# Homework 4

Due on Monday, 19 November at 10:15am sharp (right before the class).

NOTE: It is your responsibility to ask us if any part of the problem formulation is unclear.

## Problem 1

Determine for the following program its output with static and dynamic scoping. Explain the difference, if there is any.

object MyClass {
val x = 5
def foo(z: Int): Int = {
x + z
}
def bar(y: Int): Int = {
val x = 1
val z = 2
foo(y)
}
def main() {
val x = 7
println(foo(bar(3)))
}
}

## Problem 2

Consider the following grammar:

E ::= E+E
E ::= E*E
E ::= E=E
E ::= Num | true | false

where Num represents integers.

a) Consider the generalized CYK algorithm from

Run the algorithm on input:

1=2*3=true

checking whether it can be parsed. Show the content of the 'chart', that is, the set of triples , after the algorithm finishes.

b) How many parse trees can you extract from this chart?

c) Write down those parse trees that are correct according to the following types:

+ : Int x Int→Int

* : Int x Int→Int

= : Bool x Bool → Bool

= : Int x Int → Bool

d) Can you modify the CKY algorithm following the ideas from:

to introduce a semantic function that computes only those trees that are correct according to the above types of operators?

e) What does the new algorithm return on the above input?

## Problem 3

Consider the following class:

class Rectangle {
var width: Int
var height: Int
var xPos: Int
var yPos: Int

def area: Int = {
if(width > 0 && height > 0)
width * height
else
0
}
def resize(maxSize: Int) {
while(area > maxSize) {
width = width / 2
height = height / 2
}
}
}

a) Determine the environment of this class.

b) By giving the type derivation trees for each method show that this class type checks.

## Problem 4

Determine if the following piece of codes type check according to the type rules.

Show all steps and give type derivation trees where applicable.

a) The class Array has a field length in which the length of the array is stored.

def swap(lst: Array[Int], a: Int, b: Int): Array[Int] = {
if (a >= lst.length || b >= lst.length) lst else {
val swap = lst(a)
lst(a) = lst(b)
lst(b) = swap
lst
}
}

b)

Recall that we have the two type rules:

• If is a declared subclass of , then

i) Give the type rule corresponding to new.
ii) Show this code typechecks.

class Shape
class Rectangle(width: Int, length: Int) extends Shape {
def area : Int = width * length
}
class Square(length: Int) extends Rectangle(length,length)
new Square(5).area