Recursively Create ReadOnly Object in FlowJS - recursion

Question

In redux, the state should be immutable. I would like Flow to prevent anyone from mutating that state. So, given an object of arbitrary depth:
type object = {
a: {
b: {
d: string
}
},
c: number
}
How can I create a new type that is recursively readonly, so that I cannot do:
let TestFunction = (param: $RecursiveReadOnly<object>) => {
param.a.b.d = 'some string'
}
The builtin $ReadOnly utility of Flow will create a type like this, which isn't what is needed, because b & d are still writable:
{
+a: {
b: {
d: string
}
},
+c: number
}
I've been trying to use the $Call & $ObjMap(i), but I can't figure out how to recursively travel an object in Flow. The objective is to have this:
{
+a: {
+b: {
+d: string
}
},
+c: number
}

Answer 1

Thanks to kalley for his solution. From what I understood, kalley tried to make any object received by a function recursively read only. Since I really only needed known objects as parameters, this works perfectly:
// Type definition that works with arbitrary nested objects/arrays etc.
declare type RecursiveReadOnly<O: Object> = $ReadOnly<$ObjMap<O, typeof makeRecursive>>
declare type RecursiveReadOnlyArray<O: Object> = $ReadOnlyArray<$ReadOnly<$ObjMap<O, typeof makeRecursive>>>
type Recursive<O: Object> = $ObjMap<O, typeof makeRecursive>
declare function makeRecursive<F: Function>(F): F
declare function makeRecursive<A: Object[]>(A): $ReadOnlyArray<$ReadOnly<Recursive<$ElementType<A, number>>>>
declare function makeRecursive<O: Object>(O): RecursiveReadOnly<O>
declare function makeRecursive<I: string[] | boolean[] | number[]>(I): $ReadOnlyArray<$ElementType<I, number>>
declare function makeRecursive<I: string | boolean | number | void | null>(I): I
// Usage example.
type obj = {
a: {
b: {
d: string,
}
}
}
let TestFunction = (param: RecursiveReadOnly<obj>) => {
param.a.b.d = 'some string' // Flow throws an error
}