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Playing with Contravariant functors in typescript - Contravariant functor for comparison
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| Lets define a sum type `Ordering` with its data constructors: | |
| ```typescript | |
| class LT {} | |
| class EQ {} | |
| class GT {} | |
| type Ordering = LT | EQ | GT; | |
| class Comparison<A> { | |
| constructor(public runComparison: ((a: A) => (b: A) => Ordering)){} | |
| } | |
| ``` | |
| // Because of the position of the parameter we can see that this is a contravariant structure | |
| Example usage: | |
| - We can compare numbers | |
| ``` | |
| const x = new Comparison<number>((a) => b => { | |
| if (a === b) return new EQ(); | |
| if (a > b) return new GT(); | |
| if (a < b) return new LT(); | |
| }) | |
| ``` | |
| Now lets define our contravariant functor over Comparison. | |
| As you know functors map has a type of: <A, B>(f: (a: A) => B) => (a: F A) => F B. | |
| And while functors pack things (think of array, or function composition) the contravariant functors "unpack". | |
| Its type is: <A, B>(f: (b: B) => A) => (a: F A) => F B | |
| For `Comparison` this is: | |
| ```typescript | |
| type contramapT = <A, B>(f: (b: B) => A) => (a: Comparison<A>) => Comparison<B>; | |
| const contramap: contramapT = (f) => compC => { | |
| return new Comparison(a => b => compC.runComparison(f(a))(f(b))) | |
| } | |
| ``` | |
| Let say we have some users which age we would like to compare. | |
| ```typescript | |
| const compareNumbers = new Comparison<number>((a) => b => { | |
| if (a === b) return new EQ(); | |
| if (a > b) return new GT(); | |
| if (a < b) return new LT(); | |
| }); | |
| type userT = { | |
| name: string; | |
| age: number; | |
| } | |
| const user1 = { name: "Igor", age: 25 } | |
| const user2 = { name: "Ivan", age: 28 } | |
| const userAgeComparer = contramap<number, userT>(a => { | |
| return a.age; | |
| })(compareNumbers) | |
| const result = userAgeComparer.runComparison(user1)(user2); | |
| ``` | |
| As you can see from this trivial example we generated a new comparer for our user. |
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