Type-Level List Implementation in TypeScript

This challenge focuses on implementing a fundamental data structure, the linked list, entirely at the type level in TypeScript. You will leverage TypeScript's advanced type system to define and manipulate lists of types, enabling powerful static analysis and compile-time operations. This is a core concept in advanced type programming and has applications in areas like domain-specific languages and complex type transformations.

Problem Description

Your task is to define a series of TypeScript types that collectively represent a singly linked list. This list should be capable of storing types of any kind and should support basic operations like checking if the list is empty, prepending an element, and accessing the head and tail.

Key Requirements:

1. EmptyList Type: Define a type that represents an empty list.
2. Cons<Head, Tail> Type: Define a generic type Cons that represents a non-empty list.
   • Head: This type parameter represents the first element of the list.
   • Tail: This type parameter represents the rest of the list, which must itself be a valid list type (either EmptyList or another Cons).
3. IsListEmpty<List> Type: Define a type that takes a list type and resolves to true if the list is empty, and false otherwise.
4. HeadOf<List> Type: Define a type that takes a list type and resolves to the Head type if the list is non-empty. If the list is empty, it should resolve to never.
5. TailOf<List> Type: Define a type that takes a list type and resolves to the Tail type if the list is non-empty. If the list is empty, it should resolve to never.

Expected Behavior:

Your types should behave logically according to the definitions of a linked list. For example, IsListEmpty<EmptyList> should resolve to true, while IsListEmpty<Cons<number, EmptyList>> should resolve to false.

Edge Cases:

• Attempting to get the HeadOf or TailOf an EmptyList should result in a never type.
• The Tail of a Cons type must always be a valid list type.

Examples

Example 1:

// Defining an empty list
type MyEmptyList = EmptyList;

// Checking if it's empty
type IsEmptyResult1 = IsListEmpty<MyEmptyList>; // Expected: true

// Attempting to get head/tail of an empty list
type HeadOfEmpty = HeadOf<MyEmptyList>; // Expected: never
type TailOfEmpty = TailOf<MyEmptyList>; // Expected: never

Explanation: We define an EmptyList and then use IsListEmpty to confirm it's empty. Accessing the head or tail of an empty list correctly yields never.

Example 2:

// Defining a list: [number, string]
type MyList = Cons<number, Cons<string, EmptyList>>;

// Checking if it's empty
type IsEmptyResult2 = IsListEmpty<MyList>; // Expected: false

// Getting the head
type HeadResult = HeadOf<MyList>; // Expected: number

// Getting the tail
type TailResult = TailOf<MyList>; // Expected: Cons<string, EmptyList>

Explanation: We construct a list with a number head and a string tail (which itself is a list). IsListEmpty correctly returns false. HeadOf resolves to number, and TailOf resolves to the remaining list.

Example 3:

// Another list: [boolean]
type AnotherList = Cons<boolean, EmptyList>;

// Getting the head of AnotherList
type HeadOfAnother = HeadOf<AnotherList>; // Expected: boolean

// Getting the tail of AnotherList
type TailOfAnother = TailOf<AnotherList>; // Expected: EmptyList

// Checking if the tail of AnotherList is empty
type IsTailOfAnotherEmpty = IsListEmpty<TailOf<AnotherList>>; // Expected: true

Explanation: This example demonstrates a list with a single element. We successfully retrieve its head and tail, and then verify that the tail (which is an empty list) is indeed empty.

Constraints

• You must use only built-in TypeScript types and conditional types.
• No runtime JavaScript code is required; this is purely a type-level exercise.
• The solution should be efficient in terms of compile-time checks, though specific performance metrics are not defined for this theoretical challenge.

Notes

Consider how TypeScript's conditional types (T extends U ? X : Y) can be used to discriminate between different list structures. The EmptyList will likely serve as a base case for recursive type definitions. Think about how to pattern-match on the structure of a list type.