hk-type-encoding.md

A higher-kinded-type companion to ts-toolbelt

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

1. HK-Types

A HK-type is defined via an interface that extends the Kind type.

interface Length extends Kind.Kind {
  f(x: Type._$cast<this[Kind._], unknown[]>): typeof x["length"];
}

We encode the higher-kinded type parameter via this. We can further use the Type._$cast generic to encode input constraints.

2. Apply using $<>

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

export type $<F extends Kind.Kind, X> = 
Function._$returnType<
  (F & { readonly [Kind._]: Type._$cast<X, Kind._$inputOf<F>> })['f']
>

Here, we use the Kind._$inputOf and Type._$cast types to extract and constrain the input type of the higher-kinded type $F$. We then use the Function._$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