Implementing a Shift Type in TypeScript

This challenge focuses on creating a utility type in TypeScript that shifts the types within a union type. This is useful when you need to create a new union type based on an existing one, but with a specific type removed or moved to a different position. It's a common pattern in type manipulation and can simplify complex type definitions.

Problem Description

You are tasked with creating a TypeScript type called Shift<T, U> that takes two type parameters: T (a union type) and U (a type). The Shift<T, U> type should produce a new union type where the type U is removed from T and all remaining types are shifted to the beginning of the union. The resulting union type should not include U.

Key Requirements:

• The function must handle union types correctly.
• The function must remove the specified type U from the union T.
• The function must preserve the order of the remaining types in the union.
• The function should return never if T is not a union type or if U is not present in T.

Expected Behavior:

The Shift<T, U> type should effectively "shift" the types in the union T to the left, excluding U.

Edge Cases to Consider:

• T is not a union type (e.g., a primitive type, an object type).
• U is not a member of the union T.
• T is an empty union type (never).
• U is never.
• T contains duplicate types. The removal of U should only happen once.

Examples

Example 1:

Input:
T = string | number | boolean
U = number

Output:
Shift<T, U> = string | boolean
Explanation: The `number` type is removed from the union `string | number | boolean`, resulting in `string | boolean`.

Example 2:

Input:
T = 'a' | 'b' | 'c'
U = 'b'

Output:
Shift<T, U> = 'a' | 'c'
Explanation: The type 'b' is removed from the union 'a' | 'b' | 'c', resulting in 'a' | 'c'.

Example 3:

Input:
T = string | number | string
U = string

Output:
Shift<T, U> = number
Explanation: The first instance of 'string' is removed, leaving only 'number'.  Duplicates are handled correctly.

Example 4: (Edge Case)

Input:
T = string | number
U = symbol

Output:
Shift<T, U> = never
Explanation: 'symbol' is not a member of the union 'string | number', so the result is 'never'.

Constraints

• T must be a union type.
• U must be a type.
• The solution must be a valid TypeScript type definition.
• The solution should be reasonably performant (avoiding unnecessary recursion or complex logic). While performance isn't a primary concern for type definitions, excessively inefficient solutions should be avoided.

Notes

Consider using conditional types and distributive conditional types to achieve the desired behavior. Think about how to check if a type is part of a union type. The Exclude utility type might be helpful, but you'll need to combine it with other techniques to achieve the "shift" effect. Remember that TypeScript type definitions are evaluated at compile time, so runtime performance is not a factor.