CSC447

Concepts of Programming Languages

Parametric Polymorphism

Monomorphic Linked Lists (C)

Implement linked lists in C for each pointer type?


typedef struct Node Node;
struct Node {
  int  *head;
  Node *tail;
};

int *get_last (Node *xs) {
  while (xs->tail != NULL) {
    xs = xs->tail;
  }
  return xs->head;
}

Generic Linked Lists (C)

Use (void *) type in C


typedef struct Node Node;
struct Node {
  void *head;
  Node *tail;
};

void *get_last (Node *xs) {
  while (xs->tail != NULL) {
    xs = xs->tail;
  }
  return xs->head;
}

Generic Linked Lists (C)

No static protection against casts from (void *)


typedef struct Node Node;
struct Node {
  void *head;
  Node *tail;
};
int main () {
  int  *p   = (int *)  malloc (sizeof(int));
  *p        = 2123456789;
  Node *xs  = (Node *) malloc (sizeof(Node));
  xs->tail  = NULL;
  xs->head  = p;               // store int pointer
  double *q = get_last(xs);    // alias of p
  printf ("q=%f\n", *q);       // unsafe access
}


$ clang -m32 parametric-03.c && ./a.out
q=96621069057346178268049192388430659584.000000

Monomorphic Lists (Java)

Implement linked lists in Java for each reference type?


static class Node {
  Integer head;
  Node    tail;
}

static Integer getLast (Node xs) {
  while (xs.tail != null) {
    xs = xs.tail;
  }
  return xs.head;
}

Generic Linked Lists (Java)

Generic list using subtype polymorphism


static class Node {
  Object  head;
  Node    tail;
}

static Object getLast (Node xs) {
  while (xs.tail != null) {
    xs = xs.tail;
  }
  return xs.head;
}

Subtype polymorphism

ClassCastException better than unsafe access


static class Node    {
  Object  head;
  Node    tail;
}
public static void main (String[] args) {
  Integer p = Integer.valueOf(2123456789);
  Node xs   = new Node();
  xs.tail   = null;
  xs.head   = p;                      // store Integer
  Double q  = (Double) getLast(xs);   // ClassCastException
  System.out.printf ("d=%f\n", q);    // unsafe access
}


$ javac Parametric2.java
$ java Parametric2
java.lang.ClassCastException: Integer cannot be cast to Double
	at Parametric.main(Parametric2.java:10)

Generic Linked Lists (Java)

Generic list using parametric polymorphism


static Node<X> {
  X       head;
  Node<X> tail;
}

static <X> X getLast (Node<X> xs) {
  while (xs.tail != null) {
    xs = xs.tail;
  }
  return xs.head;
}

Parametric Polymorphism

Compiler errors better than runtime exceptions


static class Node<X> {
  X       head;
  Node<X> tail;
}
public static void main (String[] args) {
  Integer p = Integer.valueOf(2123456789);
  Node<Integer> xs = new Node<>();
  xs.tail   = null;
  xs.head   = p;                      // store Integer
  Double q  = (Double) getLast(xs);   // compiler error
  System.out.printf ("d=%f\n", q);    // unsafe access
}


$ javac Parametric1.java
error: incompatible types: Integer cannot be converted to Double
  Double q = (Double) getLast(xs);   // compiler error
                             ^

Java type parameter erasure

Java type parameters not stored at runtime


static class ArrayList<X> {
  X[] a;

  ArrayList(int n) {
    a = new X[n];
  }
  void put (int i, X item) { a[i] = item; }
  X    get (int i)         { return a[i]; }
}


$ javac Parametric3.java
error: generic array creation
  a = new X[n];
          ^

Java type parameter erasure

Cast is not checked at runtime


static class ArrayList<X> {
  X[] a;

  ArrayList(int n) {
    a = (X[]) new Object[n];
  }
  void put (int i, X item) { a[i] = item; }
  X    get (int i)         { return a[i]; }
}


$ javac -Xlint:unchecked Parametric4.java
warning: [unchecked] unchecked cast
    a = (X[]) new Object[n];
              ^

Java type parameter erasure

Okay to ignore, since array is empty


static class ArrayList<X> {
  X[] a;
  @SuppressWarnings("unchecked")
  ArrayList(int n) {
    a = (X[]) new Object[n];
  }
  void put (int i, X item) { a[i] = item; }
  X    get (int i)         { return a[i]; }
}


$ javac -Xlint:unchecked Parametric4.java


// works fine

Java type parameter erasure

Mix with old code:


ArrayList<String> ss = new ArrayList<>(10);
ArrayList os = ss;
os.put (1, 2123456789);
String s = ss.get (1);


$ javac Parametric6.java
Note: Parametric6.java uses unchecked or unsafe operations.
Note: Recompile with -Xlint:unchecked for details.


$ java Parametric6                     
ClassCastException: Integer cannot be cast to class String
  at Parametric.main(Parametric6.java:4)

Arrays checked when assigned

Java stores types with arrays


String[] ss = new String[10];
Object[] os = ss;
os[1] = 2123456789;
String s = ss[1];


$ javac Parametric7.java

// no warnings


$ java Parametric7                     
ArrayStoreException: Integer
   at Parametric.main(Parametric7.java:3)

Parametric Polymorphism

In Java, C#, Ada, Haskell, Scala, Rust, etc
First developed in ML (1970s)
- Modern descendants: F#, oCaml, Standard ML
- Strong connection to mathematical logic
- Leading to Agda, Coq, etc
C++ templates are different
- Template itself has no executable form:
  List<T>
- Executable generated for each instantiation:
  List<int>, List<string>