Trying to find the complexity of this problem lead me to this paper. The formal definition of the problem can be found within: this is generally called the inclusion problem The inclusion problem for R, is to test for two given expressions r, r′ ∈ R, whether r ⊆ r′. That paper has some great … Read more
Don’t listen to the naysayers. There are very good reasons one might prefer a non-Turing complete language in some contexts, if you want to guarantee termination, or simplify code, for example by removing the possibility of runtime errors. Sometimes, just ignoring things may not be sufficient. The paper Total Functional Programming argues more or less … Read more
EDIT (much later than original answer): MarkCC of Good Math, Bad Math recently wrote up an excellent discussion of the Halting problem with concrete examples. The halting problem is basically a formal way of asking if you can tell whether or not an arbitrary program will eventually halt. In other words, can you write a … Read more
I literally got assigned the halting problem, as in “write a monitor plugin to determine whether a host is permanently down”. Seriously? OK, so I’ll just give it a threshold. “No, because it might come back up afterward.” Much theoretical exposition ensued.
The compiler can easily and unequivocally prove that the first expression always results in an infinite loop, but it’s not as easy for the second. In your toy example it’s simple, but what if: the variable’s contents were read from a file? the variable wasn’t local and could be modified by another thread? the variable … Read more