Assignment No. 1 Solution

Note 1 This assignment is to be done individually




Note 2 You can discuss the assignment with others, but copying code is prohibited.




Due date: as indicated in Connex.




This assignment is worth 1% of your total course mark.




Submit electronically via Connex a single file with your solutions (hw1.sml)




Objectives




After completing this assignment, you will have experience:




Basic ML programming.




Your task, should you choose to accept it




You will write 12 ML functions (and tests for them) related to calendar dates. In all problems, a “date” is a




ML value of type:

type DATE = (int*int*int)




Download the file hw1.zip. It contains two files, hw1.sml and hw1-test.sml. The first one will contain your code. The second contains test-cases.

A “reasonable” date has a positive year, a month between 1 and 12, and a day no greater than 31 (or less depending on the month). Your solutions need to work correctly only for reasonable dates, but do not check for reasonable dates and many of your functions will naturally work correctly for some/all non-reasonable dates. A “day of year” is a number from 1 to 365 where, for example, 33 represents February 2. (We only consider leap years in one function).




Part 1: Your Code




Write a function is_older that takes two dates and evaluates to true or false. It evaluates to true if the first argument is a date that comes before the second argument. (If the two dates are the same, the result is false.)



Write a function number_in_month that takes a list of dates and a month (i.e., an int) and returns how many dates in the list are in the given month.



Write a function number_in_months that takes a list of dates and a list of months (i.e., an int list) and returns the number of dates in the list of dates that are in any of the months in the list of months. Assume the list of months has no number repeated. Hint: Use your answer to the previous problem.









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Write a function dates_in_month that takes a list of dates and a month (i.e., an int) and returns a list holding the dates from the argument list of dates that are in the month. The returned list should contain dates in the order they were originally given.



Write a function dates_in_months that takes a list of dates and a list of months (i.e., an int list) and returns a list holding the dates from the argument list of dates that are in any of the months in the list of months. Assume the list of months has no number repeated. Hint: Use your answer to the previous problem and ML’s list-append operator (@).



Write a function get_nth that takes a list of strings and an int n and returns the n-th element of the list where the head of the list is 1st . Raise the exception InvalidParameter if n is zero or larger than the length of the list.



Write a function date_to_string that takes a date and returns a string of the form January 20, 2013 (for example). Use the operator ˆ for concatenating strings and the library function Int.toString for converting an int to a string. For producing the month part, do not use a bunch of conditionals. Instead, use a list holding 12 strings and your answer to the previous prob-lem. For consistency, put a comma following the day and use capitalized English month names: January, February, March, April, May, June, July, August, September, October, November, December.



Write a function number_before_reaching_sum that takes an int called sum, which you can assume is positive, and an int list, which you can assume contains all positive numbers, and returns an int. You should return an int n such that the first n elements of the list add to less than sum, but the first n + 1 elements of the list add to sum or more. Assume the entire list sums to more than the passed in value; it is okay for an exception to occur if this is not the case.



Write a function what_month that takes a day of year (i.e., an int between 1 and 365) and returns what month that day is in (1 for January, 2 for February, etc.). Use a list holding 12 integers and your answer to the previous problem.



Write a function month_range that takes two days of the year day1 and day2 and returns an int



list [m1,m2,...,mn] where m1 is the month of day1, m2 is the month of day1+1, ..., and mn is the month of day day2. Note the result will have length day2 day1 + 1 or length 0 if day1 day2:




Write a function oldest that takes a list of dates and evaluates to a DATE option. It evaluates to NONE if the list has no dates and SOME d if the date d is the oldest date in the list.



Write a function reasonable_date that takes a date and determines if it describes a real date in the common era. A “real date” has a positive year (year 0 did not exist), a month between 1 and 12, and a day appropriate for the month. Solutions should properly handle leap years. Leap years are years that are either divisible by 400 or divisible by 4 but not divisible by 100. (Do not worry about days possibly lost in the conversion to the Gregorian calendar in the Late 1500s.)



The correct solution to the assignment should generate the following bindings:




type DATE = int * int * int

exception InvalidParameter

val is_older = fn : DATE * DATE - bool

val number_in_month = fn : DATE list * int - int




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val number_in_months = fn : DATE list * int list - int

val dates_in_month = fn : DATE list * int - DATE list

val dates_in_months = fn : DATE list * int list - DATE list

val get_nth = fn : string list * int - string

val date_to_string = fn : DATE - string

val number_before_reaching_sum = fn : int * int list - int

val what_month = fn : int - int

val month_range = fn : int * int - int list

val oldest = fn : DATE list - DATE option




val reasonable_date = fn : DATE - bool




Having these bindings does not guarantee that your solution will be correct.




Part 2: Your Tests




I have provided a file with test bindings hw1-test.sml. Make sure that everyone of the test bindings evaluates to true.




Hints




Implement one function at a time.



Remember that the REPL will keep all the bindings you define, and keep adding new ones every time you load the current file. I recommend you restart the REPL every time you change the datatype of a binding or its name.



Evaluation




Solutions should be:




Correct. We might use more tests than the ones provided. It will be run using SML/NJ.



In good style, including indentation and line breaks



Written using features discussed in class. In particular:



You must not use ML’s mutable references. You must not use arrays.




Also do not use pattern-matching; it is the focus of the next assignment.








































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