Eat (we provide) link. Eater. Goal: Eater(Self) == Self()

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1 15-251: Great Theoretical Ideas Guru: Yinmeng Zhang Assignment 12 Due: December 6, Reading Comprehension (0 points) Read the accompanying handout containing Ken Thompson s Turing Award Lecture, Reflections on Trusting Trust (also available online at In addition to being a very interesting talk by a very famous person, it discusses a number of ideas that you may find helpful for this assignment. 2 Making Auto-Cannibals (80 points) Self reference is a very important recurring theme in a number of different branches of mathematics and computer science. One of the more interesting applications of this idea in CS is in the form of programs that write programs. In the Ken Thompson paper, we saw two interesting examples of such programs: a program that printed itself out, and a scheme for a compiler with some rather interesting behavior. For this assignment, you are going to write another such program: but to make things a little more interesting, this will also be a program that reads programs. In fact, it will be a program that reads in programs that read in programs, and then spits out a new program! Suppose there is some function called Eat, which takes a string and outputs something to the screen. Your job is to automatically generate a program Self Eat, which prints Eat(Self Eat ). In other words, Self Eat prints out exactly what Eat would have printed if you had passed it Self Eat as input. This would not be very difficult if you knew what Eat was ahead of time, but you don t. So instead of writing Self Eat, you are going to write a program that automatically generates Self Eat, given the text of any function Eat. This program will be called AutoCannibalMaker, because it generates a self-eating program. The following figure illustrates the assignment. Eat (we provide) Main (we provide) link Eater link input AutoCannibalMaker (you provide) Self output Goal: Eater(Self) == Self() We will guarantee that the Eat that we give you will have the very important property that it is a total function of its inputs. That is, for any given input, Eat always produces the same output 1

2 - no matter how many times it is run. Eat for example, could just print exactly what it is given, or it could sum the characters and print the total, or anything like that. It is not allowed to do things like flip coins to decide what to print out, nor is it allowed to remember what it did the last time and do something different. Writing and submitting your program: You can choose to write this assignment in Java or C++. Start by copying all of the files from the appropriate directory below into the directory where you re going to work: /afs/andrew.cmu.edu/scs/cs/15251/student/assignment12/c++ /afs/andrew.cmu.edu/scs/cs/15251/student/assignment12/java You should modify the program called ACM.cpp or ACM.java to turn it into the AutoCannibal- Maker. The file provided reads the text of an Eat function from standard in, and passes this text to a function ACM. When you re finished, ACM should print the source code to a program Self Eat that prints the result of Eat(Self Eat ). Assume that the main function provided will work just fine for any Eat function that we give you. The length of Eat will never be more than 5000 characters. Do not worry about error checking - assume you are passed a valid function. We have provided at least one sample Eat function for you. Java If you are doing this assignment in Java, Eat will be a class containing a method called Eat. There is at most one such Eat method, which is static, takes a String as its argument, and prints some result to standard out: class Eat public static void Eat(String input) } }; Note that the compiled version of this class will be deleted before your program Self Eat is run. This means that you are not allowed to call out to Eat.Eat() in your program; you must include the text of Eat somehow. C++ If you are using C++, Eat will be a function that takes a pointer to a null-terminated character array as input and prints some result to standard out. void Eat(char *input) } 2

3 Compiling & Testing Use the Makefile that we provide. Just type make to test the entire sequence compiling Eater, compiling AutoCannibalMaker, running AutoCannibalMaker with Eat as input to generate Self Eat, then finally running Self Eat and comparing its output to Eater(Self Eat ). Do not modify the Makefile. If you type make and everything works correctly, you are finished. Restrictions You may not do any disk or network I/O of any kind on this assignment, nor may you use things like the system system call. If you use C++, you should only use functions in stdio.h, iostream.h, and string.h. If you use Java, you should only use methods of System.out or String. Note that your program must work on Andrew, which does not have the newest version of Java. Handin The only thing you should turn in is ACM.java or ACM.cpp. You should not turn in the Makefile, Self, Eat, or Eater. We will supply an Eat function (that you can t see) and use a copy of the same Makefile that we gave you. Put ACM.java or ACM.cpp in your handin directory 1 and run the check script 2 to verify that it really works. Tips Which language? You have your choice of C/C++ or Java. We have found this assignment to be slightly easier in C than in Java because Java requires that you wrap everything inside of a class, but C lets you use functions and global variables. The main idea is exactly the same, but Java requires you to worry about a couple of extra details. If you use Java, one trick you might want to use is to make all methods and class variables static, because then you never need to create any objects. This is a hacking assignment, not a well-structured programming assignment, so don t worry about how ugly your code looks. All that matters is that it works. More self-printing programs: For more examples of self-printing programs, check out These should give you many clues on how to do this assignment. Long C/C++ string constants: If you have a very long string constant in C/C++, you can put it on separate lines by closing the quotes on one line and opening on the next. The pieces are automatically concatenated by the compiler: str = "This is a very long C/C++ string " "constant. It spans multiple " "lines in the program, but when " "the program is run, this " "will just be one long string " "with one newline at the end.\n"; 1 A handin directory has been created for you at /afs/andrew/scs/cs/15251/student/assignment12/handin/andrewid/ 2 The check script is at /afs/andrew/scs/cs/15251/bin/check 3

4 Long Java string constants: If you have a very long string constant in Java, you can make it out of smaller strings concatenated with a plus sign. Note that in Java you can concatenate ints and chars with string very easily: str = "This is a very long Java string "+ "constant. It spans multiple "+ "lines in the program, but when "+ "the program is run, this "+ "will just be one long string "+ "with "+ 1 + " newline at the end.\n"; String escapes: A string constant in C++ or in Java is just a bunch of characters surrounded by quotation marks. But what if you need to include quotation marks in the string itself? The secret is that you need to precede the quote with a backslash - this is sometimes called an escape sequence (here, backslash is playing the role of escape). There are some other characters that you cannot put into a string directly, and here is how you escape them (identical in C/C++ and Java): Character Escape Sequence " \" newline \n tab \t \ (backslash) \\ Testing: The output of Self Eat must be byte-for-byte identical to the output of Eat, whitespace and all. Make sure that you don t have tabs in one and spaces in the other. The sdiff program is sometimes more useful than plain old diff for comparing your program and your output. We will be using the program cmp. Tabs and ASCII: The program od is useful for finding out the numbers corresponding to characters. It may also help you find where you have tabs in one place and spaces in another. If you use emacs as your editor, there is an untabify command you might find useful, that changes all tabs into spaces. Just type Esc-x and then type untabify. Grading: We will use the cmp program to see if your output is byte-for-byte identical to the output of Eat and grade accordingly, exactly as your Makefile does. As always, you can run check to see if your program is correct, but in this assignment, you will not find check to be very useful for debugging instead you should use the Makefile we provide. You will get partial credit if your program works on the test case(s). For the final grading, the only difference is that we will use a different Eat than the ones we give you, but if you do your program correctly this will not make a difference. 3 And Now For Something Completely Different (10 points) Let Q be a program that lists all halting programs (all programs that halt when given no input). Here is a flawed proof that Q does not exist: 4

5 Suppose for contradiction that Q exists, and its output is the list L. The ith entry of the list, L(i), is the pair (P i, O i ), where P i is the ith halting program and O i is its output. Of course, O i can be the empty output. We can now write a program P that runs Q, and when it sees itself in the list outputs something different from the corresponding O. Thus we have arrived at a contradiction, and so Q cannot exist. Explain the flaw in the above proof. 4 Pretty Pink Software (10 points) The Pretty Pink Software Corporation is having problems with its flagship product, PrettyPinkSoft, version 1.0 (PPS1), because some of the programs in PPS1 can fail to halt on certain inputs. For version 2.0 (PPS2), management has demanded backward compatibility, giving its engineers the following impressive-sounding decree: For any pair of programs (p, q) where p is a program in PPS1 and q is the corresponding program in PPS2, if p(x) halts on input x then q(x) must also halt on the same input x. Show that the Pretty Pink Software management is well-intentioned but misguided: It is undecideable to determine whether an arbitrary pair of programs (p, q) satisfies H(p) H(q), where H(f) is the set of inputs on which program f halts. 5