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by TedDoesntTalk 1420 days ago
Flow control? Imperative.

No flow control? Declarative.

What is flow control? Typically if/then/else statements.

Importantly, setting a variable with a conditional does not make the language necessarily imperative.

I wonder if a language can be Turing-complete without flow control. My guess is no?

5 comments

I'm not even sure I agree with the author with that specifically:

> Flow control? Imperative. > No flow control? Declarative.

I think I'd rather say:

Imperative: Tell the system what to do.

Declarative: Tell the system what you would like to be. The system figures out what to do to get there.

You could well have flow control to say things like "if things are like that, I want things to be such", or "here is a loop building up what I would the state of the system to look like", still without telling the system what to do to get to that state.

> I wonder if a language can be Turing-complete without flow control. My guess is no?

Depends on your definition of "flow control". Untyped lambda calculous is effectively entirely just declaration and application of anonymous functions with only one argument, but it's Turing complete.

You can even try it in any language that has lambdas as first class citizens, e.g. here's a factorial function I wrote in Lambda calculous, but implemented in python:

    fac = ((lambda p: p(p)(lambda q: lambda n: ((n(lambda e: lambda e:
      lambda a: a)(lambda i: lambda l: i))(lambda d: lambda c: c)
      (lambda m: (lambda m: lambda z: m(n(z)))(q(m)))((lambda c: lambda x:
      n(lambda g: lambda h: h(g(c)))(lambda u: x)(lambda u: u))))))
      (lambda s: lambda q: lambda w: q(s(s)(q))(w)))
Does it have flow control? Depends. No python flow control is used, but some of those lambdas implement flow control. But they're not any part of the language (Lambda calculous), we just build them.

Would I call Lambda calculous declarative? Not at all!

> Depends on your definition of "flow control".

Yep. That’s why this is a potentially useful rule of thumb for comparing programming languages, especially ones that skew very far in one direction or the other, but it’s not a rigorous definition of the concepts.

Some incredibly simple algorithms are difficult to explain naturally without it sounding like control flow. How would you describe the absolute value function without saying “if” or “when” or specifying one particular element from a set? Obviously any computer system needs to be able to determine what steps to take depending on specified conditions.

> How would you describe the absolute value function without saying “if” or “when” or specifying one particular element from a set?

I don't think you even want a conditional when describing the absolute value function on the complex numbers.

> How would you describe the absolute value function without saying “if” or “when

How is this? absolute value is distance a number is from 0.

I get your point, though.

True, the syntax will obviously depend on what primitives the language provides. Of course it could also just provide the abs() function directly.
The author seems as confused as the people he complains about.

Just his example of `x = a ? b : c`, I never saw anybody try to claim code like this makes a language imperative. Instead, I've seen many people calling this logic "functional if".

If you go with his definition, only simple variable declaration is declarative.

(By the way, a very popular definition is that imperative languages have flow, not flow control. AKA, it makes a difference if you go and execute the instructions on a different order. That one is reasonable, but then, why single out non-associativity of operations when there are many other things that no language makes non-associative?)

Prolog would like to have a word.
> I wonder if a language can be Turing-complete without flow control. My guess is no?

I agree, unless something like pattern-matching does not count as control flow. But then isn't a conditional just a basic pattern? Why does it get a pass?

> I wonder if a language can be Turing-complete without flow control. My guess is no?

I can’t imagine why not. I think you have to make the distinction between explicit control flow in the syntax, which declarative languages don’t have (according to this rule of thumb), and the notion of a computer choosing to do one thing among several options depending on some condition. Of course any Turing-complete system can do the latter, but that’s totally unrelated to the syntax of the programming language.