- 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

  1. def f (n:Int) = if n<=1 then 1 else n * f (n-1)
  2. def g (n:Int) = f (n) * g (n-1)
  3. def h (n:Int) = h (g (n), f (n))
  4. 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

  1. def f (n:Int) = if n<=1 then 1 else n * f (n-1)
  2. def g (n:Int) = f (n) * g (n-1)
  3. def h (n:Int) = h (g (n), f (n))
  4. 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

Continuation Passing

  1. def fact(n: Int) : BigInt =
  2.   require (n>=0)
  3.   if n <= 1 then 1
  4.   else n * fact(n-1)
  5. end fact

  1. def factCPS[X](n: Int, k: ______________) : X =
  2.   require (n>=0)
  3.   if n <= 1 then ________________
  4.   else factCPS(_______, _________)
  5. end factCPS
  • Fill in the blanks in the continuation passing style

Continuation Passing

  1. def fact(n: Int) : BigInt =
  2.   require (n>=0)
  3.   if n <= 1 then 1
  4.   else n * fact(n-1)
  5. end fact

  1. def factCPS[X](n: Int, k: BigInt=>X) : X =
  2.   require (n>=0)
  3.   if n <= 1 then k(1)
  4.   else factCPS(n-1, r => k(n*r))
  5. end factCPS

Scope and Lifetime: Dangling Pointers

  1. int* f(int x) { return &x; }
  2. int* g(int x) {
  3.   int* y = (int*) malloc (sizeof (int));
  4.   *y=x;
  5.   return y;
  6. }
  7. int main(void) {
  8.   int* p = f(5);
  9.   printf("%d\n", *p);
  10.   int* q = g(5);
  11. }
  • Is p pointing to the heap or stack?
  • Is p dangling? Is dereferencing it safe?
  • Does p need to be freed?
  • Is q pointing to the heap or stack?
  • Is q dangling? Is dereferencing it safe?
  • Does q need to be freed?

Scope and Lifetime: Dangling Pointers

  1. int* f(int x) { return &x; }
  2. int* g(int x) {
  3.   int* y = (int*) malloc (sizeof (int));
  4.   *y=x;
  5.   return y;
  6. }
  7. int main(void) {
  8.   int* p = f(5);
  9.   printf("%d\n", *p);
  10.   int* q = g(5);
  11. }
  • p points to the stack
  • p is dangling, and dereferencing it is not safe
  • p points already to freed memory
  • q points to the heap
  • q is not dangling, it can be dereferenced safety
  • q needs to be freed

Unsafe Memory Access

  1. int* f(int* x) {
  2.   *x = *x+1;
  3.   return x;
  4. }
  5. int main(void) {
  6.   int x = 5;
  7.   double y = 5.2;
  8.   printf("%d\n", *f(&x));
  9.   printf("%f\n", *f(&y));
  10. }
  • Does the program make an unsafe memory access?
  • If so, where?

Unsafe Memory Access

  1. int* f(int* x) {
  2.   *x = *x+1;
  3.   return x;
  4. }
  5. int main(void) {
  6.   int x = 5;
  7.   double y = 5.2;
  8.   printf("%d\n", *f(&x));
  9.   printf("%f\n", *f(&y));
  10. }
  • Program makes an unsafe memory access when dereferencing x, because it accesses memory that stores a double as if it were an int

Option Types

  1. case class Person(name: String, email: Option[String])
  3. def invite(p: Person, mailSender: String=>Boolean) : Boolean = p.email match
  4.    case _________ => ________________
  5.    case _________ => ________________
  6. end invite
  8. def email(p: Person) : String = _____________________________
  • Send an email to person p using the mailSender, depending on whether p has an email address
  • Return the email address of person p as a string, or "unknown" if they don't have an address

Option Types

  1. case class Person(name: String, email: Option[String])
  3. def invite(p: Person, mailSender: String=>Boolean) : Boolean = p.email match
  4.    case None    => false
  5.    case Some(a) => mailSender(a)
  6. end invite
  8. def invite2(p: Person, mailSender: String=>Boolean) : Boolean =
  9.   p.email.map(mailSender).getOrElse(false)
  10. end invite2
  12. def email(p: Person) : String = p.email.getOrElse("unknown")
  • Send an email to person p using the mailSender, depending on whether p has an email address
  • Return the email address of person p as a string, or "unknown" if they don't have an address

Static vs. Dynamic Scope

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

  1. var x:Int = 10
  3. def foo() =
  4.   x = 20
  5. def bar() =
  6.   var x:Int = 30
  7.   foo()
  8.   print(x)
  9. def zee() =
  10.   var x:Int = 40
  11.   bar()
  12.   print(x)
  14. print("bar: "); bar(); println(" " + x)
  15. print("zee: "); zee(); println(" " + x)
  16. print("foo: "); foo(); println(" " + x)

Static vs. Dynamic Scope

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

  1. var x:Int = 10
  3. def foo() =
  4.   x = 20
  5. def bar() =
  6.   var x:Int = 30
  7.   foo()
  8.   print(x)
  9. def zee() =
  10.   var x:Int = 40
  11.   bar()
  12.   print(x)
  14. print("bar: "); bar(); println(" " + x)
  15. print("zee: "); zee(); println(" " + x)
  16. print("foo: "); foo(); println(" " + x)
  • Static Scope
    1. bar: 30 20
    2. zee: 30 40 20
    3. foo: 20
  • Dynamic Scope
    1. bar: 20 10
    2. zee: 20 40 10
    3. foo: 20

Algebraic Datatypes

  1. enum Expr:
  2.   case Literal(x:Int)
  3.   case Variable(n:String, v: Option[Expr])
  4.   // TODO

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

Algebraic Datatypes

  1. enum Expr:
  2.   case Literal(x:Int)
  3.   case Variable(n:String, v: Option[Expr])
  4.   case Plus(l: Expr, r: Expr)  // l+r
  5.   case Minus(l: Expr, r: Expr) // l-r
  6.   case Neg(e: Expr)            // -e
  7.   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

  1. enum Expr:
  2.   case Literal(x:Int)
  3.   case Variable(n:String, v:Option[Expr])
  4.   case Plus(l: Expr, r: Expr)  // l+r
  5.   case Minus(l: Expr, r: Expr) // l-r
  6.   case Neg(e: Expr)            // -e
  7.   case Times(l: Expr, r: Expr) // l*r
  • Method toInt
    1. def toInt(e: Expr) : Int = e match
    2.   case Literal(x)           => x
    3.   case Variable(n, None)    => ???
    4.   case Variable(_, Some(e)) => toInt(e)
    5.   // TODO

Algebraic Datatypes

Finish the toInt method for arithmetic expressions

  1. enum Expr:
  2.   case Literal(x:Int)
  3.   case Variable(n:String, v:Option[Expr])
  4.   case Plus(l: Expr, r: Expr)  // l+r
  5.   case Minus(l: Expr, r: Expr) // l-r
  6.   case Neg(e: Expr)            // -e
  7.   case Times(l: Expr, r: Expr) // l*r
  • Method toInt
    1. def toInt(e: Expr) : Int = e match
    2.   case Literal(x)           => x
    3.   case Variable(n, None)    => ???
    4.   case Variable(_, Some(e)) => toInt(e)
    5.   case Plus(l, r)           => toInt(l) + toInt(r)
    6.   case Minus(l, r)          => toInt(l) - toInt(r)
    7.   case Neg(e)               => 0-toInt(e)
    8.   case Times(l, r)          => toInt(l) * toInt(r)

Call-by-value and Call-by-reference

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

  1. def f(a:Int, b:Int) = {
  2.   a = b
  3.   b = b + 1
  4. }
  6. var x = 5
  7. var y = 10
  8. f(x,y); println(s"x=$x, y=$y")
  9. f(x,x); println(s"x=$x")
  10. f(x,x+2); println(s"x=$x")

Call-by-value and Call-by-reference

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

  1. def f(a:Int, b:Int) = {
  2.   a = b
  3.   b = b + 1
  4. }
  6. var x = 5
  7. var y = 10
  8. f(x,y); println(s"x=$x, y=$y")
  9. f(x,x); println(s"x=$x")
  10. f(x,x+2); println(s"x=$x")
  • Call-by-value
    1. x=5, y=10
    2. x=5
    3. x=5
  • Call-by-reference
    1. x=10, y=11
    2. x=11
    3. x=13

Fold

  1. val l = List(1,2,3,4,5)
  3. val sum = l.foldLeft(___) {
  4.   __________________
  5. }
  7. val count = l.foldLeft(____) {
  8.   __________________
  9. }
  11. val countEven = l.foldLeft(____) {
  12.   __________________
  13. }
  • Implement functions using fold

Fold

  1. val l = List(1,2,3,4,5)
  3. val sum = l.foldLeft(0) {
  4.   (s, n) => s+n // _ + _
  5. }
  7. val count = l.foldLeft(0) {
  8.   (c, _) => c+1
  9. }
  11. val countEven = l.fold(0) {
  12.   (c, n) => if n%2 == 0 then c+1 else c
  13. }
  • Implement functions using fold

Closures

  1. def f(): String=>String = {
  2.   var s = ""
  3.   (t:String) => { s = s + t; s }
  4. }
  5. val a = f()
  6. println(a("x"))
  7. println(a("y"))
  8. 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

  1. def f(): String=>String = {
  2.   var s = ""
  3.   (t:String) => { s = s + t; s }
  4. }
  5. val a = f()
  6. println(a("x"))
  7. println(a("y"))
  8. 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?
  • a is function String=>String
  • Prints
    1. x
    2. xy
    3. xyz
  • Implement with a class
    1. public class f {
    2.   private String s = "";
    3.   public String fn(String t) {
    4.     s = s+t;
    5.     return s;
    6.   }
    7. }
    8. f a = new f()
    9. System.out.println(a.fn("x"));

Nested Closures

  1. def f(): ()=>String=>String =
  2.   var s = ""
  3.   () => {
  4.     var i = 0
  5.     (t:String) => { s = s + t + i; i = i+1; s }
  6.   }
  7. end f
  8. val factory = f()
  9. val a = factory()
  10. val b = factory()
  11. println(a("x"))
  12. println(a("y"))
  13. println(b("z"))
  • Do a and b share s? Do they share i?
  • What is printed?

Nested Closures

  1. def f(): ()=>String=>String =
  2.   var s = ""
  3.   () => {
  4.     var i = 0
  5.     (t:String) => { s = s + t + i; i = i+1; s }
  6.   }
  7. end f
  8. val factory = f()
  9. val a = factory()
  10. val b = factory()
  11. println(a("x"))
  12. println(a("y"))
  13. 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

  1. class A:
  2.   def f() = println("A.f")
  3. class B extends A:
  4.   override def f() =
  5.     println("B.f")
  6.     super.f()
  7.   end f
  8.   def g() = println("B.g")
  10. val b:A = new B() // b:B?
  11. b.f()

  1. let a = {
  2.   f: function() {
  3.     console.log("A.f"); }
  4. }
  5. let b = {
  6.   f: function() {
  7.     console.log("B.f");
  8.     this.__proto__.f(); },
  9.   g: function() {
  10.     console.log("B.g"); }
  11. }
  12. b.__proto__ = a
  13. 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

  1. class A:
  2.   def f() = println("A.f")
  3. class B extends A:
  4.   override def f() =
  5.     println("B.f")
  6.     super.f()
  7.   end f
  8.   def g() = println("B.g")
  10. val b:A = new B() // b:B?
  11. b.f()

  1. let a = {
  2.   f: function() {
  3.     console.log("A.f"); }
  4. }
  5. let b = {
  6.   f: function() {
  7.     console.log("B.f");
  8.     this.__proto__.f(); },
  9.   g: function() {
  10.     console.log("B.g"); }
  11. }
  12. b.__proto__ = a
  13. 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

  1. class A
  2. class B extends A
  3. 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 (with bs: List[B])
  • val a1: Any = as(0) // a1: A // a1: B

Parametric Types

  1. class A
  2. class B extends A
  3. 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 (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

  1. class A
  2. class B extends A
  3. val as: Array[A] = Array(new A(), new B())

Which code compiles and why/why not?

  • val bs: Array[B] = as?

With subtype wildcard

  • val bs: Array[? <: A] = as?
  • bs(0) = new B()?
  • val b: B = bs(0)?
  • val b: A = bs(0)?
  • val b: Any = bs(0)?

With supertype wildcard

  • val bs: Array[? >: B] = as?
  • bs(0) = new B()?
  • bs(0) = new A()?
  • val b: B = bs(0)?
  • val b: Any = bs(0)?

Parametric Wildcard Types

  1. class A
  2. class B extends A
  3. val as: Array[A] = Array(new A(), new B())

Which code compiles and why/why not?

  • val bs: Array[B] = as (arrays are type-invariant)

With subtype wildcard

  • val bs: Array[? <: A] = as?
  • bs(0) = new B() (subtype wildcard makes array read-only)
  • val b: B = bs(0) (parameter type of array is A)
  • val b: A = bs(0) (parameter type of array is A)
  • val b: Any = bs(0) (Any is a supertype of A)

With supertype wildcard

  • val bs: Array[? >: B] = as
  • bs(0) = new B() (supertype wildcard makes array "write-only")
  • bs(0) = new A() (B could have other supertypes)
  • val b: B = bs(0) (some supertype of B may have additional subtypes)
  • val b: Any = bs(0) (degraded read to Any is allowed)

JavaScript Objects

  1. function f() {
  2.   return {
  3.     a: 1,
  4.     b: "hello"
  5.     c: function () { return 2; }
  6.   }
  7. }
  • 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

  1. function f() {
  2.   return {
  3.     a: 1,
  4.     b: "hello"
  5.     c: function () { return 2; }
  6.   }
  7. }
  • 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

  1. function f(n) {
  2.   var fs = [];
  3.   for (var i = 0; i < n; i++) {
  4.     var x = i;
  5.     fs.push(() => x);
  6.   }
  7.   return fs;
  8. }
  • 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

  1. function f(n) {
  2.   var fs = [];
  3.   for (var i = 0; i < n; i++) {
  4.     var x = i;
  5.     fs.push(() => x);
  6.   }
  7.   return fs;
  8. }
  • f(3) returns [()=>2, ()=>2, ()=>2] 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 const or let (block-scope)