hk-type-encoding.md

A higher-kinded-type companion to ts-toolbelt

---

[Guide]: HK-Type Encoding

Higher-kinded types are encoded as a type that extends the Kind type. The Kind type is a generic that takes in a type parameter $F$, which represents the underlying type transformation being performed.

All higher-kinded types possess a property called Kind._, which is a symbol that represents the unapplied type parameter.

namespace Kind {
  export type _ = unique symbol;
}

declare abstract class Kind<F extends Function = Function> {
  abstract readonly [Kind._]: unknown;
  abstract f: F;
}

1. HK-Types

A HK-type is also defined via an abstract class, that extends the Kind type.

declare abstract class Length extends Kind {
  abstract f: (x: Cast<this[Kind._], unknown[]>) => typeof x["length"];
}

We encode the higher-kinded type parameter via this. We can further use the Cast generic to encode input constraints.

2. Apply using $<>

Finally, we can apply a higher-kinded type to a type via the $ generic.

export type $<F extends Kind, X extends Kind.InputOf<F>> = ReturnType<
  (F & {
    readonly [Kind._]: X;
  })["f"]
>;

Here, we use the InputOf type to extract and constrain the input type of the higher-kinded type. We then use the ReturnType generic to extract the return type of the higher-kinded type, after we have used & to merge the higher-kinded type with the input type.

2.1. Apply Example

import { $ } from "hkt-toolbelt";

type Result = $<Length, [1, 2, 3]>; // 3