JoinNames

type JoinNames<
    Gates extends readonly Gate<GateContextBase>[],
    Sep extends string
> = Gates extends readonly [
    infer Only extends Gate<GateContextBase>
]
    ? GateName<Only>
    : Gates extends readonly [
            infer First extends Gate<GateContextBase>,
            ...infer Rest extends readonly Gate<GateContextBase>[]
        ]
      ? `${GateName<First>}${Sep}${JoinNames<Rest, Sep>}`
      : string;

type JoinNames<
    Gates extends readonly Gate<GateContextBase>[],
    Sep extends string
> = Gates extends readonly [
    infer Only extends Gate<GateContextBase>
]
    ? GateName<Only>
    : Gates extends readonly [
            infer First extends Gate<GateContextBase>,
            ...infer Rest extends readonly Gate<GateContextBase>[]
        ]
      ? `${GateName<First>}${Sep}${JoinNames<Rest, Sep>}`
      : string;