Type-Level Pattern Matching in TypeScript

This challenge focuses on implementing sophisticated type-level pattern matching algorithms using TypeScript's advanced type system. You will create a system that can infer and manipulate types based on their structure, similar to how runtime pattern matching works, but entirely at compile time. This is crucial for building robust, type-safe libraries and frameworks where complex data structures need to be analyzed and transformed without runtime overhead.

Problem Description

Your task is to implement a generic Match type in TypeScript that takes a type T and a set of Cases. The Match type should behave like a compile-time pattern matching engine. It will analyze the structure of T against the provided Cases and return the type associated with the first matching case.

Key Requirements:

1. Generic Match Type: Define a generic type Match<T, Cases> where T is the type to be matched, and Cases is an object type representing the patterns and their corresponding results.
2. Case Structure: Each key in the Cases object represents a pattern. The value associated with a key is the result type if the pattern matches.
3. Pattern Matching Logic:
   • Literal Types: Match against primitive literal types (e.g., 'hello', 123, true).
   • Union Types: Match against specific members of a union type.
   • Tuple Types: Match against the shape of a tuple (e.g., [string, number]).
   • Object Types: Match against object structures, potentially with specific properties.
   • Wildcard ('*'): A special case key that matches anything if no other case matches.
4. Order of Matching: Cases should be evaluated in a defined order. For simplicity, assume the order is implicitly defined by the order of keys in the Cases object (though TypeScript object key order is not strictly guaranteed for non-numeric keys, we will rely on this for this challenge). The first matching case determines the output.
5. Exhaustiveness (Optional but encouraged): While not strictly enforced by the type system in this scenario, your implementation should logically attempt to cover common matching scenarios.

Expected Behavior:

The Match<T, Cases> type should resolve to the type associated with the first pattern in Cases that successfully matches T. If no specific pattern matches and a '*' case is provided, it should resolve to the type of the '*' case. If no pattern matches and there is no '*' case, the behavior is undefined (or could result in never if handled carefully).

Edge Cases:

• Matching against never.
• Matching against complex nested types.
• The absence of a wildcard case.

Examples

Example 1: Simple Literal Matching

type MyUnion = 'apple' | 'banana' | 'cherry';

type FruitMatcher = {
    'apple': 'Red fruit',
    'banana': 'Yellow fruit',
    '*': 'Unknown fruit'
};

type Result1 = Match<MyUnion, FruitMatcher>;
// Expected: 'Red fruit' | 'Yellow fruit' | 'Unknown fruit' (depending on interpretation of union matching)

// Clarification: For unions, the matcher should apply to each member.
// So if T is 'apple' | 'banana', and 'apple' matches 'Red fruit' and 'banana' matches 'Yellow fruit',
// the result should be 'Red fruit' | 'Yellow fruit'.

type Result1a = Match<'apple', FruitMatcher>;
// Expected: 'Red fruit'

type Result1b = Match<'cherry', FruitMatcher>;
// Expected: 'Unknown fruit'

Example 2: Tuple Matching

type Data = [string, number, boolean];

type TupleMatcher = {
    [string, number]: 'String-Number Pair',
    [string, boolean]: 'String-Boolean Pair',
    '*': 'Other Tuple'
};

type Result2 = Match<Data, TupleMatcher>;
// Expected: 'String-Number Pair'

Example 3: Object Property Matching

type User = {
    id: number;
    name: string;
    isAdmin?: boolean;
};

type UserMatcher = {
    { id: number, name: string }: 'Basic User Info',
    { id: number, isAdmin: true }: 'Admin User',
    '*': 'Unknown User Structure'
};

// Note: Exact object matching is complex. Let's define a simplified property-based matching.
// A pattern like { prop: Type } means 'T must be an object and have a property named prop of Type'.

// Let's refine the problem description for object matching.
// A pattern like { id: number } should match any object that HAS an 'id' property of type 'number'.
// It doesn't require *only* those properties.

type RefinedUserMatcher = {
    // Matches objects with 'id' of type number and 'name' of type string
    { id: number, name: string }: 'User with Name',
    // Matches objects with 'id' of type number and 'isAdmin' of type true
    { id: number, isAdmin: true }: 'Admin User',
    // Matches any object with an 'id' of type number
    { id: number }: 'User with ID',
    '*': 'Other Structure'
};

type Result3a = Match<{ id: 123, name: 'Alice' }, RefinedUserMatcher>;
// Expected: 'User with Name'

type Result3b = Match<{ id: 456, isAdmin: true, username: 'Bob' }, RefinedUserMatcher>;
// Expected: 'Admin User' (since { id: number, isAdmin: true } matches)

type Result3c = Match<{ id: 789, email: 'test@example.com' }, RefinedUserMatcher>;
// Expected: 'User with ID'

Constraints

• The Match type and its associated helper types must be implemented using only TypeScript's built-in type utilities (e.g., infer, extends, conditional types).
• No external libraries or custom TS transformer plugins are allowed.
• The solution should aim for reasonable compile-time performance, avoiding excessively deep recursion or overly complex conditional type chains where possible.
• The Cases object is assumed to be an object literal.

Notes

This challenge is designed to test your understanding of:

• Conditional Types: T extends U ? X : Y
• Infer Keyword: infer for type variable inference within conditional types.
• Template Literal Types: Potentially useful for string literal matching.
• Tuple and Array Types: Working with array-like structures.
• Object Type Manipulation: Inferring and matching properties.
• Recursive Type Definitions: For handling nested structures or complex logic.

Consider how you will handle the order of operations. You might need to create helper types to check for matches sequentially. Think about how to represent patterns like "any number" or "any string" within your Cases structure if exact literal matching isn't sufficient. For object property matching, a pattern like { prop: Type } should likely be interpreted as "the type T must be an object, and it must have a property prop whose type extends Type".