(x : Natural) → λ(y : List Natural) → [ (x + 2) + 1 ] # y) ([] : List Natural) } ```Let me know if I forgot anything!