another function combine that takes program and an input string as parameters function combine modifies to store as static variable and further modifies all calls to input functions within to instead get their input from call the resulting program it should take no stretch of the imagination to believe that any decent compiler could be modified to take computer programs and input strings and produce new computer program that has been modified in this way nowtake and feed it to ehalt if ehalt says that will haltthen we know that would halt on input in other wordswe now have procedure for solving the original halting problem the only assumption that we made was the existence of ehalt thusthe problem of determining if program will halt on no input must be unsolvable example for arbitrary program pdoes there exist any input for which haltsproofthis problem is also uncomputable assume that we had function ahalt thatwhen given program as input would determine if there is some input for which halts we could modify our compiler (or write function as part of programto take and some input string wand modify it so that is hardcoded inside pwith reading no input call this modified program nowp always behaves the same way regardless of its inputbecause it ignores all input howeverbecause is now hardwired inside of the behavior we get is that of when given as input sop will halt on any arbitrary input if and only if would halt on input we now feed to function ahalt if ahalt could determine that halts on some inputthen that is the same as determining that halts on input but we know that that is impossible thereforeahalt cannot exist there are many things that we would like to have computer do that are unsolvable many of these have to do with program behavior for exampleproving that an arbitrary program is "correct,that isproving that program computes particular functionis proof regarding program behavior as suchwhat can be accomplished is severely limited some other unsolvable problems includedoes program halt on every inputdoes program compute particular functiondo two programs compute the same functiondoes particular line in program get executed