Implementing Continuation Types in TypeScript

Continuation-passing style (CPS) is a programming paradigm where functions do not return values directly. Instead, they take an additional argument, a "continuation" function, and call it with their result. This challenge focuses on implementing CPS in TypeScript, which can be incredibly useful for managing asynchronous operations, complex control flow, and enabling advanced functional programming techniques.

Problem Description

Your task is to implement a mechanism for representing and working with continuation types in TypeScript. This involves defining a generic type that captures a function's signature and transforms it into a continuation-accepting function. You will then need to create a function that can "convert" a standard synchronous function into its CPS equivalent.

Key Requirements:

1. Continuation Type: Define a generic TypeScript type called Continuation<T> that represents a function that accepts a single argument of type T and returns void. This type will serve as the signature for our continuations.

   // Expected signature: (result: T) => void
   type Continuation<T> = ...
   

2. CPSConvertible Type: Define a generic TypeScript type called CPSConvertible<F> which takes a function type F and returns a new function type. This new function type should accept all the arguments of F except the last one, and the last argument should be replaced with a Continuation of the original function's return type.

   For example, if F is (a: number, b: string) => boolean, then CPSConvertible<F> should be (a: number, b: string) => void.

   If F is (x: number) => string, then CPSConvertible<F> should be (x: number) => void.

   This type needs to be flexible enough to handle functions with varying numbers of arguments.

3. toCPS Function: Implement a function toCPS<F extends (...args: any[]) => any>(fn: F): CPSConvertible<F>. This function should take a regular synchronous function fn and return a new function that implements the CPS version of fn. When the returned function is called, it should invoke the original fn with its arguments and then pass the result of fn to the continuation function.

Expected Behavior:

• The toCPS function should correctly transform any given synchronous function into its continuation-passing style equivalent.
• The transformed function should accept all original arguments except the final continuation, and then execute the original function, passing its result to the continuation.

Edge Cases to Consider:

• Functions with no arguments.
• Functions that return void.

Examples

Example 1:

// Original synchronous function
function add(a: number, b: number): number {
  return a + b;
}

// Convert to CPS
const addCPS = toCPS(add);

// Call the CPS version. The last argument is the continuation.
addCPS(5, 3, (result: number) => {
  console.log(`The sum is: ${result}`); // Expected output: The sum is: 8
});

Explanation: The toCPS function transforms add into a function that accepts two numbers and a continuation. When addCPS(5, 3, ...) is called, it executes add(5, 3) and passes the result 8 to the provided continuation function, which logs "The sum is: 8".

Example 2:

// Original synchronous function
function greet(name: string): string {
  return `Hello, ${name}!`;
}

// Convert to CPS
const greetCPS = toCPS(greet);

// Call the CPS version
greetCPS("Alice", (message: string) => {
  console.log(message); // Expected output: Hello, Alice!
});

Explanation: greet is converted to a function that takes a string and a continuation. greetCPS("Alice", ...) calls greet("Alice"), gets "Hello, Alice!", and passes it to the continuation.

Example 3: (Function returning void)

// Original synchronous function that returns void
function logMessage(message: string): void {
  console.log(`Logging: ${message}`);
}

// Convert to CPS
const logMessageCPS = toCPS(logMessage);

// Call the CPS version. The continuation will be called with `undefined` (or whatever void maps to).
logMessageCPS("Task completed", () => {
  console.log("Continuation called after logging.");
});
// Expected output:
// Logging: Task completed
// Continuation called after logging.

Explanation: Even though logMessage returns void, toCPS correctly handles it. The continuation is invoked after logMessage has executed its side effect. The value passed to the continuation for a void function is effectively undefined.

Constraints

• The solution must be implemented entirely in TypeScript.
• The toCPS function should be generic enough to handle functions with up to 10 arguments. (This is a practical limit for a reasonable challenge; you do not need to support an arbitrary number of arguments with complex variadic tuple types for this problem).
• The solution should be clear, readable, and adhere to good TypeScript practices.

Notes

• This challenge requires a solid understanding of TypeScript's advanced type features, including generic types, conditional types, mapped types, and potentially variadic tuple types.
• Think about how to extract the return type and the argument types from a given function type.
• Consider how to construct the new function signature for the CPS version.
• The core of the toCPS implementation will involve creating a new function that acts as a wrapper around the original function, managing the call to the continuation.