Polymorphism in C++

Question

AFAIK:

C++ provides three different types of polymorphism.

• Virtual functions
• Function name overloading
• Operator overloading

In addition to the above three types of polymorphism, there exist other kinds of polymorphism:

• run-time
• compile-time
• ad-hoc polymorphism
• parametric polymorphism

I know that runtime polymorphism can be achieved by virtual functions and static polymorphism can be achieved by template functions

But for the other two

• ad-hoc polymorphism
• parametric polymorphism the website says,

ad-hoc polymorphism:

If the range of actual types that can be used is finite and the combinations must be individually specified prior to use, this is called ad-hoc polymorphism.

parametric polymorphism:

If all code is written without mention of any specific type and thus can be used transparently with any number of new types it is called parametric polymorphism.

I can hardly understand them :(

can anyone explain them both if possible with an example? I hope the answers to this questions would be helpful for many new passouts from their colleges.

Answer 1

Understanding of / requirements for polymorphism

To understand polymorphism - as the term is used in Computing Science - it helps to start from a simple test for and definition of it. Consider:

    Type1 x;
    Type2 y;

    f(x);
    f(y);

Here, f() is to perform some operation and is being given values x and y as inputs.

To exhibit polymorphism, f() must be able to operate with values of at least two distinct types (e.g. int and double), finding and executing distinct type-appropriate code.

---

C++ mechanisms for polymorphism

Explicit programmer-specified polymorphism

You can write f() such that it can operate on multiple types in any of the following ways:

• Preprocessing:

  #define f(X) ((X) += 2)
  // (note: in real code, use a longer uppercase name for a macro!)
  

• Overloading:

  void f(int& x)    { x += 2; }
  
  void f(double& x) { x += 2; }
  

• Templates:

  template <typename T>
  void f(T& x) { x += 2; }
  

• Virtual dispatch:

  struct Base { virtual Base& operator+=(int) = 0; };
  
  struct X : Base
  {
      X(int n) : n_(n) { }
      X& operator+=(int n) { n_ += n; return *this; }
      int n_;
  };
  
  struct Y : Base
  {
      Y(double n) : n_(n) { }
      Y& operator+=(int n) { n_ += n; return *this; }
      double n_;
  };
  
  void f(Base& x) { x += 2; } // run-time polymorphic dispatch
  

Other related mechanisms

Compiler-provided polymorphism for builtin types, Standard conversions, and casting/coercion are discussed later for completeness as:

• they're commonly intuitively understood anyway (warranting a "oh, that" reaction),
• they impact the threshold in requiring, and seamlessness in using, the above mechanisms, and
• explanation is a fiddly distraction from more important concepts.

Terminology

Further categorisation

Given the polymorphic mechanisms above, we can categorise them in various ways:

• When is the polymorphic type-specific code selected?

  • Run time means the compiler must generate code for all the types the program might handle while running, and at run-time the correct code is selected (virtual dispatch)
  • Compile time means the choice of type-specific code is made during compilation. A consequence of this: say a program only called f above with int arguments - depending on the polymorphic mechanism used and inlining choices the compiler might avoid generating any code for f(double), or generated code might be thrown away at some point in compilation or linking. (all mechanisms above except virtual dispatch)
    
    

• Which types are supported?

  • Ad-hoc meaning you provide explicit code to support each type (e.g. overloading, template specialisation); you explicitly add support "for this" (as per ad hoc's meaning) type, some other "this", and maybe "that" too ;-).

  • Parametric meaning you can just try to use the function for various parameter types without specifically doing anything to enable its support for them (e.g. templates, macros). An object with functions/operators that act like the template/macro expects¹ is all that template/macro needs to do its job, with the exact type being irrelevant. The "concepts" introduced by C++20 express and enforce such expectations - see cppreference page here.

    • Parametric polymorphism provides duck typing - a concept attributed to James Whitcomb Riley who apparently said "When I see a bird that walks like a duck and swims like a duck and quacks like a duck, I call that bird a duck.".

      template <typename Duck>
      void do_ducky_stuff(const Duck& x) { x.walk().swim().quack(); }
      
      do_ducky_stuff(Vilified_Cygnet());
      

  • Subtype (aka inclusion) polymorphism allows you to work on new types without updating the algorithm/function, but they must be derived from the same base class (virtual dispatch)

¹ - Templates are extremely flexible. SFINAE (see also std::enable_if) effectively allows several sets of expectations for parametric polymorphism. For example, you might encode that when the type of data you're processing has a .size() member you'll use one function, otherwise another function that doesn't need .size() (but presumably suffers in some way - e.g. using the slower strlen() or not printing as useful a message in the log). You can also specify ad-hoc behaviours when the template is instantiated with specific parameters, either leaving some parameters parametric (partial template specialisation) or not (full specialisation).

"Polymorphic"

Alf Steinbach comments that in the C++ Standard polymorphic only refers to run-time polymorphism using virtual dispatch. General Comp. Sci. meaning is more inclusive, as per C++ creator Bjarne Stroustrup's glossary (http://www.stroustrup.com/glossary.html):

polymorphism - providing a single interface to entities of different types. Virtual functions provide dynamic (run-time) polymorphism through an interface provided by a base class. Overloaded functions and templates provide static (compile-time) polymorphism. TC++PL 12.2.6, 13.6.1, D&E 2.9.

This answer - like the question - relates C++ features to the Comp. Sci. terminology.

Discussion

With the C++ Standard using a narrower definition of "polymorphism" than the Comp. Sci. community, to ensure mutual understanding for your audience consider...

• using unambiguous terminology ("can we make this code reusable for other types?" or "can we use virtual dispatch?" rather than "can we make this code polymorphic?"), and/or
• clearly defining your terminology.

Still, what's crucial to being a great C++ programmer is understanding what polymorphism's really doing for you...

    letting you write "algorithmic" code once and then apply it to many types of data

...and then be very aware of how different polymorphic mechanisms match your actual needs.

Run-time polymorphism suits:

• input processed by factory methods and spat out as an heterogeneous object collection handled via Base*s,
• implementation chosen at runtime based on config files, command line switches, UI settings etc.,
• implementation varied at runtime, such as for a state machine pattern.

When there's not a clear driver for run-time polymorphism, compile-time options are often preferable. Consider:

• the compile-what's-called aspect of templated classes is preferable to fat interfaces failing at runtime
• SFINAE
• CRTP
• optimisations (many including inlining and dead code elimination, loop unrolling, static stack-based arrays vs heap)
• __FILE__, __LINE__, string literal concatenation and other unique capabilities of macros (which remain evil ;-))
• templates and macros test semantic usage is supported, but don't artificially restrict how that support is provided (as virtual dispatch tends to by requiring exactly matching member function overrides)

Other mechanisms supporting polymorphism

As promised, for completeness several peripheral topics are covered:

• compiler-provided overloads
• conversions
• casts/coercion

This answer concludes with a discussion of how the above combine to empower and simplify polymorphic code - especially parametric polymorphism (templates and macros).

Mechanisms for mapping to type-specific operations

> Implicit compiler-provided overloads

Conceptually, the compiler overloads many operators for builtin types. It's not conceptually different from user-specified overloading, but is listed as it's easily overlooked. For example, you can add to ints and doubles using the same notation x += 2 and the compiler produces:

• type-specific CPU instructions
• a result of the same type.

Overloading then seamlessly extends to user-defined types:

std::string x;
int y = 0;

x += 'c';
y += 'c';

Compiler-provided overloads for basic types is common in high-level (3GL+) computer languages, and explicit discussion of polymorphism generally implies something more. (2GLs - assembly languages - often require the programmer to explicitly use different mnemonics for different types.)

> Standard conversions

The C++ Standard's fourth section describes Standard conversions.

The first point summarises nicely (from an old draft - hopefully still substantially correct):

-1- Standard conversions are implicit conversions defined for built-in types. Clause conv enumerates the full set of such conversions. A standard conversion sequence is a sequence of standard conversions in the following order:

• Zero or one conversion from the following set: lvalue-to-rvalue conversion, array-to-pointer conversion, and function-to-pointer conversion.

• Zero or one conversion from the following set: integral promotions, floating point promotion, integral conversions, floating point conversions, floating-integral conversions, pointer conversions, pointer to member conversions, and boolean conversions.

• Zero or one qualification conversion.

[Note: a standard conversion sequence can be empty, i.e., it can consist of no conversions. ] A standard conversion sequence will be applied to an expression if necessary to convert it to a required destination type.

These conversions allow code such as:

double a(double x) { return x + 2; }

a(3.14);
a(42);

Applying the earlier test:

To be polymorphic, [a()] must be able to operate with values of at least two distinct types (e.g. int and double), finding and executing type-appropriate code.

a() itself runs code specifically for double and is therefore not polymorphic.

But, in the second call to a() the compiler knows to generate type-appropriate code for a "floating point promotion" (Standard §4) to convert 42 to 42.0. That extra code is in the calling function. We'll discuss the significance of this in the conclusion.

> Coercion, casts, implicit constructors

These mechanisms allow user-defined classes to specify behaviours akin to builtin types' Standard conversions. Let's have a look:

int a, b;

if (std::cin >> a >> b)
    f(a, b);

Here, the object std::cin is evaluated in a boolean context, with the help of a conversion operator. This can be conceptually grouped with "integral promotions" et al from the Standard conversions in the topic above.

Implicit constructors effectively do the same thing, but are controlled by the cast-to type:

f(const std::string& x);
f("hello");  // invokes `std::string::string(const char*)`

Implications of compiler-provided overloads, conversions and coercion

Consider:

void f()
{
    typedef int Amount;
    Amount x = 13;
    x /= 2;
    std::cout << x * 1.1;
}

If we want the amount x to be treated as a real number during the division (i.e. be 6.5 rather than rounded down to 6), we only need change to typedef double Amount.

That's nice, but it wouldn't have been too much work to make the code explicitly "type correct":

void f()                               void f()
{                                      {
    typedef int Amount;                    typedef double Amount;
    Amount x = 13;                         Amount x = 13.0;
    x /= 2;                                x /= 2.0;
    std::cout << double(x) * 1.1;          std::cout << x * 1.1;
}                                      }

But, consider that we can transform the first version into a template:

template <typename Amount>
void f()
{
    Amount x = 13;
    x /= 2;
    std::cout << x * 1.1;
}

It's due to those little "convenience features" that it can be so easily instantiated for either int or double and work as intended. Without these features, we'd need explicit casts, type traits and/or policy classes, some verbose, error-prone mess like:

template <typename Amount, typename Policy>
void f()
{
    Amount x = Policy::thirteen;
    x /= static_cast<Amount>(2);
    std::cout << traits<Amount>::to_double(x) * 1.1;
}

So, compiler-provided operator overloading for builtin types, Standard conversions, casting / coercion / implicit constructors - they all contribute subtle support for polymorphism. From the definition at the top of this answer, they address "finding and executing type-appropriate code" by mapping:

• "away" from parameter types

  • from the many data types polymorphic algorithmic code handles

  • to code written for a (potentially lesser) number of (the same or other) types.

• "to" parametric types from values of constant type

They do not establish polymorphic contexts by themselves, but do help empower/simplify code inside such contexts.

You may feel cheated... it doesn't seem like much. The significance is that in parametric polymorphic contexts (i.e. inside templates or macros), we're trying to support an arbitrarily large range of types but often want to express operations on them in terms of other functions, literals and operations that were designed for a small set of types. It reduces the need to create near-identical functions or data on a per-type basis when the operation/value is logically the same. These features cooperate to add an attitude of "best effort", doing what's intuitively expected by using the limited available functions and data and only stopping with an error when there's real ambiguity.

This helps limit the need for polymorphic code supporting polymorphic code, drawing a tighter net around the use of polymorphism so localised use doesn't force widespread use, and making the benefits of polymorphism available as needed without imposing the costs of having to expose implementation at compile time, have multiple copies of the same logical function in the object code to support the used types, and in doing virtual dispatch as opposed to inlining or at least compile-time resolved calls. As is typical in C++, the programmer is given a lot of freedom to control the boundaries within which polymorphism is used.