Partial Application for any number of arguments

bind.ts

// Find the first item of a list.
export type Head<List extends readonly unknown[]> =
	0 extends keyof List ? List[0] : never;

// Find the last item of a list.
export type Last<List extends readonly unknown[]> =
	List["length"] extends 0 ? never
	: List extends [] ? never
	: number extends List["length"] ? List[1e+309]
	: List[Tail<List>["length"]];

// Produce a list skipping the first item.
export type Tail<List extends readonly unknown[]> =
	List extends readonly unknown[] ? ((...args: List) => never) extends ((_: any, ...args: infer U) => never) ? U : never : never;

// Produce a list skipping the last item.
export type Init<List extends readonly unknown[]> =
	number extends List["length"] ? List
	: $Init<List>;
export type $Init<
	List extends readonly unknown[],
	_Tail extends any[] = Tail<List>
> = {
	[I in keyof _Tail]: I extends keyof List ? List[I] : never
};

// "unshift" the type H onto the beginning of List.
export type Unshift<List extends readonly unknown[], H> =
	List extends readonly unknown[] ? ((_: H, ...args: List) => any) extends (...args: infer U) => any ? U : never : never;

// Shift values from the beginning of List.
export type Shift<
	List extends readonly unknown[],
	C extends readonly unknown[] = [unknown]
> = List extends readonly unknown[] ? C extends readonly unknown[] ? $Shift<List, C> : never : never;
export type $Shift<
	List extends readonly unknown[],
	C extends readonly unknown[]
> = {
	0: ((...args: List) => any) extends(...args: infer U) => any ?U: [],
	1: Shift<((...args: List) => any) extends (_: any, ...args: infer U) => any ? U : [], ((...args: C) => any) extends (_: any, ...args: infer U) => any ? U : []>,
	2: []
}[number extends C["length"] ? 2 : C["length"] extends 0 ? 0 : 1];

// Produce an analogous tuple with the same length as the tuple
// prefix of List, but with different value types.
type ExtractTupleAnalog<List extends readonly unknown[]> =
	List extends readonly unknown[] ? {
		0: List,
		1: $ExtractTupleAnalog<List>
	}[number extends List["length"] ? 1 : 0] : never;
type $ExtractTupleAnalog<
	List extends readonly unknown[],
	C extends readonly any[] = [],
> = {
	0: C,
	1: $ExtractTupleAnalogStep<List, C>,
}[List[0][] extends List ? 0 : 1];
type $ExtractTupleAnalogStep<
	List extends readonly unknown[],
	C extends readonly any[],
	_Tail extends any[] = Tail<List>
> = $ExtractTupleAnalog<_Tail, Unshift<C, List[0]>>;

// Find all the suffixes of a list
export type Suffixes<
	List extends readonly unknown[],
	_Tail extends any[] = Tail<List>
> = {
	0: List,
	1: List | Suffixes<_Tail>,
	2: List[1e309][]
}[
	_Tail["length"] extends 0
		? 0
		: number extends List["length"]
			? List[0][] extends List ? 2 : 1
			: 1
];

// Find all the prefixes of a list
export type Prefixes<List extends readonly unknown[]> =
	number extends List["length"]
		? List[0][] extends List
			? List
			: $Prefixes<ExtractTupleAnalog<List>> | List
		: (List extends readonly any[] ? $Prefixes<List> : never)
type $Prefixes<
	Tuple extends readonly unknown[],
	_Suffixes = Suffixes<Tuple>
> = {
	[I in keyof _Suffixes]: I extends keyof Tuple ? Tuple[I] : never;
};

// Remove some prefix of parameters from a function without checking types.
export type BlindBind<
	F,
	B extends unknown[],
	_Tail extends any[] = ((..._: B) => any) extends ((_: any, ...tail: infer U) => any) ? U : []
> = {
	0: F,
	1: BlindBind<F extends (this: infer T, _: any, ...args: infer U) => infer V ? (this: T, ...args: U) => V : F, _Tail>
}[B["length"] extends 0 ? 0 : 1];

// Remove some prefix of parameters from a function.
export type Bind<
	F extends (...args: any[]) => any,
	B extends [] | Prefixes<Parameters<F>>
> = B extends any[] ? BlindBind<F, B> : never;

type H = Bind<(x: number, y: string, ...z: number[]) => void, [number, string, number]>