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Homework 6 Solution
This assignment has 4 questions. I want the complete code for questions 1 and 2 in one file called a6.sml. It is not acceptable to submit just the sections that you wrote. You must include all the outline code that I supplied. We want to be able to run the programs. I will post the outline on the web page. Question 3 should be in a file called a6q3.txt(or .pdf) and Question 4 should be in a file called a6q4.txt(or .pdf). Please do not submit zip files or files in Word format or rich text format. Any such assignments will be given zero. Question 1. [20 points] Write an Sml function that takes two integers in succession and returns the stream that gives the infinite decimal expansion of the number. Of course, often the decimal expansion terminates after a finite number of steps. In that case, I want the stream to end with an infinite sequence of zeros. Here is the type and two examples.
val infiniteDecimal = fn : int - int - int str
- val oneHalf = infiniteDecimal 1 2; val oneHalf = Str {hd=0,tl=Susp fn} : int str - take 5 oneHalf; val it = [0,5,0,0,0] : int list - take 10 threeSeventh; val it = [0,4,2,8,5,7,1,4,2,8] : int list
Question 2. [30 points] Write an Sml version of the sieve of Erasthosthenes. You will need filter and some other utilities. I will put the code you need on the web site. Please submit your code together with the code I provide so that we can run your program. If you just submit the code you wrote I will give you zero.
val primes = Str {hd=2,tl=Susp fn} : int str
printIntStr primes 25; 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
1
Question 3. [25 points] What is the result of evaluating the following expression? Explain your answer drawing the relevant environment diagrams. This expression just returns a unit type, however, I want to know what is printed on the screen. I am not interested in extraneous things like val it = () : unit. I am interested in what the three print statements produce.
let val x = ref 1 in let val y = x in let fun f u = ((u := (!u) + 1); (!u + !x)) in (print("x is "^Int.toString(!x)^"; ")); (print("f(y) is "^Int.toString(f(y))^"; ")); (print("x is "^Int.toString(!x)^". ")) end end end
Question 4. [25 points] Informally derive the most general type for the following function. I will give you zero if you instantiate everything to, for example, int, or some other monomorphic type.
fun tricomp f g h = fn x = (f (g (h x)))
val infiniteDecimal = fn : int - int - int str
- val oneHalf = infiniteDecimal 1 2; val oneHalf = Str {hd=0,tl=Susp fn} : int str - take 5 oneHalf; val it = [0,5,0,0,0] : int list - take 10 threeSeventh; val it = [0,4,2,8,5,7,1,4,2,8] : int list
Question 2. [30 points] Write an Sml version of the sieve of Erasthosthenes. You will need filter and some other utilities. I will put the code you need on the web site. Please submit your code together with the code I provide so that we can run your program. If you just submit the code you wrote I will give you zero.
val primes = Str {hd=2,tl=Susp fn} : int str
printIntStr primes 25; 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
1
Question 3. [25 points] What is the result of evaluating the following expression? Explain your answer drawing the relevant environment diagrams. This expression just returns a unit type, however, I want to know what is printed on the screen. I am not interested in extraneous things like val it = () : unit. I am interested in what the three print statements produce.
let val x = ref 1 in let val y = x in let fun f u = ((u := (!u) + 1); (!u + !x)) in (print("x is "^Int.toString(!x)^"; ")); (print("f(y) is "^Int.toString(f(y))^"; ")); (print("x is "^Int.toString(!x)^". ")) end end end
Question 4. [25 points] Informally derive the most general type for the following function. I will give you zero if you instantiate everything to, for example, int, or some other monomorphic type.
fun tricomp f g h = fn x = (f (g (h x)))
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