Shortest program that continuously allocates memory

Funge-98 (cfunge), 1 byte

9

I would have posted this earlier, but decided to test it, and it took a while to get my computer back to a usable state. cfunge stores the Funge stack on the operating system's heap (which is easily verifiable by running the program with a small memory limit, something that I should have done earlier!), so an infinitely growing stack (as with this program, which just pushes 9 repeatedly; Funge programs wrap from the end of a line back to the start by default) will allocate memory forever. This program likely also works in some Befunge-93 implementations.

More interesting:

"NULL #(4

This was my first idea, and is an infinite allocation that doesn't rely on the Funge stack (although it blows up the Funge stack too). To start with, the " command pushes a copy of the rest of the program to the stack (it's a string, and the program wraps round, so the close quote also serves as the open quote). Then the N reflects (it has no meaning by default), causing the program to run backwards. The " runs again, and pushes the program to the stack – the other way round this time, with the N at the top of the stack – then the program wraps around, loading a library with a 4-letter name (4(; the NULL library is part of cfunge's standard library). NULL defines all uppercase letters to do reflect, so the L reflects, the # skips the library load on the way back, the 4 pushes junk we don't care about to the stack and the whole program repeats from the start. Given that loading a library multiple times has an effect, and requires the library's command list to be stored once for each copy of the library (this is implied by Funge-98's semantics), it leaks memory via non-stack storage (which is an alternative method of defining "heap", relative to the language rather than the OS).

Brainfuck, 5 bytes

+[>+]

This requires an interpreter that has no limit on the length of the tape.

Bash + coreutils, 5

or

Ruby, 5

`yes`

yes produces endless output. Putting yes in backticks tells the shell to capture all output and then execute that output as a command. Bash will continue allocating memory for this unending string until the heap runs out. Of course the resulting output would end up being an invalid command, but we should run out of memory before that happens.

Thanks to @GB for pointing out this is a polyglot in ruby too.