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

//
// Assignment Four (Due: Wednesday, June 16, 2010)
//
// Total points: 110 points
//
// Assgn4Ex1: 20 points
// Assgn4Ex2: 30 points
// Assgn4Ex3: 30 points
// Assgn4Ex4: 30 points
//
(* ****** ****** *)
//
//
// Assgn4Ex1: 20 points
//
//
(*
//
// The following function is so-called MacCarthy's 91-function:
//
// f91(x) = f91 (f91 (x+11)) if x <= 100;
// f91(x) = x - 10 if x > 100.
//
// Please give (1) an implementation of [f91] in direct-style and
// (2) another one in continyuation-pass style.
// 
// Note that 5 points are given for part (1) and 15 points for part (2)
*)

(* ****** ****** *)
//
//
// Assgn4Ex2: 30 points
//
//
datatype ltree (a:t@ype) =
  | ltree_nil (a) of ()
  | ltree_cons (a) of (a, ref int(*size*), ref (ltree a), ref (ltree a))
// end of [ltree]

// Please implement in-place left (BST) rotation
fun{a:t@ype} ltree_rotate_l (t: ltree a): ltree a

// Please implement in-place right (BST) rotation
fun{a:t@ype} ltree_rotate_r (t: ltree a): ltree a

// Please implement a function that changes the root of a given BST to
// a randomly choosen node inside the tree while maintaining the BST status
// of the tree
fun{a:t@ype} ltree_random_root (t: ltree a): ltree a

(* ****** ****** *)
//
// Assgn4Ex3: 30 points
// Implement a procedure that takes two matrices and returns their
// product. Note that two matrices can be multiplied only if they are of
// dimensions $p\times q$ and $q \times r$ for some natural numbers $p,q,r$.
//
typedef matrx = list0 (list0 double)
fun mul_matrx_matrx (A: matrx, B: matrx): matrx

(* ****** ****** *)
//
// Assgn4Ex4: 30 points
// Please implement a program in cairo for drawing the picture titled
// "The wave of an earthquake" on the following page:
// http://www.ritsumei.ac.jp/~akitaoka/wave-e.html
//
(* ****** ****** *)

(* end of [assignment4.sats] *)