The document discusses the concepts and principles of generic programming (GP). Some key points: - GP aims to develop reusable software libraries by categorizing abstractions into concepts and implementing generic algorithms based on concepts. - Generic libraries are reusable across user-defined types, composable by operating on types from other libraries, and efficient by having performance on par with hand-coded implementations. - The generic programming process involves lifting algorithms to higher levels of abstraction through concepts while balancing reusability and efficiency. This allows single generic algorithms to support many concrete types.

1. Generic programming
Anton.Kolotaev@gmail.com

2. Please visit:
www.generic-programming.org
www.boost.org

3. Generic Programming
• Programming paradigm for developing efficient,
reusable software libraries
• Three primary tasks:
• Categorize abstractions in a domain into
concepts
• Implement generic algorithms based on
concepts
• Build concrete models for the concepts

4. Characteristics of Generic Libraries
• Reusable: able to operate on user-defined types
• Composable: able to operate on data types
defined in another library
• Efficient: performance on par with non-generic,
hand-coded implementations

5. Generic Programming Process
1. The Generic Programming process focuses on finding
commonality among similar implementations of the same algorithm,
then providing suitable abstractions in the form of concepts so that
a single, generic algorithm can realize many concrete
implementations.
2. This process, called lifting, is repeated until the generic algorithm
has reached a suitable level of abstraction, where it provides
maximal reusability without sacrificing performance.
3. Dual to the lifting process is specialization, which synthesizes
efficient concrete implementations for particular uses of a generic
algorithm. Only by balancing the lifting and specialization processes
can we ensure that the resulting generic algorithms are both
reusable and efficient.

6. Lifting Basic Types
int sum(int* array, int n) {
int result = 0;
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;
}
float sum(float* array, int n) {
float result = 0;
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;
}
template<typename T>
T sum(T* array, int n) {
T result = 0;
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;
}

7. Lifting Basic Types
std::string concatenate(std::string* array,
int n) {
std::string result = "";
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;
}
// Requirements:
// T must have a default constructor that produces the identity value
// T must have an additive operator +
// T must have an assignment operator
// T must have a copy constructor
template<typename T>
T sum(T* array, int n) {
T result = T();
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;}

8. Lifting Containers
// Requirements:
// T must have a default constructor that produces the identity
// value
// T must have an additive operator +
// T must have an assignment operator
// T must have a copy constructor
// Container must have an indexing operator [] that returns a T
template<typename Container, typename T>
T sum(const Container& array, int n) {
T result = T();
for (int i = 0; i < n; ++i)
result = result + array[i];
return result;
}

9. Lifting Iteration
template<typename T>
struct list_node {
list_node<T>* next;
T value;
};
struct linked_list {
list_node<T>* start;
};
template<typename T>
T sum(list_node<T> list, int n) {
T result = 0;
for (list_node<T>* current = list.start;
current != NULL; current = current->next)
result = result + current->value;
return result;
}

10. Lifting Iteration
// Requirements:
// T must have an additive operator +
// T must have an assignment operator
// T must have a copy constructor
// I must have an inequality operator !=
// I must have a copy constructor
// I must have an operation next() that moves to the next value in
// the sequence
// I must have an operation get() that returns the current value (of
// type T).
template<typename I, typename T>
T sum(I start, I end, T init) {
for (I current = start; current != end; current = next(current))
init = init + get(current);
return init;
}

11. Concepts
// Requirements:
// T must have an equality operator ==
// T must have a copy constructor
// I must have an inequality operator !=
// I must have a copy constructor
// I must have an assignment operator
// I must have an operation next() that moves to the next value in
// the sequence
// I must have an operation get() that returns the current value
// (of type T).
template<typename I, typename T>
I find(I start, I end, T value) {
for (I current = start; current != end; current = next(current))
if (get(current) == value)
return current;
return end;
}

12. Concepts
Concept Requirements
CopyConstructible<T> T must have a copy constructor
Assignable<T> T must have an assignment operator
Addable<T> T must have an operator+ that takes two T values and returns a T
EqualityComparable<T> T must have an operator== comparing two Ts and returning a bool.
T must have an operator!= comparing two Ts and returning a bool.
Iterator<I, T> I must have an operator== comparing two Is and returning a bool.
I must have an operator!= comparing two Is and returning a bool.
I must have a copy constructor.
I must have an assignment operator.
I must have an operation next() that moves to the next value in the
sequence.
I must have an operation get() that returns the current value (of type T).

13. Concepts
// Requirements: Addable<T>, Assignable<T>, CopyConstructible<T>,
// Iterator<I, T>
template<typename I, typename T>
T sum(I start, I end, T init);
// Requirements: EqualityComparable<T>, Assignable<T>,
// CopyConstructible<T>, Iterator<I, T>
template<typename I, typename T>
I find(I start, I end, T value);

14. Nested Requirements
Concept Requirements
Iterator<I, T> EqualityComparable<I>, CopyConstructible<I>, Assignable<I>
I must have an operation next() that moves to the next value in the sequence.
I must have an operation get() that returns the current value (of type T).

15. Associated Types
Concept Requirements
Iterator<I> EqualityComparable<I>, CopyConstructible<I>, Assignable<I>
I must have an operation next() that moves to the next value in the sequence.
value_type is an associated type, accessible via iterator_traits<I>::value_type
I must have an operation get() that returns the current value (of type value_type).
// Requirements: Iterator<I>, Addable<value_type>,
// Assignable<value_type>, CopyConstructible<value_type>
template<typename I>
typename iterator_traits<T>::value_type
sum(I start, I end, typename iterator_traits<T>::value_type init) {
for (I current = start; current != end; current = next(current))
init = init + get(current);
return init;
}
template<typename T>
struct iterator_traits<T*> { typedef T value_type; };

16. Concept Refinement
Concept Requirements
BidirectionalIterator<I> Refines Iterator<I>
I must have an operation prev() that moves to the previous value in the
sequence.
I must have an operation set() that sets the current value.

17. Specialization
// Requirements: Polygon<P>
template<typename P>
double circumference(P p) {
double result = 0;
for (int i = 0; i < num_sides(p); ++i)
result += side_length(p, i);
return result;
}
// Requirements: EquilateralPolygon<P>
template<typename P>
double circumference(P p) {
return num_sides(p) * side_length(p, 0);
}

18. Anatomy of a Concept
A concept is a set of requirements consisting of valid expressions, associated types,
invariants, and complexity guarantees. A type that satisfies the requirements is
said to model the concept. A concept can extend the requirements of another
concept, which is called refinement.
• Valid Expressions are C++ expressions which must compile successfully for the
objects involved in the expression to be considered models of the concept.
• Associated Types are types that are related to the modeling type in that they
participate in one or more of the valid expressions. Typically associated types can be
accessed either through typedefs nested within a class definition for the modeling
type, or they are accessed through a traits class.
• Invariants are run-time characteristics of the objects that must always be true, that
is, the functions involving the objects must preserve these characteristics. The
invariants often take the form of pre-conditions and post-conditions.
• Complexity Guarantees are maximum limits on how long the execution of one of the
valid expressions will take, or how much of various resources its computation will
use.

19. Traits classes
A traits class provides a way of associating information with a compile-time
entity (a type, integral constant, or address) in non-intrusive (!!!) way
template <class T>
struct iterator_traits <T*>{
typedef random_access_iterator_tag iterator_category;
typedef T value_type;
typedef ptrdiff_t difference_type;
typedef T* pointer;
typedef T& reference;
};

20. Tag Dispatching
namespace std {
struct input_iterator_tag { };
struct bidirectional_iterator_tag : input_iterator_tag { };
struct random_access_iterator_tag : bidirectional_iterator_tag { };
template <class InputIterator, class Distance>
void advance(InputIterator& i, Distance n) {
typename iterator_traits<InputIterator>::iterator_category category;
detail::advance_dispatch(i, n, category);
}
}

21. Tag Dispatching
namespace detail {
template <class InputIterator, class Distance>
void advance_dispatch(InputIterator& i, Distance n, input_iterator_tag ) {
while (n--) ++i;
}
template <class BidirectionalIterator, class Distance>
void advance_dispatch(BidirectionalIterator& i, Distance n,
bidirectional_iterator_tag ) {
if (n >= 0)
while (n--) ++i;
else
while (n++) --i;
}
template <class RandomAccessIterator, class Distance>
void advance_dispatch(RandomAccessIterator& i, Distance n,
random_access_iterator_tag ) {
i += n;
}

22. Fragile C++ Templates
template <class InputIterator, typename T>
InputIterator find(InputIterator first, InputIterator beyond,
const T& value)
{
while (first < beyond && !(*first == value)) ++first;
return first;
};
std::vector<int> v;
find(v.begin(), v.end(), 42); // Ok
std::list<int> l;
find(l.begin(), l.end(), 42); // error

23. Concepts for C++: Goals
• Support for the core ideas of GP in C++
• Modular type checking for C++ templates
• Performance equivalence to C++ templates
• Complete backward compatibility
• Simplicity
• C++0x

24. Concepts Overview
• Concepts definitions: Specify the behaviour
of types via requirements
• Where clauses: Specify constraints on
template parameters in terms of concepts
• Concept maps: Specify how types meet the
requirements of concepts

25. Constrained Templates
• Place constraints on template parameters via a
where clause
template <typename T>
where LessThanComparable<T>
const T& min(const T& x, const T& y)
{
return x < y ? x : y;
}

26. Concept Definitions
• Concept definitions state requirements on type
parameters
concept LessThanComparable<typename T> {
bool operator < (T, T);
axiom Irreflexivity(T x) { !(x < x); }
axiom Assymetry(T x, T y) {
if (x < y) !(y < x);
}
axiom Transitivity(T x, T y, T z) {
if (x < y && y < z) x < z;
}
}

27. Member Function Requirements
concept CopyConstructable<typename T> {
T::T(T const &); // copy constructor
T::~T(); // desctructor
}

28. Iterators and Nested Requirements
concept InputIterator <typename Iter> {
Iter& operator ++ (Iter&);
Iter operator ++ (Iter&,int);
bool operator == (Iter, Iter);
bool operator != (Iter, Iter);
???? operator * (Iter);
};

29. Iterators and Nested Requirements
concept InputIterator <typename Iter> {
typename value_type;
typename difference_type;
where SignedIntergral<difference_type>;
Iter& operator ++ (Iter&);
Iter operator ++ (Iter&,int);
bool operator == (Iter, Iter);
bool operator != (Iter, Iter);
value_type operator * (Iter);
};

30. Using Associated Types
template <class Iter, typename T>
where
InputIterator<Iter> &&
EqualityComparable<InputIterator<Iter>::value_type, T>
Iter find(Iter first, Iter beyond, const T& value)
{
while (first != beyond && !(*first == value))
++first;
return first;
};

31. Concept Maps
bool contains(int const * array, int n, int value) {
return find(array, array + n, value) != array + n;
}
• Concept maps satisfy concept constraints
template <class T>
concept_map InputIterator<T*> {
typedef T value_type;
typedef ptrdiff_t difference_type;
}

32. Concept Refinement
// A bidirectional iterator can move backward
concept BidirectionalIterator<typename Iter>
: InputIterator<Iter>
{
Iter& operator -- (Iter&);
Iter operator -- (Iter&, int);
}
// A random access iterator can jump around
concept RandomIterator<typename Iter>
: BidirectionalIterator<Iter>
{
Iter operator + (Iter, difference_type);
// ...
}

33. Concept-based overloading
template <InputIterator Iter>
void advance(Iter & x, Iter::difference_type n)
{
for (; n > 0; --n) ++x; // O(n)
}
template <RandomAccessIterator Iter>
void advance(Iter & x, Iter::difference_type n)
{
x += n; // O(1)
}