- Concepts of Programming Languages

Exercises

Instructor:

Exercise Topics

• Tail recursion
• Safety, scope and lifetime
• Algebraic datatypes
• Argument passing
• Closures
• Inheritance and delegation
• JavaScript objects and scope

Tail Recursion

def f (n:Int) = if n<=1 then 1 else n * f (n-1)
def g (n:Int) = f (n) * g (n-1)
def h (n:Int) = h (g (n), f (n))
def i (n:Int) = n * n

• Is f recursive? tail-recursive?
• Is g recursive? tail-recursive?
• Is h recursive? tail-recursive?
• Is i recursive? tail-recursive?

Tail Recursion

def f (n:Int) = if n<=1 then 1 else n * f (n-1)
def g (n:Int) = f (n) * g (n-1)
def h (n:Int) = h (g (n), f (n))
def i (n:Int) = n * n

• f is recursive, but not tail-recursive (multiplication n*f(n-1))
• g is recursive, but not tail-recursive (multiplication f(n) * g(n-1))
• h is tail-recursive (recursive call to h last)
• i is not recursive at all

Scope and Lifetime: Dangling Pointers

int* f(int x) { return &x; }
int* g(int x) { 
  int* y = (int*) malloc (sizeof (int)); 
  *y=x; 
  return y; 
}
int main(void) {
  int* p = f(5);
  printf("%d\n", *p);
  int* q = g(5);              
}

Scope and Lifetime: Dangling Pointers

int* f(int x) { return &x; }
int* g(int x) { 
  int* y = (int*) malloc (sizeof (int)); 
  *y=x; 
  return y; 
}
int main(void) {
  int* p = f(5);
  printf("%d\n", *p);
  int* q = g(5);              
}

Unsafe Memory Access

int* f(int* x) {
  *x = *x+1;
  return x; 
}
int main(void) {
  int x = 5;
  double y = 5.2;
  printf("%d\n", *f(&x));
  printf("%f\n", *f(&y));
}

• Does the program make an unsafe memory access?
• If so, where?

Unsafe Memory Access

int* f(int* x) {
  *x = *x+1;
  return x; 
}
int main(void) {
  int x = 5;
  double y = 5.2;
  printf("%d\n", *f(&x));
  printf("%f\n", *f(&y));
}

• Program makes an unsafe memory access when dereferencing x, because it accesses memory that stores a double as if it were an int

Static vs. Dynamic Scope

What is printed in a statically-scoped vs. dynamically-scoped language?

var x:Int = 10
def foo() =
  x = 20
def bar() = 
  var x:Int = 30
  foo()
  print(x)                
def zee() = 
  var x:Int = 40
  bar()
  print(x)
print("bar: "); bar(); println(" " + x)
print("zee: "); zee(); println(" " + x)
print("foo: "); foo(); println(" " + x)

Static vs. Dynamic Scope

What is printed in a statically-scoped vs. dynamically-scoped language?

var x:Int = 10
def foo() =
  x = 20
def bar() = 
  var x:Int = 30
  foo()
  print(x)                
def zee() = 
  var x:Int = 40
  bar()
  print(x)
print("bar: "); bar(); println(" " + x)
print("zee: "); zee(); println(" " + x)
print("foo: "); foo(); println(" " + x)

Algebraic Datatypes

enum Expr:
  case Literal(x:Int)
  case Variable(n:String, v: Option[Expr])
  // TODO

Extend the algebraic datatype for arithmetic expressions with operators +, -, *
Are there more than one - operator?

Algebraic Datatypes

enum Expr:
  case Literal(x:Int)
  case Variable(n:String, v: Option[Expr])
  case Plus(l: Expr, r: Expr)  // l+r
  case Minus(l: Expr, r: Expr) // l-r
  case Neg(e: Expr)            // -e
  case Times(l: Expr, r: Expr) // l*r

Extend the algebraic datatype for arithmetic expressions with operators +, -, *
Are there more than one - operator?

Algebraic Datatypes

Finish the toInt method for arithmetic expressions

enum Expr:
  case Literal(x:Int)
  case Variable(n:String, v:Option[Expr])     
  case Plus(l: Expr, r: Expr)  // l+r
  case Minus(l: Expr, r: Expr) // l-r
  case Neg(e: Expr)            // -e
  case Times(l: Expr, r: Expr) // l*r

Algebraic Datatypes

Finish the toInt method for arithmetic expressions

enum Expr:
  case Literal(x:Int)
  case Variable(n:String, v:Option[Expr])     
  case Plus(l: Expr, r: Expr)  // l+r
  case Minus(l: Expr, r: Expr) // l-r
  case Neg(e: Expr)            // -e
  case Times(l: Expr, r: Expr) // l*r

Call-by-value and Call-by-reference

What is printed in a call-by-value vs. a call-by-reference language?

def f(a:Int, b:Int) = {
  a = b
  b = b + 1
}
var x = 5
var y = 10
f(x,y); println(s"x=$x, y=$y")
f(x,x); println(s"x=$x")
f(x,x+2); println(s"x=$x")

Call-by-value and Call-by-reference

What is printed in a call-by-value vs. a call-by-reference language?

def f(a:Int, b:Int) = {
  a = b
  b = b + 1
}
var x = 5
var y = 10
f(x,y); println(s"x=$x, y=$y")
f(x,x); println(s"x=$x")
f(x,x+2); println(s"x=$x")

Closures

def f(): String=>String = {
  var s = ""
  (t:String) => { s = s + t; s }
}
val a = f()
println(a("x"))
println(a("y"))
println(a("z"))

• Does the program compile?
• What is the type of a?
• What is printed?
• What is an OOP approach to the code above?

Closures

def f(): String=>String = {
  var s = ""
  (t:String) => { s = s + t; s }
}
val a = f()
println(a("x"))
println(a("y"))
println(a("z"))

Nested Closures

def f(): ()=>String=>String =
  var s = ""
  () => {
    var i = 0
    (t:String) => { s = s + t + i; i = i+1; s }
  }
end f
val factory = f()
val a = factory()
val b = factory()
println(a("x"))
println(a("y"))
println(b("z"))

• Do a and b share s? Do they share i?
• What is printed?

Nested Closures

def f(): ()=>String=>String =
  var s = ""
  () => {
    var i = 0
    (t:String) => { s = s + t + i; i = i+1; s }
  }
end f
val factory = f()
val a = factory()
val b = factory()
println(a("x"))
println(a("y"))
println(b("z"))

• a and b share s, but do not share i (each has their own i)
• a and b append to the same s, but increment their own i, so prints x0, x0y1, and x0y1z0

Inheritance vs. Delegation

class A:
  def f() = println("A.f")
class B extends A:
  override def f() = 
    println("B.f")
    super.f() 
  end f
  def g() = println("B.g")
val b:A = new B() // b:B?
b.f()

let a = {
  f: function() { 
    console.log("A.f"); }
}
let b = {
  f: function() { 
    console.log("B.f"); 
    this.__proto__.f(); },
  g: function() { 
    console.log("B.g"); }
}
b.__proto__ = a
b.f();

• Does the program compile? If yes, what is printed?
• Does b.g() compile? If yes, what is printed?
• If no, would it compile with val b:B = new B()?

Inheritance vs. Delegation

class A:
  def f() = println("A.f")
class B extends A:
  override def f() = 
    println("B.f")
    super.f() 
  end f
  def g() = println("B.g")
val b:A = new B() // b:B?
b.f()

let a = {
  f: function() { 
    console.log("A.f"); }
}
let b = {
  f: function() { 
    console.log("B.f"); 
    this.__proto__.f(); },
  g: function() { 
    console.log("B.g"); }
}
b.__proto__ = a
b.f();

• The program compiles and prints B.f A.f
• b.g() does not compile, because variable b is of static type A
• The program would compile with val b:B = new B() and would print B.g
• For JavaScript: program executes and also prints B.f A.f

Parametric Types

class A
class B extends A
var as: List[A] = List(new A(), new B())

Which code compiles and why/why not?

• val bs: List[B] = as
• val bs: List[B] = List(new B(), new B())
• as = bs
• val a1: Any = as(0) // a1: A // a1: B

Parametric Types

class A
class B extends A
var as: List[A] = List(new A(), new B())

Which code compiles and why/why not?

• val bs: List[B] = as
• val bs: List[B] = List(new B(), new B())
• as = bs (in Scala, List is covariant, List[B] <: List[A] from B <: A)
• val a1: Any = as(0), val a1: A = as(0), val a1: B = as(0)

Parametric Wildcard Types

class A
class B extends A
val as: Array[A] = Array(new A(), new B())

Which code compiles and why/why not?

• val bs: Array[B] = as?

Parametric Wildcard Types

class A
class B extends A
val as: Array[A] = Array(new A(), new B())

Which code compiles and why/why not?

• Does not compile: val bs: Array[B] = as (arrays are type-invariant)

JavaScript Objects

function f() {
  return {
    a: 1,
    b: "hello"
    c: function () { return 2; }
  }
}

• What is the result type of function f?
• What is the result of f().a?
• What is the result of f().d?
• What is the result of f().c()?

JavaScript Objects

function f() {
  return {
    a: 1,
    b: "hello"
    c: function () { return 2; }
  }
}

• Function f returns an object
• f().a returns 1
• f().d returns undefined (because property d is not present in the object)
• f().c() returns 2

JavaScript: Function-Scoped Variables

function f(n) {
  var fs = [];
  for (var i = 0; i < n; i++) {
    var x = i;
    fs.push(x);
  }
  return fs;
}

• What is the result of f(3) and why?
• How can we make the result of f(3) be [0,1,2]?

JavaScript: Function-Scoped Variables

function f(n) {
  var fs = [];
  for (var i = 0; i < n; i++) {
    var x = i;
    fs.push(x);
  }
  return fs;
}

• f(3) returns 0 because var makes x function-scoped and var x is therefore hoisted outside the loop to the start of function f
• f(3) becomes [0,1,2] when we use let (block-scope)