Polymorphism (Ad-hoc and Universal)

Polymorphism (Ad-hoc and Universal
Sérgio Souza Costa
Universidade Federaldo Maranhão
3 de julho de 2016
Sérgio Souza Costa (Universidade Federaldo Maranhão) Paradigmas de Programação 3 de julho de 2016 1 / 20

Based in On understanding types, data abstraction, and polymorphism (Luca Cardelli and Peter
Wegner)

Summary
Static and Strong Typing
Polymorphism
Kinds of Polymorphism
Ad-hoc - Overloading
Ad-hoc - Coercion
Parametric polymorphism
Inclusion polymorphism

In mathematics as in programming, types impose constraints which help to enforce
correctness.
To prevent type violations, we generally impose a static type structure on programs. Types
are associated with constants, operators, variables, and function symbols.
A type inference system can be used to infer the types of expressions when little or no type
information is given explicitly.
In languages like Pascal and Ada, the type of variables and function symbols is deﬁned by
redundant declarations and the compiler can check the consistency of deﬁnition and use.
In languages like ML, explicit declarations are avoided wherever possible and the system
may infer the type of expressions from local context, while still establishing

Deﬁnição
Programming languages in which the type of every expression can be determined by static
program analysis are said to be statically typed.
Static typing is a useful property, but the requirement that all variables and expressions are
bound to a type at compile time is sometimes too restrictive.
It may be replaced by the weaker requirement that all expressions are guaranteed to be
type-consistent although the type itself may be statically unknown; this can be generally
done by introducing some run-time type checking.
Deﬁnição
Languages in which all expressions are type-consistent are called strongly typed languages.

Pros:
In general, we should strive for strong typing, and adopt static typing whenever possible..
Static typing allows type inconsistencies to be discovered at compile time and guarantees
that executed programs are type-consistent.
It facilitates early detection of type errors and allows greater execution-time efficiency. It
enforces a programming discipline on the programmer that makes programs more
structured and easier to read.
Cons:
Static typing may also lead to a loss of flexibility and expressive power by prematurely
constraining the behavior of objects to that associated with a particular type.
Traditional statically typed systems exclude programming techniques which, although
sound, are incompatible with early binding of program objects to a specific type. For
example they exclude generic procedures, e.g. sorting, that capture the structure of an
algorithm uniformly applicable to a range of types.

Polymorphism
Conventional typed languages, such as Pascal, are based on the idea that functions and
procedures, and hence their operands, have a unique type. Such languages are said to be
monomorphic, in the sense that every value and variable can be interpreted to be of
one and only one type.
Polymorphic languages in which some values and variables may have more than one
type.
Polymorphic functions are functions whose operands (actual parameters) can have more
than one type.
Polymorphic types are types whose operations are applicable to values of more than one
type.

Cardelli classiﬁcation

Ad-hoc polymorphism is obtained when a function works, or appears to work, on
several different types (which may not exhibit a common structure) and may behave in
unrelated ways for each type.
Universally polymorphic functions will normally work on an infinite number of types
(all the types having a given common structure), while an ad-hoc polymorphic function
will only work on a finite set of different and potentially unrelated types.
In terms of implementation, a universally polymorphic function will execute the same
code for arguments of any admissible type, while an ad-hoc polymorphic function may
execute different code for each type of argument.
Universal polymorphism is considered true polymorphism, while ad-hoc polymorphism is
some kind of apparent polymorphism

Ad-hoc - Overloading
In overloading the same variable name is used to denote diﬀerent functions, and the
context is used to decide which function is denoted by a particular instance of the name.
Example (c++):
1 main(){
2 int a = 2, b = 3;
3 float x = 1.5, y = 3.4;
4 a = a + b; // a = somaint (a, b);
5 x = x + y; // x = somafloat (x, y);
6 }

Ad-hoc - Coercion
A coercion is instead a semantic operation which is needed to convert an argument to the
type expected by a function, in a situation which would otherwise result in a type error.
Coercions can be provided statically, by automatically inserting them between arguments
and functions at compile time, or may have to be determined dynamically by run-time
tests on the arguments.
Implicit conversion between types.
Example (c++):
1 main() {
2 int w = 3;
3 float x;
4 float y = 5.2;
5 x = x + y; // x = somafloat (x, y)
6 x = x + w; // x = somafloat (x, intToFloat (w) );
7 }

Universal - Parametric polymorphism
Deﬁnição
In parametric polymorphism, a polymorphic function has an implicit or explicit type parameter,
which determines the type of the argument for each application of that function.
Example in Java
class Comparators {
public static <T extends Comparable<T>> T max (T a, T b) {
if (a.compareTo(b) > 0) return a;
else return b;
}
}

C++
1 template <class T>
2 T maior (T a, T b) {
3 return ( (a>b)? a : b );
4 }
Haskell
1 maior :: (Ord a) => a -> a -> a
2 maior a b
3 | a > b = a
4 | otherwise = b

The functions that exhibit parametric polymorphism are also called generic functions.
For example, the length function from lists of arbitrary type to integers is called a generic
length function.
1 length :: [a] -> Int
A generic function is one which can work for arguments of many types, generally doing the
same kind of work independently of the argument type.

Parametric type and operator overloading
1 template <class T>
2 class Point {
3 public:
4 T x, y;
5 Point (T x1, T y1):x(x1),y(y1) {}
6 Point operator + (Point& other) {
7 return Point (x+other.x,y+other.y);
8 }
9 friend ostream& operator << (ostream& out, Point p) {
10 out << p.x << "-" << p.y << endl;
11 return out;
12 }
13 };

1 int main() {
2 Point<string> p1("ab","cd");
3 Point<string> p2("fg","de");
4 Point<string> p3 = p1 + p2;
5
6 cout << p3 << endl;
7
8 return 0;
9 }
Observação
Parametric polymorphism is supported in Java through Generic Types.

Inclusion polymorphism
Definição
Inclusion polymorphism is a type system in which a type may have subtypes, which inherit
operations from that type. Where a type T is a set of values, equipped with some operations.
A subtype of T is a subset of the values of T, equipped with the same operations as T. Every
value of the subtype is also a value of type T, and therefore may be used in a context where a
value of type T is expected (David Watt).
In inclusion polymorphism an object can be viewed as belonging to many different classes
which need not be disjoint, i.e. there may be inclusion of classes.
Inclusion polymorphism as a relation among types which allows operations to be applied to
object of different types related by inclusion.

Inclusion polymorphism - Example
class Point {
protected double x, y;
public void draw () {. . .} // Draw this point.
. . . // other methods
class Circle extends Point {
private double r;
public void draw () {. . .} //Draw this circle.
class Rectangle extends Point {
private double w, h;
public void draw () {. . .} // Draw this rectangle.

Java allows objects of any subclass to be treated like objects of the superclass. Consider
the following variable:
Point p;
...
p = new Point(3.0, 4.0);
...
p = new Circle(3.0, 4.0, 5.0);
This variable may refer to an object of class Point or any subclass of Point. In other
words, this variable may refer to any value of type Point.

Polymorphism (Ad-hoc and Universal)

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