typescript.js

```ts
type Tail<F extends Function, S extends Number> =
  S extends 0 ? (F extends (...args: infer TArgs) => any ? TArgs : never) :
  S extends 1 ? (F extends (a: any, ...args: infer TArgs) => any ? TArgs : never) :
  S extends 2 ? (F extends (a: any, b: any, ...args: infer TArgs) => any ? TArgs : never) :
  S extends 3 ? (F extends (a: any, b: any, c: any, ...args: infer TArgs) => any ? TArgs : never) :
  S extends 4 ? (F extends (a: any, b: any, c: any, d: any, ...args: infer TArgs) => any ? TArgs : never) :
  S extends 5 ? (F extends (a: any, b: any, c: any, d: any, e: any, ...args: infer TArgs) => any ? TArgs : never) :
  S extends 6 ? (F extends (a: any, b: any, c: any, d: any, e: any, f: any, ...args: infer TArgs) => any ? TArgs : never) :
  never

type TailArray<A extends any[], S extends Number> =
  Tail<(...args: A) => any, S>

type Args<T extends Function> =
  T extends (...args: infer TArgs) => any ? TArgs
  : never

type PartialArgs<T extends Function> =
  T extends (...args: infer TArgs) => any ? Partial<TArgs>
  : never

type Curried<T extends (...args: any) => any, TReturn = ReturnType<T>> =
  <
    TArgs extends PartialArgs<T>,
    TRest extends TailArray<Args<T>, TArgs['length']>
  >(...args: TArgs) =>
    TRest extends []
      ? TReturn
      : Curried<(...args: TRest) => TReturn>

type Curry = <TFunc extends (...args: any) => any>(func: TFunc) => Curried<TFunc>

declare const curry: Curry

const curried = curry((a: 1 | undefined, b: number | number[], c: string) => 1)

// works :D
const a = curried(1)([2])('x')
const b = curried(1)(2, 'x')
const c = curried(1, 2)('x')
const d = curried(1, 2, 'x')


// the only problem is that `undefined` is accepted
// Partial<[1, 2]> => [1 | undefined, 2 | undefined]
curried(undefined)(2)(undefined)
```

```ts
type Init<T extends any[], TTail extends any[] = TailArray<T>> = CastArray<{
  [K in keyof TTail]: T[keyof T & K];
}>

type PotentialArgs<T extends any[], TResult extends any[] = T> = {
  "continue": PotentialArgs<Init<T>, TResult | Init<T>>;
  "end": TResult;
}[T extends [] ? "end" : "continue"]

type Args<T extends Function> =
  T extends (...args: infer TArgs) => any ? TArgs
  : never

type TailArgs<F extends Function> =
  F extends (head: any, ...tail: infer TTail) => any ? TTail :
  never

type TailArray<A extends any[]> = TailArgs<(...args: A) => any>

type CastArray<T> = T extends any[] ? T : []

type DropFromArraySize<TSource extends any[], TSize extends any[]> = CastArray<{
  "continue": DropFromArraySize<TailArray<TSource>, TailArray<TSize>>,
  "end": TSource,
}[TSize extends [] ? "end" : "continue"]>

type PartialArgs<T extends Function> =
  T extends (...args: infer TArgs) => any ? Partial<TArgs>
  : never

type Curried<T extends (...args: any) => any> =
  <
    TInitArgs extends PotentialArgs<Args<T>>,
    TTailArgs extends DropFromArraySize<Args<T>, TInitArgs>
  >(...args: TInitArgs) =>
    TTailArgs extends []
      ? ReturnType<T>
      : Curried<(...args: TTailArgs) => ReturnType<T>>

type Curry = <TFunc extends (...args: any) => any>(func: TFunc) => Curried<TFunc>

declare const curry: Curry

const curried = curry((a: 1 | undefined, b: number | number[], c: string) => 1)

// works :D
const a = curried(1)([2])('x')
const b = curried(1)(2, 'x')
const c = curried(1, 2)('x')
const d = curried(1, 2, 'x')
const e = curried(undefined)(2)('2')

curried(undefined)(2)(undefined) // notify error
```