[rer0tsaz]

Iterative loops are much easier to analyze and reason about, by humans and by computers. For example, they always terminate. To paraphrase Dijkstra, "I regard general recursion as an order of magnitude more complicated than just repetition, and I don't like to crack an egg with a sledgehammer."

https://tinyletter.com/programmingphilosophy/letters/i-don-t...

[nbevans]

Dijkstra was from a different era from when mutable state wasn't frowned upon.

Note to self: This may not go down well here but I'm willing to take the flack.

[rer0tsaz]

He actually discusses it a bit in the previous paragraph, which does not seem to be online anywhere:

> When programming languages emerged, the "dynamic" nature of the assignment statement did not seem to fit too well into the "static" nature of traditional mathematics. For lack of an adequate theory mathematicians did not feel to easy about it, and, because it is the repetitive construct that creates the need for assignment to variables, mathematicians did not feel to easy about repetition either. When programming languages without assignments and without repetition --such as pure LISP-- were developed many felt greatly relieved. They were back on familiar grounds and saw a glimmer of hope of making programming an activity with a firm and respectable mathematical basis. (Up to this very day there is among the more theoretically inclined computing scientists still a widespread feeling that recursive programs "come more naturally" than repetitive ones.)

Continued https://tinyletter.com/programmingphilosophy/letters/i-don-t...

[douche]

I've always felt that imperative programming is more in line with the way the overwhelming majority of people are exposed to algorithmic instructions; cookbooks, furniture instructions, Lego construction, driving directions, pick-your-own-adventure books, etc. Especially given how piss-poor most mathematics instruction is, unless you happen to be a mathematician and have put in the effort to recast your brain along those lines, it's easier to come to grips with the imperative style vs more mathematically inspired paradigms.

[nbevans]

I wasn't slighting Dijkstra but merely commenting on the era of the time.

You can for example see how primitive things were back then by describing "mutable state" as "dynamic" and "immutable" as "static". Dynamic and static these days have entirely different connotations typically more associated with type systems.

Things have moved on and now in 2016 mutable state is increasingly being pushed out of codebases in favour of immutable practices. Recursion is (and always has been) one way of doing that.

:)

[pjmlp]

> For example, they always terminate.

How do you terminate?

   for(;;) {
   }

[meggar]

break;

[pjmlp]

Not all programming languages have break; C syntax was just an example.

Also break is no different from using return (to keep C syntax as example) when recursing.

If you guard break with if then you also need to prove if the "if" condition does indeed provide a dataflow path to break.

[AnimalMuppet]

> If you guard break with if then you also need to prove if the "if" condition does indeed provide a dataflow path to break.

In all cases, for all possible inputs.

On the other hand, if that's what your for loop looks like, you probably have the same problem of proving that your recursion terminates (in all cases, for all possible inputs).

[pjmlp]

Of course, I was just arguing against the OP that all loops terminate.

[mafribe]

    Iterative loops are much easier to analyze and reason about,

This is not the case. Loops and recursion can be translated into each other, hence are of equal complexity in terms of reasoning. And you see that when you write down the Hoare-logic axioms for either.

What Dijkstra had in mind was probably simple, syntactically constrained forms of loops, like for-loops where the loop variable is read-only in the loop body. They are simpler than general recursion, sure. But there are corresponding simpler forms of recursion, e.g. primitive recursion or tail recursion that are much simpler than general recursion.

[AnimalMuppet]

> Loops and recursion can be translated into each other...

True.

> ... hence are of equal complexity in terms of reasoning.

False. That's like saying that Stokes' Theorem says that the integral of a differential form over the boundary of a manifold is equal to the integral of it's derivative over the whole manifold, and therefore the two integrals are equally easy to do. In fact, the two integrals are often not equally easy to do, which is the primary practical reason that we care about Stokes' Theorem - it gives us a way to convert hard integrals into easier ones.

You cannot use formal equivalence to prove practical ease of doing the problem.

But the situation isn't even that simple. A blanket statement that "loops are much easier to analyze and reason about" is also false. It depends on the situation, and often on who's doing the reasoning. Different people think in different ways.

[Jtsummers]

> You cannot use formal equivalence to prove practical ease of doing the problem.

Agree completely, but want to bring it back to another computing topic: Technically, anything that can be computed with one Turing-complete language can be computed with another. And every language clearly is not equivalent in terms of ease of understanding and reasoning about as every other language.

Trivially, compare computations in brainfuck to computations in C. Compare the recursive definition of tree traversal available in lisps to languages without recursion (some BASIC variants and others) where you have to jump through hoops and self-manage a stack.

[mafribe]

    compare computations in brainfuck to computations in C. 

I'd suggest that this is an orthogonal issue. It's better to compare two otherwise identical languages, one where Turing-completeness is achieved by loops, another where the same is done by recursion. (Or a language that offers both). Then formal reasoning is of the same complexity.

[mafribe]

    You cannot use formal equivalence to prove 

I'm afraid I have to disagree here. There is a mechanical translation from loops to recursion and back. Likewise, there is an associated mechanical translation from Hoare-triples and associated proofs for reasoning about loops to Hoare-triples and associated proofs for reasoning about recursion and back.

So in a hard way, the complexity of formal reasoning about the correctness of loops and recursion must be the same.

[AnimalMuppet]

That doesn't mean that the reasoning in a human brain is equally difficult, or equally error-prone. If nothing else, doing the transformations (and back) adds to the cognitive burden.

[mafribe]

That depends primarily on the programmer's experience, if you are used to loops but not recursion, then obviously the former is simpler than the latter, and vice versa. If you are equally familiar with both, they then thinking about it is equally difficult.

[rer0tsaz]

Yes, that is the point I tried to make. Use simple, constrained forms such as (C) "for(int i = 0; i < n; i++) { ... }" with n an int and no modification of i in the body, or (Python) "for e in l:" where l is a list that is not modified in the body. Then your code is very easy to analyze, not just in theory but also in practice for compilers, tools and people reading your code. Many language designers have realized this and provide special syntax for this very common case. I'm not aware of any language that has special syntax for primitive recursion, but it's an interesting idea.

My apologies for making an absolute statement with unclear terms, thus inviting uncharitable interpretations.

[mafribe]

I agree, that simple loops that you describe are easier to analyse than full recursion.

But simple loops are not as expressive as full loops (where you can modify the loop variable). As a simple example, try to phrase the Euclid's algorithm for computing the GCD using "for(int i = 0; i < n; i++) { ... }" where "i" is not modified in the loop body.

[rer0tsaz]

Just use n = max(a, b). Of course that doesn't help you much unless you're adhering to strict safety standards (e.g. power of ten rules), it just shifts the burden of proof from termination to correctness. And there's no such trick with the Ackermann function.

I'm really just advocating a rule of least power. Don't go into full general recursion just because you can.

[mafribe]

Why is this being down-voted? Could somebody please explain why they think what I wrote is wrong? I'd be happy to learn something new about loops and recursion.

[conceit]

Wasn't me, but it's probably because iterative loops are believed to be easier to reason about. OTOH the recursive definition for the Fibonacci or factorial numbers seem easier, for one because they map to the literal explanation.

[mafribe]

    iterative loops are believed to be easier to reason about.

This cannot be the case, because you can translate loops into recursion and vice versa, so every reasoning problem that one finds with loops is also a problem in reasoning about recursion and vice versa. If you look at the Hoare-logic rules this shows up clearly. In both case you need a suitably invariant, and you need a termination argument.

[conceit]

Does the translation come for free? If not, it's probably complicated to reason about.

[nilved]

Loops aren't any safer than recursion. A loop is a special case of recursion and is just as susceptible to the halting problem.

[chriswarbo]

> Iterative loops are much easier to analyze and reason about, by humans and by computers. For example, they always terminate.

It's a bit of an apples-to-oranges comparison to compare (proper, bounded) for-loops to general recursion. A more appropriate question would be whether humans and computers find, say, primitive recursion or structural recursion easier to analyse and reason about than for-loops.

The difference between general- and primitive-recursion becomes very apparent when working in Coq, for example!

[_pmf_]

> For example, they always terminate.

No. In fact, it's a huge problem in imperative code at all layers.