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Type-Level Set Operations in TypeScript

TypeScript's strength lies in its powerful type system, allowing us to express complex relationships and constraints at compile time. This challenge focuses on leveraging this power to implement set operations directly within the type system. You'll create generic types that represent sets and then implement operations like union, intersection, and difference for these type-level sets. This is useful for building robust type-safe libraries, data validation, and even domain-specific languages within TypeScript.

Problem Description

Your task is to create a set of TypeScript generic types that can represent finite sets of primitive types (numbers, strings, booleans) and perform common set operations at the type level.

Key Requirements:

  1. Set<T...> Type:

    • A generic type Set<T...> that accepts a variadic list of types T... representing the elements of the set.
    • Crucially, the Set type should enforce that its elements are unique. If a type appears more than once in the Set's type arguments, it should result in a type error.
    • Define a type IsUnique<T...> that returns true if all types in T... are unique, and false otherwise. Set<T...> should only be constructible if IsUnique<T...> is true.

  2. Set Operations:

    • Union<A, B>: Takes two Set types, A and B, and returns a new Set type containing all elements from both A and B. Duplicates should be automatically handled.
    • Intersection<A, B>: Takes two Set types, A and B, and returns a new Set type containing only the elements that are present in both A and B.
    • Difference<A, B>: Takes two Set types, A and B, and returns a new Set type containing elements that are in A but not in B.

  3. Helper Types: You'll likely need helper types, such as a way to check if an element is present in a set or to remove an element from a set.

Expected Behavior:

  • Attempting to create a Set with duplicate elements should result in a TypeScript compilation error.
  • The Union, Intersection, and Difference types should correctly compute the resulting set types.

Edge Cases:

  • Empty sets (represented by Set<>).
  • Sets with a single element.
  • Operations involving empty sets.

Examples

Example 1: Basic Set Creation and Uniqueness

// Input:
type MySet1 = Set<1, 'a', true>; // Should be valid

// Input:
// type MySet2 = Set<1, 'a', 1>; // Should be invalid (duplicate '1')

// Expected Output for MySet1:
// A valid type representing the set {1, 'a', true}

// Expected Behavior for MySet2:
// TypeScript compilation error: Type '1' is not assignable to type 'never'.
// (Or a similar error indicating a type clash due to duplication)

Example 2: Union Operation

// Input:
type SetA = Set<1, 'a'>;
type SetB = Set<'a', 2, 'b'>;

type UnionAB = Union<SetA, SetB>;

// Expected Output for UnionAB:
// A type equivalent to Set<1, 'a', 2, 'b'>

// Explanation:
// The union combines all unique elements from SetA and SetB.

Example 3: Intersection Operation

// Input:
type SetC = Set<1, 2, 3, 'x'>;
type SetD = Set<2, 3, 4, 'y'>;

type IntersectionCD = Intersection<SetC, SetD>;

// Expected Output for IntersectionCD:
// A type equivalent to Set<2, 3>

// Explanation:
// Only elements 2 and 3 are present in both SetC and SetD.

Example 4: Difference Operation

// Input:
type SetE = Set<1, 2, 3, 'a'>;
type SetF = Set<2, 4, 'a', 'b'>;

type DifferenceEF = Difference<SetE, SetF>;
type DifferenceFE = Difference<SetF, SetE>;

// Expected Output for DifferenceEF:
// A type equivalent to Set<1, 3>

// Expected Output for DifferenceFE:
// A type equivalent to Set<4, 'b'>

// Explanation:
// DifferenceEF contains elements in SetE but not in SetF.
// DifferenceFE contains elements in SetF but not in SetE.

Example 5: Edge Case - Empty Sets

// Input:
type EmptySet = Set<>;
type SetG = Set<1, 2>;

type UnionEmptyG = Union<EmptySet, SetG>;
type IntersectionEmptyG = Intersection<EmptySet, SetG>;
type DifferenceEmptyG = Difference<EmptySet, SetG>;
type DifferenceGEmpty = Difference<SetG, EmptySet>;

// Expected Output for UnionEmptyG:
// A type equivalent to Set<1, 2>

// Expected Output for IntersectionEmptyG:
// A type equivalent to Set<>

// Expected Output for DifferenceEmptyG:
// A type equivalent to Set<>

// Expected Output for DifferenceGEmpty:
// A type equivalent to Set<1, 2>

Constraints

  • The sets should only contain primitive types: number, string, boolean. (You may extend to bigint or symbol if you wish, but it's not required).
  • The types within a set must be distinct. Duplicates will cause type errors.
  • Solution should be achievable using TypeScript's conditional types, mapped types, and utility types.
  • Focus on correctness and type safety over runtime performance (as these are compile-time operations).

Notes

  • Consider how you will extract the individual elements from a Set<T...> type to perform operations.
  • Think about how to check for the presence of an element within a variadic tuple of types.
  • The uniqueness constraint for Set<T...> is a critical part of its definition.
  • You might find it helpful to create a type that "flattens" or processes a variadic tuple of types into a more manageable form for certain operations.
  • Remember that TypeScript type inference and conditional logic are your primary tools.
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