(*
** Course: Concepts of Programming Languages (BU CAS CS 320)
** Semester: Summer I, 2010
** Instructor: Hongwei Xi (hwxi AT cs DOT bu DOT edu)
*)

//
// Assignment Two (Due: Wednday, June 2, 2010)
//
// Total points: 100 + 30(extra)
//

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(*

Exercise 1: 10 points

Please implement a function for testing whether a string is a palindrome,
that is, whether it equals its mirror image.

*)

fun palindrome_test (s: string): bool

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(*

Exercise 2: 15 points

Please implement a function for testing whether one string is a permuation
of another. An implementation of qudratic time-complexity is acceptable.

*)

fun string_perm_test (s1: string, s2: string): bool

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(*

Exercise 3: 15 points

The simple rule for translating into "Pig Latin" is to take a word that
begins with a vowel and add "yay", while taking any word that begins with
one or more consonants and transferring them to the back before appending
"ay". For example, "able" becomes "ableyay" and "stripe" becomes
"ipestray". Write a function that converts a string of letters into its Pig
Latin translation.

*)

fun piglatin_trans (word: string): string

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(*

Exercise 4: 20 points

Given a natural number n >= 3, please draw a circle and (1) choose n
distint points on the circle randomly and (2) connect these points to form a
polygon and fill it with whatever color you like.

*)

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(*

Exercise 5: 40 points

The following declaration introduces a datatype mylist(a) for representing
lists whose elements are of type a:

datatype mylist (a:t@ype) =
  | Nil (a)
  | Cons (a) of (a, mylist a)
  | Append (a) of (mylist a, mylist a)
  | Reverse (a) of mylist a
// end  of[mylist]

The list append and reverse functions can be implemented as follows:

fun append {a:t@ype} (xs: mylist a, ys: mylist a) = Append (xs, ys)
fun reverse {a:t@ype} (xs: mylist a) = Reverse xs

In other words, both [append] and [reverse] are O(1)-time functions, that
is, they take constant time to finish.  Please implement the following
functions:

fun{a:t@ype} mylist_length (xs: mylist): int
fun{a:t@ype} mylist_is_empty (xs: mylist a): bool
fun{a:t@ype} mylist_nth (xs: mylist a, n: int): a
fun{a:t@ype} mylist_to_list0 (xs: mylist a): list0 a

Note that nth(xs, i) returns the i_th element in the list represented by xs
for 0 <= i < n, where n is the length of xs.  The meaning of all other
functions should be obvious.  \end{exercise}

*)

datatype mylist (a:t@ype) =
  | Nil (a) of ()
  | Cons (a) of (a, mylist a)
  | Append (a) of (mylist a, mylist a)
  | Reverse (a) of mylist a
// end of [mylist]

fun{a:t@ype} mylist_length (xs: mylist a): int
fun{a:t@ype} mylist_is_empty (xs: mylist a): bool
fun{a:t@ype} mylist_nth (xs: mylist a, n: int): a
fun{a:t@ype} mylist_to_list0 (xs: mylist a): list0 a

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(*

Exercise 6 (extra): 30 points
Please use cairo and gtk to give an illustration of Pascal's theorem.
See the file [assgn2ex6.dats] for more details.

*)

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(* end of [assignment2.sats] *)