sec impossible problems ( ( ( ( fnew ( figure illustration for the argument that the number of integer functions is uncountable that the halting problem cannot be computed by any computer program the proof is by contradiction we begin by assuming that there is function named halt that can solve the halting problem obviouslyit is not possible to write out something that does not existbut here is plausible sketch of what function to solve the halting problem might look like if it did exist function halt takes two inputsa string representing the source code for program or functionand another string representing the input that we wish to determine if the input program or function halts on function halt does some work to make decision (which is encapsulated into some fictitious function named program haltsfunction halt then returns true if the input program or function does halt on the given inputand false otherwise bool halt(string progstring inputif (program halts(proginput)return trueelse return falsewe now will examine two simple functions that clearly can exist because the complete code for them is presented here