Instructions
This assignment must be done individually.
Please create and share your repository with the instructor and the TAs.
1. Programming with Lists
1.1. Take
Write an Oz function Take which takes two arguments, a list
.B Xs and a number N and evaluates to the first N elements of the list if N is a positive number less than the list length, to nil if N is either 0 or negative, and evaluates to the whole list if the list is
shorter than N
[10 points]
1.2. Last
Write an Oz function Last which takes two arguments, a list Xs and a number N and evaluates to the last N elements of the list if N is a positive number at most the list length, to nil if N is either 0 or neg ative, and evaluates to the whole list if N is longer than the list.
[10 points]
1.3. Merge
Write an Oz function Merge which takes two sorted lists of integers as arguments, and evaluates to a merged list in sorted order. The two lists need not be of equal length.
[10 points]
2. Higher-Order Programming
2.1. ZipWith
Write an Oz function ZipWith which takes 3 arguments - the first, a 2-argument function BinOp followed by two lists, Xs and Ys , and outputs the list whose ith position is got by evaluating BinOp on the ith elements in Xs and Ys.
[15points]
2.2. Map Using FoldR
Rewrite Map using FoldR
[15points]
2.3. FoldL
Write an Oz function FoldL which folds a binary operation from the left. For example,
{FoldL Sum [1 2 3] 0} should evaluate to
{Sum {Sum {Sum 0 1} 2} 3}.
[10 points]
3.
3.1.
Write a lazy Oz function to generate the Taylor series for sin(x). Write the function to produce a list of successive terms in the Taylor series.
[10 points]
3.2.
Write a function {Approximate S Epsilon} which takes a Taylor series S and evaluates it until the point where successive terms differ from each other by at most Epsilon. It should then return the sum of the terms taken until then. The series S may have infinitely many terms.
[10 points]
4. Suppose a square matrix
a a a
11 12 13 a a a
21 22 23 a a a
31 32 33
is represented in row-major manner as
[[a11 a12 a13]
[a21 a22 a23] [a31 a32 a33]].
Write an Oz function {IsDiagonal M} which takes a square matrix represented in row-major manner, and returns true if it is a diagonal matrix, and false otherwise. You can assume that M is always a square matrix, but it need not be a 3 × 3 matrix.
