/**
 * Represents the common keys between two types.
 * @template A - The first type.
 * @template B - The second type.
 */
export type CommonKeys<A, B> = Extract<keyof A, keyof B>

export type Extend<T extends readonly object[]> = (
    T extends readonly [
        infer Super,
        infer Self,
        ...infer Rest extends readonly object[],
    ]
        ? Pick<Self, CommonKeys<Self, Super>> extends Pick<Super, CommonKeys<Self, Super>>
            ? Extend<readonly [
                Omit<Super, CommonKeys<Self, Super>> & Self,
                ...Rest,
            ]>
            : never
        : T extends readonly [infer Self]
            ? Self
            : {}
)

export type Override<T extends readonly object[]> = (
    T extends readonly [
        infer Super,
        infer Self,
        ...infer Rest extends readonly object[],
    ]
        ? Override<readonly [
            Omit<Super, CommonKeys<Self, Super>> & Self,
            ...Rest,
        ]>
        : T extends readonly [infer Self]
            ? Self
            : {}
)

/**
 * Merges an inheritance tree defined by an array of types without allowing overrides.
 * @template T - An array of types representing the inheritance tree.
 */
export type ExtendWithoutOverriding<T extends readonly any[]> = (
    T extends [infer Super, infer Self, ...infer Rest]
        ? Pick<Self, CommonKeys<Self, Super>> extends Pick<Super, CommonKeys<Self, Super>>
            ? ExtendWithoutOverriding<[
                Super & Self,
                ...Rest,
            ]>
            : never
        : T extends [infer Self]
            ? Self
            : void
)