TypeScript Tuple Type Utilities

This challenge focuses on leveraging TypeScript's powerful type system to create robust and reusable utilities for working with tuple types. You will implement generic types that allow for common tuple manipulations, enhancing type safety and code clarity when dealing with fixed-size, ordered collections of elements with potentially different types.

Problem Description

Your task is to create several generic TypeScript utility types that operate on tuple types. These utilities will allow you to perform common operations such as extracting specific elements, combining tuples, and reversing tuples, all while maintaining strong type safety.

Key Requirements:

• Nth<T, N>: A type that extracts the Nth element from a tuple type T.
• Prepend<T, U>: A type that prepends an element U to the beginning of a tuple type T.
• Append<T, U>: A type that appends an element U to the end of a tuple type T.
• Reverse<T>: A type that reverses the order of elements in a tuple type T.

Expected Behavior:

• The utility types should be generic and work with any valid tuple type.
• The types should accurately reflect the resulting tuple or element type after the operation.
• Ensure that type inference works correctly when these utilities are applied.

Edge Cases:

• Consider empty tuples for Reverse.
• Nth should handle valid index positions within the tuple's bounds. Behavior for out-of-bounds indices can be defined (e.g., never or undefined).

Examples

Example 1: Nth

Input: Tuple type: [string, number, boolean] Index: 1

Output: number

Explanation: The Nth utility type, when given the tuple [string, number, boolean] and index 1, correctly extracts the element at that position, which is number.

Example 2: Prepend

Input: Tuple type: [number, boolean] Element to prepend: string

Output: [string, number, boolean]

Explanation: The Prepend utility type adds string to the beginning of the tuple [number, boolean], resulting in a new tuple [string, number, boolean].

Example 3: Append

Input: Tuple type: [string, number] Element to append: boolean

Output: [string, number, boolean]

Explanation: The Append utility type adds boolean to the end of the tuple [string, number], resulting in a new tuple [string, number, boolean].

Example 4: Reverse

Input: Tuple type: [string, number, boolean]

Output: [boolean, number, string]

Explanation: The Reverse utility type reverses the order of elements in the tuple [string, number, boolean], yielding [boolean, number, string].

Example 5: Reverse (Empty Tuple)

Input: Tuple type: []

Output: []

Explanation: Reversing an empty tuple should result in an empty tuple.

Constraints

• Your solution must be written entirely in TypeScript.
• You should define these as type aliases or interface definitions, not functions.
• The types should be generic and accept type parameters.
• Focus on correctness and clarity of the type definitions. Performance of the type checker is not a primary concern for this challenge.

Notes

• Remember that tuples in TypeScript are represented as arrays with a fixed length and specific types for each element.
• You'll likely need to use conditional types and mapped types.
• Consider how you will handle indexing for Nth. You might find recursive conditional types useful for Reverse.
• For Nth, decide on a return type for out-of-bounds indices. never is a good choice to indicate an invalid operation.