(*
** Course: Concepts of Programming Languages (BU CAS CS 320)
** Semester: Summer I, 2009
** Instructor: Hongwei Xi (hwxi AT cs DOT bu DOT edu)
*)

//
// Assignment Four (Due: Tuesday, June 16, 2009)
//
// Total points: 130 points
//
// Assgn4Ex1: 10 points
// Assgn4Ex2: 10 points
// Assgn4Ex3: 30 points
// Assgn4Ex4: 30 points
// Assgn4Ex5: 20 points
// Assgn4Ex6: 30 points
//

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(*

// Assgn4Ex1: 10 points
// The following is a well-known series:
// 
// ln 2 = 1 - 1/2 + 1/3 - 1/4 + ...
//
// Please implement a stream consisting of all the partial sums of this
// series. Then compute an accurate approximation to ln2 by using Euler's
// transform.

*)

val theAssgn4Ex1Stream : stream double 
val ln2 : double

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(*

// Assgn4Ex2: 10 points
// For each $i\geq 1$, we use $P_i$ for the $i^{\it th}$ prime number.  For
// instance, $P_1$ is $2$, $P_2$ is $3$ and $P_3$ is $5$.  Please implement a
// stream consisting of all the sums of the form
// $\Sigma_{i=1}^{n}\frac{1}{P_i}$ for $n\geq 1$.

*)

val theAssgn4Ex2Stream : stream double 

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(*

// 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

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(*

// Assgn4Ex4: 30 points
// A natural number $n$ is a Ramanujan number if there exist two distinct
// pairs of natural numbers $(i_1,j_1)$ and $(i_2,j_2)$ such that
// $n=i_1^3+j_1^3=i_2^3+j_2^3$. For instance, $1729$ is a Ramanujan number as
// $1729=1^3+12^3=9^3+10^3$.  Please construct a stream of {\em all} Ramanujan
// numbers and then use it to find the first twenty Ramanujan numbers.

*)

val theRamanujanStream: stream int
val theFirstTwentyRamanujanNumbers : list0 int 

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(*

// Assgn4Ex5: 20 points
// Please write a function that extracts out the (first) longest line in a given file.
// The implementation should be stream-based.

*)

fun longest_line_get (inp: FILEref): string

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//
// Assgn4Ex6: 30 points
//

datatype ltree (a:t@ype) =
  | ltree_nil (a) of ()
(*
  // it was incorrectly declared as follows:
  | ltree_cons (a) of (a, int(*size*), ref (ltree a), ref (ltree a))
*)
  | 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 tree to
// a randomly choosen node inside the tree:
fun{a:t@ype} ltree_random_root (t: ltree a): ltree a

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(* end of [assignment4.sats] *)