CNS 4450 Analysis of Programming Languages Homework Assignments Fall 2011

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1 CNS 4450 Analysis of Programming Languages Homework Assignments Fall 2011 Chapter 4 2 (all), 9; plus the additional problem below. Chapter 5 3, 4, 5, 7, 9, 10, 11, 14, 15 (See #13 for a hint for #14); you should only need 3 comparisons on #4; do #14 a little differently: only check divisors up to the square root of the number (you can do this without Math.sqrt!). Turn in both code and execution results that verify the answers. Chapter 6 1, 2, 4 (note: part g should read X := X + Y ); plus additional problem below. For #2, you are given a set in each part of the problem. Write the corresponding ML type for that set. Chapter 7 3, 4, 5, 7 (Note: for #5, do not use Math.pow or write your own power function; 7 requires doing 6, which can be found in Chapter 12; do not use features we haven t covered yet, like List.partition and let rec) Chapter 8 1, 3, 5 (all; turn in 2 versions for 5: one before verifying the answers, one after) Chapter 9 3, 5, 9-11, 18-19, 22 (Note instructions in book for 1-25!). Also, additional problem below. Chapter 10 3, 4, additional problem below Chapter 11 3, 4, 5, 9, 10; plus additional problem and program (due separately) below Chapter 12 1, 2, 3, 7, 8, plus additional problem below Chapter 16 3, plus additional problem below. You might find it useful to use a table for #3. Chapter 18 3, 6 D Homework TBD Additional Problem for Chapter 4 A. Indicate the binding times for each of the following for a typical language: a. The built-in functions provided in the standard library b. The variable declaration corresponding to a particular use of the variable c. The maximum length allowed for a string literal d. The address of a particular library function

2 Additional Problem for Chapter 6 Write a C++ program that reads a 64-bit machine instruction and extracts the values for its components from certain bits, specified as follows: Bits 0-4 Bits 5-8 Bits 9-12 Bits Bits Bits Bits code (the instruction code) ladrm (left address mode) radrm (right address mode) si (short immediate) lreg (left register) rreg (right register) li (long immediate) You will be given a string of 16 hexadecimal digits, such as D2, which represents the numeric value of the 64 bits to be analyzed. The output for this input string should be: Instruction: D2 ladrm = 1 code = 1 li = 1234 To get full credit for this program, you ll need to use a union and a bit-field structure. Any C book and most C++ books talk about these language features. Use no bitwise operators. If you re using an Intel machine, remember that it is a little-endian machine, which means you ll have to reverse the order of the bit layout to extract the correct values. Use the following input to test your program: D2 E E E The output should be: Instruction: D2 ladrm = 1 code = 1 li = 1234 Instruction: E E radrm = 10 code = 28 li = 142

3 Instruction: rreg = 3 si = 4 radrm = 8 ladrm = 2 code = 2 li = 0 Instruction: rreg = 3 radrm = 1 code = 10 li = 0 Instruction: E code = 29 li = 32 Hint for Chapter 7, Problem 5 Any polynomial can be rewritten by factoring x out of each term as follows: 3 3x 7x 2 + 5x 3 = 3 + x(5 + x( 7 + x(3+ x 0))) Problem for Chapter 9 Write a curried function, compose, that takes two arguments: a list of like-typed, unary functions, and an argument for those functions. It computes the composition of those functions. For example, the call compose [f, g, h] x computes f(g(h(x))). The following example of partial function application should also work: - val c = compose [~, fn (x) => x + 1]; val c = fn : int -> int - c 4; val it = ~5 : int compose should be able to compose any number of functions. Problem for Chapter 10

4 Name two examples from C++ where a variable is live (in use) but not in scope. Extra Problem for Chapter 11 Following the example of intsfrom in streamtest.sml, write a function, fib ( ), which creates a stream of all the Fibonacci numbers. Fibonacci numbers are defined as follows: f 0 = 0 f 1 = 1 f n = f n-1 + f n-2, where n > 1 You will need to save state inside of fib somewhere (hint: use a local function defined inside if fib that computes the next Cons). You should be able to obtain the following output: - val f = fib ( ); val f = Cons (0,fn) : int stream - printstrm 10 f; val it = () : unit Program for Chapter 11 Write functions for processing a semimap a combination of a map and a set. A semimap is a polymorphic list of two possible items: (key,value) pairs or singleton keys. Keys must be unique. The following functions are required: paircount returns the number of pairs in the semimap singcount returns the number of singleton entries in the semimap haskey returns whether a key exists in a semimap getitem returns the pair or singleton containing a given key as an option, to allow for NONE getvalue returns the value for a key as an option if it is in a pair, or NONE getkeys returns all the keys in the semimap as a list getvalues returns all the values from the pairs in the semimap as a list

5 insertitem returns a new semimap with a new pair or singleton inserted, unless the key is already in use (in which case return the list unchanged; order is not important) removeitem returns a new semimap with the pair or singleton with a given key removed, if it was there All functions with more than one parameter should be curried. Here is a sample execution: (* ML Statements *) val stuff = [(P (1,"one")), S 2]; paircount stuff; singcount stuff; getitem stuff 1; getitem stuff 10; getvalue stuff 1; getvalue stuff 10; getkeys stuff; getvalues stuff; removeitem stuff 1; insertitem stuff (P (3,"three")); stuff; (* Output *) val stuff = [P (1,"one"),S 2] : (int,string) semipair list val it = 1 : int val it = 1 : int val it = SOME (P (1,"one")) : (int,string) semipair option val it = NONE : (int,string) semipair option val it = SOME "one" : string option val it = NONE : string option val it = [2,1] : int list val it = ["one"] : string list val it = [S 2] : (int,string) semipair list val it = [P (3,"three"),P (1,"one"),S 2] : (int,string) semipair list val it = [P (1,"one"),S 2] : (int,string) semipair list Problem for Chapter 12 As mentioned in class and in the book, languages that do not support recursion, like classical Fortran, can statically allocate activation records instead of placing them on the stack. Even for such languages, why might it be advantageous to allocate activation records on the stack in such languages? Problem for Chapter 16 Consider the example class hierarchies (the A, V, and Y hierarchies) on the last slide for Chapter 16. Rework the problem, using the method of creating an ordered list of most derived functions, with the following change: the order of the parameters in the function f is reversed (i.e., the Y argument comes first, then the V argument, then the A argument). Then rewrite multimeth.cpp to correctly handle the new version of f (you may use C# or Java instead, if you like). Turn in the work you did in developing the ordered list as well as working code and the associated printed output.