This is easy in any dependently-typed language. Type-checking general dependent types is undecidable since it may require arbitrarily complex computations (Turing-complete). You can simply encode in a dependent type a too-large value. Then the type-checker will use all available memory and crash. For instance, in Coq, ReyCharles gives the example of Compute 70000.ReyCharles gives the example of Compute 70000., which causes the type-checker to construct a giant Peano numeral and crash.
In more common languages that support some sort of macro expansion or metaprogramming, you can do something similar. For example, you can use all available memory in C:
#include <stdio.h>
#define a printf("%s", "Hello, world!\n");
#define b a a a a a a a a a a a a a a a a
#define c b b b b b b b b b b b b b b b b
#define d c c c c c c c c c c c c c c c c
#define e d d d d d d d d d d d d d d d d
#define f e e e e e e e e e e e e e e e e
// ...
#define z y y y y y y y y y y y y y y y y
int main() { z }
The D programming language allows compile-time function execution. This can be used to compute something at compile time that is too large to fit in memory. Something similar can be achieved using C++ template metaprogramming.
In XML (not a compiled programming language, but an XML processor is analogous to a compiler), expanding entities can make the processor run out of memory:
<?xml version="1.0"?>
<!DOCTYPE lolz [
<!ENTITY lol "lol">
<!ENTITY lol1 "&lol;&lol;&lol;&lol;&lol;&lol;&lol;&lol;&lol;&lol;">
<!ENTITY lol2 "&lol1;&lol1;&lol1;&lol1;&lol1;&lol1;&lol1;&lol1;&lol1;&lol1;">
<!ENTITY lol3 "&lol2;&lol2;&lol2;&lol2;&lol2;&lol2;&lol2;&lol2;&lol2;&lol2;">
...
]>
<lolz>&lol999;</lolz>
This is called the billion laughs attack.
