Mastering Curried Function Types in TypeScript

Currying is a functional programming technique where a function that takes multiple arguments is transformed into a sequence of functions, each taking a single argument. In TypeScript, defining accurate and flexible types for curried functions can be challenging. This problem will test your ability to leverage advanced TypeScript generics and conditional types to create robust type definitions for curried functions.

Problem Description

Your task is to create a TypeScript type, let's call it Curried<T>, that takes a function type T and returns a new type representing its curried version.

What needs to be achieved:

You need to define a generic type Curried<T> that transforms a function T into its curried equivalent.

Key requirements:

The Curried<T> type should correctly handle functions with any number of arguments (including zero).
Each intermediate function in the curried sequence should return a function that expects the next argument.
The final function in the sequence should return the original function's return type.
The types should be as precise as possible, inferring argument types and the final return type correctly.

Expected behavior:

When Curried<T> is applied to a function type (...args: Args) => ReturnType, it should produce a type that represents a sequence of nested functions, where each function takes one argument from Args in order and the last function returns ReturnType.

Edge cases to consider:

Functions with zero arguments.
Functions with one argument.
Functions with multiple arguments.
Functions with complex argument types (e.g., union types, intersection types).

Examples

Example 1:

type Add = (a: number, b: number) => number;
type CurriedAdd = Curried<Add>;

// Expected type for CurriedAdd:
// (a: number) => (b: number) => number

const curriedAdd: CurriedAdd = (a: number) => (b: number) => a + b;
const result = curriedAdd(5)(10); // result should be 15

Explanation: The Add function takes two numbers and returns a number. Curried<Add> transforms this into a function that takes the first number (a), and returns another function that takes the second number (b) and finally returns the sum.

Example 2:

type Greet = (greeting: string, name: string, punctuation: string) => string;
type CurriedGreet = Curried<Greet>;

// Expected type for CurriedGreet:
// (greeting: string) => (name: string) => (punctuation: string) => string

const curriedGreet: CurriedGreet = (greeting: string) => (name: string) => (punctuation: string) => `${greeting}, ${name}${punctuation}`;
const message = curriedGreet("Hello")("World")("!"); // message should be "Hello, World!"

Explanation: This example demonstrates currying for a function with three arguments. Each step in the curried function chain takes one argument and returns a function for the next.

Example 3:

type NoArgs = () => string;
type CurriedNoArgs = Curried<NoArgs>;

// Expected type for CurriedNoArgs:
// () => string

const curriedNoArgs: CurriedNoArgs = () => "This is a test";
const value = curriedNoArgs(); // value should be "This is a test"

Explanation: For a function with no arguments, the curried type should simply be the original function type.

Constraints

The Curried<T> type must be a valid TypeScript generic type.
It should work with functions of arity 0 up to a reasonable number (e.g., 10-15 arguments, though ideally unlimited).
No runtime code generation is required; this is purely a type-level challenge.

Notes

This challenge will require a deep understanding of TypeScript's advanced type system, including:

Generics: To make the Curried type reusable for any function.
Conditional Types: To check if a function has more arguments to process.
Inferred types within generics (infer keyword): To extract argument types and return types from the input function T.
Recursive type definitions: To build the chain of nested functions.

Consider how to unwrap the function type T to access its parameters and return type. You'll likely need to use tuple types to represent the arguments.