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Comment by tlb | Hacker News Reader

The argument against f77 being Turing-complete is that you can't dynamically allocate memory, or specify infinite arrays, or recurse. You have to declare a finite size for everything. So a program embodies a fixed limit on how big a problem it can handle.

In C (the abstract machine with arbitrary-sized ints) you can allocate an arbitrary amount of memory. It may, of course, not run on any given machine. But the language itself allows it.

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f90 introduced recursion and allocatable (dynamically sized) arrays.

So (in reference to tombert's comment), f90 and beyond doesn't have those limitations. It also introduced conveniences like operator overloading and element-wise array operations, so I think it's a really simple/convenient language for basic scientific computing, if you want to code up some algorithm. That said, I always reach for Julia instead.

If that makes F77 not Turing-complete, nor is C. There is a finite amount of memory you can allocate in C, since a pointer must have finite size, implying there is a finite number of things it can point to.

The C language specification doesn't require a pointer to have finite size. Just because every C implementation has a limit, it doesn't mean the language itself does.

Doesn't it imply that it must be finite, because you can use sizeof() to find its size, which yields something of type size_t, which has maximum size SIZE_MAX?

The idea is that theoretically a perfectly portable C program could be written and work on problems of any size given sufficiently large hardware and a compiler implementation that takes advantage of that hardware.

Unlike a Fortran77 program, a portable C program doesn't have to change to support orders of magnitude changes in problem size.

You did not answer the question of SIZE_MAX being the limit. So here it is once again:

> Doesn't it imply that it must be finite, because you can use sizeof() to find its size, which yields something of type size_t, which has maximum size SIZE_MAX?

You could take the exact same C program and run it on a compiler+computer with sizeof(void *) == 64 or 128 or 1000000, and it should handle a correspondingly huge problem.

I am not sure that would be valid. You could also use a defined constant as the limit in the Fortran program. In other words, you could argue that SIZE_MAX is part of the program, the same as the Fortran array size is defined in the program. But I am not sure it would be invalid either... just wondering.

Wouldn't it be possible to, with a really strange number format for integers, define SIZE_MAX as INFINITY? C doesn't require twos-compliment numbers, after all.

> Wouldn't it be possible to, with a really strange number format for integers, define SIZE_MAX as INFINITY?

That's a very interesting question that got me thinking for quite a while and the only conclusion I reached is that you deserve an upvote.

Fortran can read and write arrays to disk so I think that satisfies Turing equivalency.

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