CS403: Programming Languages

Assignment 2

Printable Version

Preliminary information

This is your second Scam assignment. At the top of your assignment, place a definition similar to the following:
    (define (author)
        (println "AUTHOR: Rita Recursion rrita@crimson.ua.edu")
with the name and email replaced by your own name and email.

For each numbered task (unless otherwise directed), you are to provide a function with a name of the form runN, with the N corresponding to the task number (as in run1, run2, etc.). This function is in addition to all other requested functions. These run functions will test your implementation and are to take no arguments. For example, if task 5 is:
5. Implement factorial so that it implements a recursive process. Name your function fact.
you should provide a run function similar to:
    (define (run5)
        (exprTest (fact 0) 1)
        (exprTest (fact 3) 6)
Woe betide students who provide insufficient testing should their implementations prove to be incorrect! If you do not complete an exercise, do not provide a run function for that exercise. If you omit the run function corresponding to an exercise, it will be assumed that you are skipping that part and you will receive no credit for that exercise.

When you have completed testing of your run functions, comment out any calls to them (but do not comment out the definitions).

I will provide a test script which performs minimal testing of your implementation. If your program does not pass the provided test script without failing, I will not grade your exercise and you will receive zero credit for the assignment.

There is a test script which performs minimal testing of your implementation. If your program does not pass the provided test script without failing, I will not grade your exercise and you will receive zero credit for the assignment. If your program passes the provided test script, it will be graded with a more thorough set of tests. You can get the test script with the command:
    wget beastie.cs.ua.edu/proglan/test2.scm

You may not use assignment (e.g. assign or set!) in any of the code you write, unless otherwise instructed. Nor may you use any looping function such as while or for.

You will also be graded on style, including, but not limited to, the proper nesting of helper functions that are not expected to be called directly.


  1. You are to define an iterator loop that binds each item in a list, in turn, to a variable. With a binding accomplished, the loop executes its body. Here is an example:
        (iterate i (list 1 2 3 4)
            (inspect i)
            (inspect (* i i))
    which should produce the output:
        i is 1
        (* i i) is 1
        i is 2
        (* i i) is 4
    You will need to grab the calling environment and delay the evaluation of the arguments. Construct an appropriate lambda-like list and then evaluate the lambda-like list in the calling environment. Use the resulting closure to process each item in the second argument.

    See the TSRM chapter on parameter passing.
  1. Partial function evaluation is the process of breaking up the arguments to a function into two groups. When the first group of arguments and the function itself is passed to a partial-evaluator, a function that accepts the remaining arguments is returned. Define a variadic function, named peval, that partially evaluates a given function and some of the supplied arguments. The missing arguments are marked by the symbol MISSING. As an example, the last six expressions in the following list should evaluate to the same result:
        (define . 'MISSING)
        (define (f x y z) (+ x y z))
        (f a b c)
        ((peval f . . .) a b c)
        ((peval f . b .) a c)
        ((peval f . . c) a b)
        ((peval f a . c) b)
        ((peval f a b c))
  1. Define the following classes and methods:
    • Stack: constructor Stack; methods push, pop, speek, ssize
    • Queue: constructor Queue: methods enqueue, dequeue, qpeek, qsize
    Note: any method that would normally modify the state of the data structure has to return a new data structure, instead. All methods must work in amortized constant time. You may assume that every call to a peek method is followed by a pop or a dequeue, as the case may be.

    Here is a routine which uses such classes:
        (define (loop stack queue)
            (define x (readInt))
            (if (eof?)
                (list stack queue)
                (loop (push stack x) (enqueue queue x))
        (define (popper s)
                ((!= (ssize s) 0)
                    (inspect (speek s))
                    (popper (pop s))
        (define (dequeuer q)
                ((!= (qsize q) 0)
                    (inspect (qpeek q))
                    (dequeuer (dequeue q))
    Here is a call:
        (define oldstream (setPort (open "data.ints" 'read)))
        (define data (loop (Stack) (Queue)))
        (popper (car data))
        (dequeuer (cadr data))
        (setPort oldStream)
  1. Define a function named no-locals which takes a source code list representing a legal Scam function definition and returns a source code list representing an equivalent definition with local defines replaced by a lambda. For example,
                (define (nsq a)
                    (define x (+ a 1))
                    (* x x)
    should evaluate to the list:
        (define (nsq a)
            ((lambda (x) (* x x))
                (+ a 1)
    You may assume that any and all local defines are at the beginning of the function body. Note: Scam's local defines may refer to previous local definitions and are processed sequentially. You may also assume that all local defines are of the form:
        (define varname expr)
    You do not need to recursively remove local defines, just those at the top level of the function body.
  1. Implement the function pred, suitable for taking the predecessor of the style of Church numerals found in the textbook. The function should take a Church numeral as its sole argument and return the appropriate Church numeral as its result.

    You will likely need to peruse the web for this task.
  1. Define a function, named treedepth, which computes that average depth of the leaves of a binary tree. The depth of any particular leaf in a tree is the number of nodes on the path from the root of the tree to the leaf, exclusive of the root.

    Assume a binary tree is represented as a triple:
    • the root value
    • the left subtree
    • the right subtree
    with the following constructor:
        (define (treeNode value left right)
            (list value left right)
    Given a non-empty binary tree as its sole argument, treedepth should return a real number representing the average depth. The only helper function you can use is the treeflatten function, which you must define. That function produces a list of leaf depth - leaf value pairs. You are to determine the final average using treeflatten, map, and accumulate, exclusively, with no other user-defined functions.
  1. Exercise 2.42 in the text. Unlike the textbook version, the return value of the queens function should be a list of row-column lists with the row numbers in decreasing order. For example, here is an example return value for a board size of eight:
        (((7 4) (6 7) (5 3) (4 4) (3 6) (2 1) (1 5) (0 0)) ...)
    Note that the row numbers and column numbers start with 0 (unlike the textbook version). Note also that the first solution in the above return value is incorrect.

    If there is no solution, queens should return the empty list.
  1. Define a function, named cxr, which when given a symbol composed of 'as and 'ds, generates a list function that extracts the appropriate element(s). An 'a implies taking the car while a 'd implies taking the cdr. Actions should be performed from right to left. For example:
        (cxr 'd)
    should return a function equivalent to cdr. Also,
        (cxr 'da)
    should return a function equivalent to (lambda (x) (cdr (car x))).
        (cxr 'ad) 
    should return a function equivalent to (lambda (x) (car (cdr x))). Here's one last example:
        ((cxr 'add) '(1 2 3 4 5 6))
    should return 3.

    To convert a symbol to a string, one uses the string function. Like lists, one can take the head and tail of a string:
        (car (string 'add))
        (cdr (string 'add))
    The two expressions above evaluate to "a" and "dd".

    To compare two strings, one should use the equal? function, which tests for structural equality, not the eq? function, which tests for pointer equality. Finally, the empty string "" is equivalent to nil.
  1. In this exercise, you will overload the + operator to call a supersized addition function. You will accomplish this task (and others) using a data-directed approach. In particular, you will implement the following logic for adding, subtracting, multiplying and dividing strings and integers.
        (+ "x" "y")   ->  "xy"
        (+ "123" 4)   ->  "1234"
        (+ 123 "4")   ->  127
        (- 123 "4")   ->  119
        (- "abc" 1)   ->  "bc"
        (* "abc" 3)   ->  "abcabcabc"
        (* 3 "33")    ->  99
        (/ 8 "2")     ->  4
    Note, you can convert anything to a string with the string function and anything to an integer with the int function.

    Next, you will need to include the table.scm file, which you can get with this command:
        wget beastie.cs.ua.edu/proglan/table.scm
    This file contains definitions for getTable and putTable (analogous to the SICP's get and put). You can get the type of an entity with the type function:
        (type 3)  ->  INTEGER
    Then, you will save old versions of the operators and define a function named install-generic for redefining operators to use the apply-generic function (from the text). and for installing the appropriate mathematical functions into the table:
        (define old+ +)
        (define old- -)
        (define old* *)
        (define old/ /)
        (define (install-generic)
            (set! + (lambda (a b) (apply-generic '+ a b)))
            (set! - (lambda (a b) (apply-generic '- a b)))
            (set! * (lambda (a b) (apply-generic '* a b)))
            (set! / (lambda (a b) (apply-generic '/ a b)))
            (putTable '+ '(STRING STRING) addStrings)
            (putTable '* '(STRING INTEGER) mulStringInteger)
            ;other functions installed here
    You will also define a method for uninstalling your changes:
        (define (uninstall-generic)
            (set! + old+)
            (set! - old-)
            (set! * old*)
            (set! / old/)
    Your version of apply-generic should take exactly three arguments (operator and two operands) and should call the old version of the operator if get fails to find a function. Do this by installing the old version of the operator into the table with some special type symbols and have apply-generic retrieve it. NOTE: your version of apply-generic should not throw any errors.

    Also, do not use assignment anywhere except as shown in install-generic and uninstall-generic.
  1. Implement the function coerce using a data-directed approach. It should be able to perform the following coercions:
    • integer to real
    • integer to string
    • real to integer
    • real to string
    • string to integer
    • string to real
    • list to string
    Lists will be restricted to lists of integers, reals, strings (recursively).

    Use table.scm (see Task 9) to install your coercion functions. Your coerce function should grab the type of its first argument and retrieve the correct coercion function from the table. It should then return the result of applying the recursion function. Name your function for installing coercion functions in the table install-coercion.

        scam> (coerce "123.4" 'INTEGER)
        scam> (coerce '(1 (2.2) ((3 4) "5")) 'STRING)
        (1 (2.2) ((3 4) "5"))
        scam> (type (coerce '(1 (2.2) ((3 4) "5")) 'STRING))

Assignment submission

Submitting the assignment The entire assignment should be contained in a single file named assign2.scm. Any explanatory text should be in the form of Scam comments, which begin with a semicolon. The file should load into the Scam interpreter cleanly. The last line of your file should be:
    (println "assignment 2 loaded!")
If you do not see the message "assignment 2 loaded" when executing your file with the Scam interpreter, then there is an error somewhere that needs to be fixed. If your file does not load properly (i.e. I do not see the message), you will receive no credit for your work. To submit your assignment, delete extraneous files from your working directory. Then, while in your working directory, type the command:
    submit proglan lusth assign2
The submit program will bundle up all the files in your current directory and ship them to me. Thus it is very important that only the files related to the assignment are in your directory (you may submit test cases and test scripts). This includes subdirectories as well since all the files in any subdirectories will also be shipped to me, so be careful. You may submit as many times as you want before the deadline; new submissions replace old submissions.