> Only if you ignore the dynamic state of the language, of associated libraries, of processor architectures, and so on

I don't understand why any of this means you can't have a compile as a pure function. A pure function can cope with things changing internally - it just creates new data structures to represent things that have changed in the old data structures and then passes the new data structures onto the next phase.

A pure function just means you can't do something like a package manager that needs to read files from disk or download things.

> but so many useful systems rely on mutable state

You don't have to argue this to me - I wrote the first half of my PhD on the importance of mutable state.

I'm just arguing against the nonsense that it is impossible to write a useful real-world application as a pure function.

I work in the VM research group at Oracle, and guess what? Our JIT compiler is basically a pure function. It takes in some bytecode and produces some machine code. It's structured a little differently in reality, but it is logically, and almost in practice, a pure function from one to the other.

I'm writing a presentation about this right now.