I don't think that's true. I think you could design a purely functional language where everything is immutable, but something contains a circular loop by definition. You could just declare that l is the list of integers going from 0 to 5 and then back to 0 ad infinitum. IMO, circular references can exist without mutation, if the language specifies that something is circular/recursive at the moment it's created. Defining a circular linked list in a declarative way rather than in terms of the instructions that build the linked list. The list is created all at once. It comes into existence with a cycle into it.

Like, say, Prolog?

    A = [a | A]

Prolog implementations provide destructive operations and mutation, but here above this is done with unification only. Arguably, you could say that unification performs mutation (but only once).

Better than that, you can "mutate" if you're not invalidating information about the variable. Oz (not incidentally, developed by Prolog people) lets you add constraints to a variable as long as they don't contradict the previous ones. Binding to a specific value is just a very strong constraint. Re-binding to the same value is okay.

This is less strict than pure functional programming, but still feels declarative and makes concurrent programming easy: no piece of code that looked previously at your variable will have its assumptions about it broken.

Arguably we could argue that everything flips 1's to 0's and back under the hood, though. Instantiation of a new lexical environment with fresh bindings mutates something in the machine.

Make that a functional programming language without mutually recursive first class local functions. (In the case of Lisp/Scheme, no labels or letrec)

xs = 1:xs

Lazy evaluation makes it possible to construct circular data structures without mutation.

Or in Lisp one could write #1=(1 . #1#), eg:

    CL-USER> (subseq '#1=(1 2 3 . #1#) 0 10)
    (1 2 3 1 2 3 1 2 3 1)

Ah that's interesting. I was going to say that in principle a strict language could have a special syntax for defining circular data structures, but I didn't know about that particular corner of CL.

You also know that your program is not Turing-complete.

Had a complicated discussion here, but it's ridiculous, because:

Church-Turing thesis says lambda calculus is turing complete and it is purely functional with no pointers at all.

But it does have fixpoints... right? You need recursion somehow.

In Standard ML, all recursive value definitions must have function literals as their right-hand sides. Thus, at runtime, recursion is guaranteed to go through functions (which normally aren't allocated in the heap) and/or mutable data structures (which can be handled in a special way by the garbage collector). Immutable data structures are generally guaranteed to be cycle-free.

That being said, reference counting is a really bad fit for functional languages for several other reasons.

You don't need the type of fixed points that cause the issues with circular pointers. Recursion can be done with (appropriately for HN) the Y combinator. The kind of tricks I'm talking about rely on laziness and are pretty complicated. See: http://stackoverflow.com/questions/37366222/why-is-this-vers...

How would you implement recursion then?