I mean, there's ample evidence on this thread to suggest we're not going to reach a productive conclusion here but I guess I'll keep biting.

It's not clear to me if you are suggesting that a dynamic routing table with different kinds of routes cannot be implemented in a type-safe manner in a statically typed language, or if you're working with an analogy where a routing table is like a dynamic programming language at runtime, in that a static set of entities and relations are known ahead of time and those are modified by runtime input. If it's the latter I'm not really sure how the analogy works—if programming languages are to routers as types are to routing entries, what in a router is analogous to a value of a given type?

I can speak more to the former possibility; here's a rough sketch of how one could implement a routing table using the tools available in a statically typed environment (and in a type-safe way). One way to do it (I believe the common way, and certainly the only one I've seen in commercial router implementations) is to treat statically populated and dynamically learned routes more or less uniformly in the data structures used to perform data-plane lookups. Each such route entry has the same fields and gets inserted into a data structure with a predefined shape. Where special behavior is needed for routes of different kinds, that behavior can be implemented by using dynamic dispatch in the sense it's usually used in C++, Java, Rust, etc. to call a method associated with a route entry, or using other techniques common to statically compiled languages—there is a fixed set of such operations defined up front. Adding and removing entries from the routing table at runtime does not typically implicate type safety because the types used to describe the table describe all of its possible valid states. For instance, the type for a node in a radix trie might describe how it can either be leaf node or contain subnodes, etc.

> The schema need not change. The entries/relations between objects changing is sufficient to violate type-safety.
>
> Route add( str1, str2) to Number.add().

It's obviously not always true that entries or relations changing will validate type safety; any non-trivial system will let you perform some kinds of data manipulation at runtime. Conventional static type systems will allow some kinds of mutations (like changing around pointers in a radix trie to insert a new node) but will not have the flexibility to support some others (like changing the shape of a dispatch table at runtime).

One kind of call pattern which is incompatible with statically compiled dynamic dispatch is where the types of parameters change along with the base type which owns the dispatch table; I think this is what your add() example is getting at—you need the type of the second parameter to match the first, which you can't validate without runtime checks if you don't know what concrete implementations will be in use at runtime. In the case of a routing table I don't think this kind of polymorphism is needed though; I can't think of an instance where an operation would fundamentally require a fixed relation in the concrete types of different routes. For instance, when routes overlap you can derive a priority value for each one to decide which one to use, rather than directly implementing some kind of function whichIsBetter(a, b) which relies on knowing what concrete route kinds a and b are.