Polymorphism

Polymorphism : 

1 Polymorphism

Introduction : 

Chapter Eight Modern Programming Languages 2 Introduction Compare these function types The ML function is more flexible, since it can be applied to any pair of the same (equality-testable) type int f(char a, char b) { return a==b; } - fun f(a, b) = (a = b);val f = fn : ''a * ''a -> bool ML: C:

Polymorphism : 

Chapter Eight Modern Programming Languages 3 Polymorphism Functions with that extra flexibility are called polymorphic A difficult word to define: Applies to a wide variety of language features Most languages have at least a little We will examine four major examples, then return to the problem of finding a definition that covers them

Outline : 

Chapter Eight Modern Programming Languages 4 Outline Overloading Parameter coercion Parametric polymorphism Subtype polymorphism Definitions and classifications

Overloading : 

Chapter Eight Modern Programming Languages 5 Overloading An overloaded function name or operator is one that has at least two definitions, all of different types Many languages have overloaded operators Some also allow the programmer to define new overloaded function names and operators

Predefined Overloaded Operators : 

Chapter Eight Modern Programming Languages 6 Predefined Overloaded Operators Pascal: a := 1 + 2; b := 1.0 + 2.0; c := "hello " + "there"; d := ['a'..'d'] + ['f'] ML: val x = 1 + 2; val y = 1.0 + 2.0;

Adding to Overloaded Operators : 

Chapter Eight Modern Programming Languages 7 Adding to Overloaded Operators Some languages, like C++, allow additional meanings to be defined for operators class complex { double rp, ip; // real part, imaginary partpublic: complex(double r, double i) {rp=r; ip=i;} friend complex operator+(complex, complex); friend complex operator*(complex, complex);}; void f(complex a, complex b, complex c) { complex d = a + b * c; …}

Operator Overloading In C++ : 

Chapter Eight Modern Programming Languages 8 Operator Overloading In C++ C++ allows virtually all operators to be overloaded, including: the usual operators (+,-,*,/,%,^,&,|,~,!,=,<,>, +=,-=,=,*=,/=,%=,^=,&=,|=,<<,>>,>>=,<<=,==, !=,<=,>=,&&,||,++,--,->*,,) dereferencing (*p and p->x) subscripting (a[i]) function call (f(a,b,c)) allocation and deallocation (new and delete)

Defining Overloaded Functions : 

Chapter Eight Modern Programming Languages 9 Defining Overloaded Functions Some languages, like C++, permit the programmer to overload function names int square(int x) { return x*x;}double square(double x) { return x*x;}

To Eliminate Overloading : 

Chapter Eight Modern Programming Languages 10 To Eliminate Overloading int square(int x) { return x*x;}double square(double x) { return x*x;} void f() { int a = square(3); double b = square(3.0);} You could rename each overloaded definition uniquely… square_i square_d

How To Eliminate Overloading : 

Chapter Eight Modern Programming Languages 11 How To Eliminate Overloading int square_i(int x) { return x*x;}double square_d(double x) { return x*x;} void f() { int a = square_i(3); double b = square_d(3.0);} Then rename each reference properly (depending on the parameter types)

Implementing Overloading : 

Chapter Eight Modern Programming Languages 12 Implementing Overloading Compilers usually implement overloading the same way: Create a set of monomorphic functions, one for each definition Invent a mangled name for each, encoding the type information Have each reference use the appropriate mangled name, depending on the parameter types

Example: C++ Implementation : 

Chapter Eight Modern Programming Languages 13 Example: C++ Implementation int shazam(int a, int b) {return a+b;}double shazam(double a, double b) {return a+b;} shazam__Fii: lda $30,-32($30) .frame $15,32,$26,0 … shazam__Fdd: lda $30,-32($30) .frame $15,32,$26,0 … C++: Assembler:

Outline : 

Chapter Eight Modern Programming Languages 14 Outline Overloading Parameter coercion Parametric polymorphism Subtype polymorphism Definitions and classifications

Coercion : 

Chapter Eight Modern Programming Languages 15 Coercion A coercion is an implicit type conversion, supplied automatically even if the programmer leaves it out double x;x = (double) 2;double x;x = 2; Explicit type conversion in Java: Coercion in Java:

Parameter Coercion : 

Chapter Eight Modern Programming Languages 16 Parameter Coercion Languages support different coercions in different contexts: assignments, other binary operations, unary operations, parameters… When a language supports coercion of parameters on a function call (or of operands when an operator is applied), the resulting function (or operator) is polymorphic

Example: Java : 

Chapter Eight Modern Programming Languages 17 Example: Java void f(double x) { … } f((byte) 1); f((short) 2);f('a'); f(3); f(4L); f(5.6F); This f can be called with any typeof parameter Java is willing tocoerce to type double

Defining Coercions : 

Chapter Eight Modern Programming Languages 18 Defining Coercions Language definitions often take many pages to define exactly which coercions are performed Some languages, especially some older languages like Algol 68 and PL/I, have very extensive powers of coercion Some, like ML, have none Most, like Java, are somewhere in the middle

Example: Java : 

Chapter Eight Modern Programming Languages 19 Example: Java 5.6.1 Unary Numeric Promotion Some operators apply unary numeric promotion to a single operand, which must produce a value of a numeric type: If the operand is of compile-time type byte, short, or char, unary numeric promotion promotes it to a value of type int by a widening conversion (§5.1.2). Otherwise, a unary numeric operand remains as is and is not converted. Unary numeric promotion is performed on expressions in the following situations: the dimension expression in array creations (§15.9); the index expression in array access expressions (§15.12); operands of the unary operators plus + (§15.14.3) and minus - (§15.14.4) ... The Java Language SpecificationJames Gosling, Bill Joy, Guy Steele

Coercion and Overloading: Tricky Interactions : 

Chapter Eight Modern Programming Languages 20 Coercion and Overloading: Tricky Interactions There are potentially tricky interactions between overloading and coercion Overloading uses the types to choose the definition Coercion uses the definition to choose a type conversion

Example : 

Chapter Eight Modern Programming Languages 21 Example Suppose that, like C++, a language is willing to coerce char to int or to double Which square gets called for square('a') ? int square(int x) { return x*x;} double square(double x) { return x*x;}

Example : 

Chapter Eight Modern Programming Languages 22 Example Suppose that, like C++, a language is willing to coerce char to int Which f gets called for f('a', 'b') ? void f(int x, char y) { …} void f(char x, int y) { …}

Outline : 

Chapter Eight Modern Programming Languages 23 Outline Overloading Parameter coercion Parametric polymorphism Subtype polymorphism Definitions and classifications

Parametric Polymorphism : 

Chapter Eight Modern Programming Languages 24 Parametric Polymorphism A function exhibits parametric polymorphism if it has a type that contains one or more type variables A type with type variables is a polytype Found in languages including ML, C++ and Ada

Example: C++ Function Templates : 

Chapter Eight Modern Programming Languages 25 Example: C++ Function Templates template<class X> X max(X a, X b) { return a>b ? a : b; } void g(int a, int b, char c, char d) { int m1 = max(a,b); char m2 = max(c,d); } Note that > can be overloaded, so X is not limited to types for which > is predefined.

Example: ML Functions : 

Chapter Eight Modern Programming Languages 26 Example: ML Functions - fun identity x = x; val identity = fn : 'a -> 'a - identity 3; val it = 3 : int - identity "hello"; val it = "hello" : string - fun reverse x = = if null x then nil = else (reverse (tl x)) @ [(hd x)]; val reverse = fn : 'a list -> 'a list

Implementing Parametric Polymorphism : 

Chapter Eight Modern Programming Languages 27 Implementing Parametric Polymorphism One extreme: many copies Create a set of monomorphic implementations, one for each type parameter the compiler sees May create many similar copies of the code Each one can be optimized for individual types The other extreme: one copy Create one implementation, and use it for all True universal polymorphism: only one copy Can’t be optimized for individual types Many variations in between

Outline : 

Chapter Eight Modern Programming Languages 28 Outline Overloading Parameter coercion Parametric polymorphism Subtype polymorphism Definitions and classifications

Subtype Polymorphism : 

Chapter Eight Modern Programming Languages 29 Subtype Polymorphism A function or operator exhibits subtype polymorphism if one or more of its parameter types have subtypes Important source of polymorphism in languages with a rich structure of subtypes Especially object-oriented languages: we’ll see more when we look at Java

Example: Pascal : 

Chapter Eight Modern Programming Languages 30 Example: Pascal type Day = (Mon, Tue, Wed, Thu, Fri, Sat, Sun); Weekday = Mon..Fri; function nextDay(D: Day): Day; begin if D=Sun then nextDay:=Mon else nextDay:=D+1 end; procedure p(D: Day; W: Weekday); begin D := nextDay(D); D := nextDay(W) end; Subtype polymorphism: nextDay can be called with a subtype parameter

Example: Java : 

Chapter Eight Modern Programming Languages 31 Example: Java class Car { void brake() { … }}class ManualCar extends Car { void clutch() { … }} void g(Car z) { z.brake();} void f(Car x, ManualCar y) { g(x); g(y);} A subtype of Car is ManualCar Function g has an unlimited number of types—one for every class we define that is a subtype of Car That’s subtype polymorphism

More Later : 

Chapter Eight Modern Programming Languages 32 More Later We’ll see more about subtype polymorphism when we look at object-oriented languages

Outline : 

Chapter Eight Modern Programming Languages 33 Outline Overloading Parameter coercion Parametric polymorphism Subtype polymorphism Definitions and classifications

Polymorphism : 

Chapter Eight Modern Programming Languages 34 Polymorphism We have seen four kinds of polymorphic functions There are many other uses of polymorphic: Polymorphic variables, classes, packages, languages Another name for runtime method dispatch: when x.f() may call different methods depending on the runtime class of the object x Used in many other sciences No definition covers all these uses, except the basic Greek: many forms Here are definitions that cover our four…

Definitions For Our Four : 

Chapter Eight Modern Programming Languages 35 Definitions For Our Four A function or operator is polymorphic if it has at least two possible types It exhibits ad hoc polymorphism if it has at least two but only finitely many possible types It exhibits universal polymorphism if it has infinitely many possible types

Overloading : 

Chapter Eight Modern Programming Languages 36 Overloading Ad hoc polymorphism Each different type requires a separate definition Only finitely many in a finite program

Parameter Coercion : 

Chapter Eight Modern Programming Languages 37 Parameter Coercion Ad hoc polymorphism As long as there are only finitely many different types can be coerced to a given parameter type

Parametric Polymorphism : 

Chapter Eight Modern Programming Languages 38 Parametric Polymorphism Universal polymorphism As long as the universe over which type variables are instantiated is infinite

Subtype Polymorphism : 

Chapter Eight Modern Programming Languages 39 Subtype Polymorphism Universal As long as there is no limit to the number of different subtypes that can be declared for a given type True for all class-based object-oriented languages, like Java

Slide 40: 

Chapter Eight Modern Programming Languages 40