In a nutshell: What your teacher probably meant is that the semantics of while is pretty much the same in most languages, while the semantics of for may change considerably (see discussion below). Hence, abstract language independent proof are more reliable with a while, but one should be careful that a proof with a for loop may not match the semantics of the for loop in many languages.

Your question is not precise enough (though that may not be your
fault).

The point is that, afaik, there is no official, ISO supported
standard, or otherwise officially accepted reference definition of
for and while loops. The definition depends on the programming
language.

Hence you cannot make any general statement regarding their
equivalence before you have defined precisely what each can do. I
adress that more precisely, since it is one of the main argument used
in other answers (and the discussion will be useful in what follows).

On intertranslatability of for and while loops

Summary: it depends on the programming language, but is always
possible a long as you can have one infinite loop and a way to get out
of it.

But you can make such a statement for a specific programming language,
and the answer will depend on the features fo the language.

That also means that there is no general proof, but only one for each
programming language.

One thing that is generally true is that a while loop can generally
mimic a for loop, because the while loop can do the exit condition
testing of the for loop, doing the initialisation of the control
variable with an assignment before entering the loop, and doing the
incrementation at the end of the loop body, so that

for i from 1 by 2 to 10 do { xxx }

becomes

i=1
while i≤11 do { xxx; i←i+2 }

This more or less works for most languages, but it is not as obvious as
it seem, and there may be many “details” to worry about.

For example, in many languages, the for loop evaluates it 3
arguments (initial value, increment, and final value) as strict
arguments, evaluated once before entering the loop, while others will
take then as thunk arguments to be reevaluated at each turn, or
possibly as lazy argument to be evaluated only when first needed.

Another point may be that the increment variable may be local to the
for loop, or have to be a local variable of the function where the
loop appears.

Depending on such issues, the translation of a for to a while may
vary widely, though it is usually possible to achieve it.

The same holds for the converse, thranslating a while into a for loop.

Th first problem is that a while loop will always reevaluate the
exit condition at each turn. But some for loops do not provide for a
condition that is reevaluated at each turn, other than comparison of
the control variable with some fixed value computed on loop entry.
Then the translation is not possible unless there is some other mean
to jump out of the loop on some arbitrary conditions.

That is achievable with various devices, usually starting with a
conditional statement testing the condition, followed by an a jump out
implemented, as available, by a loop exit statement, a return
statement (after encapsulating the loop in a function), a goto
statement or an exception raising.

In other words, it is again very dependent on languages, and possibly
on subtle features of languages.

This say, as answered by @milleniumbug, the intertranslation is easy
in the language C, because a for lopp is essentially a while loop
plus some extra for an incremented control variable.

But this does not necessarily apply to other languages, and most
likely not in the same way.

This being said, programming languages are usually supposed to have
Turing power with only one of these loops, since all you need for it
is one infinite loop. So, as long as you have some way of looping for
ever, and possibly deciding to stop, you are pretty sure you can mimic
any other construct … but not necessarily easily.

Regarding proofs

Summary: There is no reason known to me to assert that proofs should be significantly harder with one or the other (unless some weird feature of the language).

There is probably a misunderstanding, or your teacher had his mind on
something else.

Formals semantics can be defined for the various kinds of loops
defined in programming languages, and then used for proving
properties.

It may be, again depending on the language, that conducting formal
proofs regarding programs may be more complex in some cases. But that
depends on the language.

I cannot imagine a reason why proofs should be significantly harder with one construct more than with the other. The for loop may be more complex since it can offer, as in C, all that is done with a while plus other things. But if you did it with a while, you would have to add the extras in some other form.

I could use the formal general argument of intertranslatability, as long as there is the possibility for a single infinite loop. I will however refrain from doing that, as the constructions involved are nothing you want to deal with in a proof, and it would clearly be an unfair statement, at least in practice.

Following the above discussion, however, we have seen that the difficulties for intertranslatability come from the great variability of the for loop from language to language. Hence the following conclusion which is probably the right answer:

One possibility to understand your teacher’s statement is that the semantics of the while loop is pretty much the same in all programming languages, while the syntax and semantics of the for loop can vary significantly from language to language. Hence, it is possible to make general “abstract” proofs with while loops that have language independent semantics to a good extent, while this is not possible for the for loop that has syntax and semantics changing too much from language to language. But this does not apply within a given language, when the semantics of both are precisely defined.

My best suggestion is that you should ask your teacher what he precisely meant, and whether he can give you an example. Misphrasing or misunderstanding is a common event.

In the C language you can rewrite every for loop to an equivalent while loop and vice versa.

while -> for transformation:

Rewrite

while(condition) { instructions; }

to

for(; condition; ) { instructions; }

for -> while transformation:

This is slightly more complicated, especially if you have continue statement in your loop.

Rewrite:

for(init; condition; next) { instructions; }

to:

{
    init;
    while(condition)
    {
        instructions;
    next_label:
        next;
    }
}

but replace every continue; statement with goto next_label; statement. If condition is a null instruction, replace it with true.

As you can see, in C language neither is more “provable” (whatever that means) than the other, since even if one of the loop was, you could rewrite it in terms of another loop.

Now, there exist other languages where this while <-> for equivalency doesn’t exist. For example, in Pascal, you can assume more about the for loop. This means that you can’t express every concept when writing a for loop, but you can prove more about the flow of the code:

for i:=1 to n do
    instructions;

Here, the n is saved at the beginning of the loop, so changes to n don’t make any influence on iteration count, and you can’t modify i in the body of the loop. This means you can trivially prove this loop will eventually end (as n is finite, and you can’t modify i).

In Floyd-Hoare logic, the most common formal system for reasoning about the correctness of computer programs, there is the while rule.

In words, if you have a guard clause (the expression in brackets in the while()), a variant function (an expression with discrete values that can be shown to decrease monotonically each time the loop runs, and always be positive), and a loop invariant (a logic statement that is always true before and after every time the loop runs), you can prove that the while loop will finish (because the variant function can’t keep decreasing) and that eventually the guard clause will be false and the loop invariant be true.

Floyd-Hoare logic doesn’t have rules for for loops or whatever constructs actual languages may have.

However, as other answers explain, for loops can always be written in terms of while loops. That means that they can be reasoned about, it just takes a little more work.

If your teacher had courses at university where he had to provide correctness proofs of his programs, he probably wrote programs using only while loops. I know I did. And once you are used to thinking in terms of guards and variant functions and loop invariants, they seem very natural. Overusing while loops is a habit you see with CS graduates, I had to learn to stop doing that in my first months as a professional developer.

Somewhere down the line, your teacher misremembered all this as “good programmers use while loops”, whereas what really happens is more like “some CS graduates turn their correctness proof habits into practical programming habits”.

Actually, in some sense, the exact opposite is true.

A language with only for-loops is not Turing-complete, it can only compute the primitive-recursive functions, not all Turing-computable functions. Since all computation in a language with only for-loops always terminates, the Halting Problem and all the other Decidability Problems based upon it, simply don’t arise, so it is possible to mechanically decide many more static properties of programs than in a language with while-loops.

OTOH, a language with only natural numbers, a single variable, and while-loops is Turing-complete, and so it is not possible to decide even the simplest of properties: will this program return a result?

I would like to say that in reality, there is no difference .Your question is irrelevant.
May be your teacher might have meant to use while-loop when no. of iterations is not known beforehand.In many cases we need to use a while loop to extract digits of a no. when the user enters the no. which can be of any length. Technically speaking, the similarity between for & while loop is that both are entry-controlled loops wherein the (test-expression/condition) is evaluted before entering into the loop body.This is the distinction between while & do-while loops.

It likely comes from early C programming where, by todays norms, loops were widely abused and misused, especially the conditional being modified. As programmers started to understand the effect certain programming styles had, the abuse and misuse of loop conditionals fell out of favor, and the statement, while (arguably) once valid, no longer holds any truth.

The statement holds absolutely no truth if you look solely at the language definition and syntax and ignore how it was being used.

The statement itself does however offer a valuable lesson to anyone who wants to understand it, its history and why its no longer considered true. – Whats the expression about learning, mistakes and repeating them…..

Your teacher is correct!

The reason is the following is valid C

for (int x = 1 ; x < 20 ; x++ ) {
   x = x + 9;
}

You cannot guarantee the condition variables have not been tampered with!