generic programming in the stl and beyond david r. musser rensselaer polytechnic institute

Generic Programmingin the STL and Beyond

David R. MusserRensselaer Polytechnic Institute

Generic programming starts with algorithms

Lift

Minimal requirements: works with maximal

family of types

Concrete algorithm: requires specific data type

Less specialized: works with more

than one type

A 0

A 1

Lift

Lift

A m

Remove an unneeded

requirement on the type

Generic algorithm

. . .

Start here

Maximal with respect to what?

Lift

Maintain usefulness of the algorithm – make efficiency part of the

requirements

Concrete algorithmA 0

A 1

Lift

Lift

A mGeneric

algorithm

. . .

float max_element(float a[], int N) { if (N == 0) throw MaxElementEmptyArrayError; int first = 0; float max = a[0]; while (++first < N) if (max < a[first]) max = a[first]; return max;}

int max_element(float a[], int first, int last) { if (first == last) return first; int result = first; while (++first != last) if (a[result] < a[first]) result = first; return result;}

float_list_node* max_element(float_list_node* first, float_list_node* last) { if (first == last) return first; float_list_node* result = first; while (first->next != last) if (result->data < first->data) result = first; return result;}

int max_element(float a[], int first, int last) { if (first == last) return first; int result = first; while (++first != last) if (a[result] < a[first]) result = first; return result;}

template <typename E>int max_element(E a[], int first, int last) { if (first == last) return first; int result = first; while (++first != last) if (a[result] < a[first]) result = first; return result;}

template <typename T>T*max_element(T* first, T* last) { if (first == last) return first; T* result = first; while (++first != last) if (*result < *first) result = first; return result;}

template <typename ForwardIterator>ForwardIterator max_element(ForwardIterator first, ForwardIterator last){ if (first == last) return first; ForwardIterator result = first; while (++first != last) if (*result < *first) result = first; return result;}

int a[] = {6, 3, 7, 5};

int* ai = max_element(a, a+4);

vector<int> v(a, a+4);vector<int>::iterator vi = max_element(v.begin(), v.end());

list<int> x(a, a+4); list<int>::iterator li = max_element(x.begin(), x.end());

. . .

Forward Container

Concept

max_element

max_element

max_element

373

7

Generic algorithm

on

j kj k

k = ++j*j = 3*k = 7

++i*ii==j

What is a concept?

Concept

Intension Extension

Requirement 1

Requirement 2....Requirement N

Abstraction 1

Abstraction 2...Abstraction K...

Polygon Concept

Intension Extension

Closed plane figure

N sides

. . .

Container Concept

Intension Extension

Must be a type whose objects can store other objects (elements)

Must have an associated iterator type that can be used to iterate through the elements.

. . .

vector<T>, for any Tdeque<T> for any Tlist<T> for any Tslist<T> for any Tset<T> for any Tmap<T> for any Tself_adjusting_bag

A

Algorithm A works with every type T in concept C

Definition: an algorithm is generic if it works with every type in a concept

“works”: is correct and efficient

CT…

…

What does it mean to refine a concept?

Requirement 1Requirement 2. . .Requirement N

refine

Requirement 1Requirement 2. . .Requirement NRequirement N+1

Abstraction 1Abstraction 2. . .Abstraction K. . .

Abstraction 1

Abstraction 3. . .

. . .

Abstraction 2. . .Abstraction K. . .

More Requirements,

FewerAbstractions

Polygon Concept

Closed plane figureN sides

refine

Closed plane figureN sidesN = 3

Triangle Concept

. . .

. . .

Requirement 1Requirement 2. . .Requirement N

refine

Requirement 1Requirement 2. . .Requirement NRequirement N+1

Abstraction 1Abstraction 2. . .Abstraction K. . .

Abstraction 1

Abstraction 3. . .

. . .

Abstractionsthat remain are ones that are morespecialized.

Polygon Concept

Closed plane figureN sides

refine

Closed plane figureN sidesEqual side lengths

EquilateralPolygon Concept

. . .

. . .

Container Concept

refine

refine

refine

Forward Container

Concept

Reversible Container

Concept

Random Access Container

Concept

Forward Container Concept

Intension Extension

Container Intension

Elements must be arranged in a definite order

Iterator type must model Forward Iterator concept

. . .

vector<T> for any Tdeque<T> for any Tlist<T> for any Tslist<T> for any Tset<T> for any Tmap<T> for any T

self_adjusting_bag

Reversible Container Concept

Intension Extension

Forward Container Intension

Must have an associated reverse iterator type

Iterator and reverse iterator types must model Bidirectional Iterator concept . . .

vector<T> for any Tdeque<T> for any Tlist<T> for any T

set<T> for any Tmap<T> for any T

slist<T> for any T

Random Access Container Concept

Intension Extension

Reversible Container Intension

Iterator types must model Random Access Iterator concept . . .

vector<T> for any Tdeque<T> for any T

list<T> for any Tset<T> for any Tmap<T> for any T

A more refined conceptpermits

better algorithms

refine

A

Algorithm B can be more efficient than A

(B doesn’t have to work with as many types as A)

B

C

D

For any Polygon P

Circumference(P) =

sum = 0; for s in sides(P) sum += length(s)

For any Equilateral Polygon P

Circumference(P) =

N * side_length(P)

Container

refine

refine

refine

Forward Container



enables generic algorithms copy, equal, transform, …

enables find, merge, fill, replace, remove, unique, rotate, max_element, …

enables reverse, partition, rotate, inplace_merge, …

enables sort, binary_search, rotate random_shuffle, …

RequiresInput Iterators

Forward Iterators

Bidirectional

Iterators

Random Access Iterators

Container

refine

refine

refine

Forward Container



enables generic algorithms copy, equal, transform, …

enables find, merge, fill, replace, remove, unique, rotate, max_element, …

enables reverse, partition, rotate, inplace_merge, …

enables sort, binary_search, rotate, random_shuffle, …

RequiresInput Iterators

Forward Iterators

Bidirectional

Iterators

Random Access Iterators

Container

Forward Container



Sequence

Front InsertionSequence

Back InsertionSequence

VectorDequeSlist

List

…

Concept C

Intension Extension

A models C A is in Extension of C

A

A satisfies Intension of C (A makes R , …, R true)

R , …, R

N1

1 N

. . .

. . .

Output Iterator

Forward Iterator

Bidirectional Iterator

Random Access Iterator

Vector iterator

Input Iterator

Deque iterator

Slist iterator

List iterator

Istream iterator Ostream iterator

template <typename Iterator models Forward Iterator>Iterator max_element(Iterator first, Iterator last){ if (first == last) return first; Iterator result = first; while (++first != last) if (*result < *first) result = first; return result;}

int a[] = {6, 3, 7, 5};

int* ai = max_element(a, a+4);

vector<int> v(a, a+4);vector<int>::iterator vi = max_element(v.begin(), v.end());

list<int> x(a, a+4); list<int>::iterator li = max_element(x.begin(), x.end());

int a[] = {6, 3, 7, 5};assert int* models Forward Iterator;int* ai = max_element(a, a+4);

vector<int> v(a, a+4);assert vector<int>::iterator models Forward Iterator;vector<int>::iterator vi = max_element(v.begin(), v.end());

list<int> x(a, a+4); assert list<int>::iterator models Forward Iterator;list<int>::iterator li = max_element(x.begin(), x.end());

template <typename T models C>

Assume that T satisfies Intension of C when checking uses of T in the algorithm. We need to use both the syntactic and the semantic properties listed in the intension.

assert T models C;

Check that T satisfies Intension of C.

Should check that both the syntactic and the semantic requirements are satisfied.

What’s this aboutsemantic requirements?

template <typename ForwardIterator, typename StrictWeakOrder>ForwardIterator max_element(ForwardIterator first, ForwardIterator last, StrictWeakOrder compare){ if (first == last) return first; ForwardIterator result = first; while (++first != last) if (compare(*result,*first)) result = first; return result;}

Strict Weak Order:assumed in all STL

sorting-related algorithms

<:TTbool

Transitive[E/<]E(x,y) not(x<y) & not(y<x)

Binary Relation

for all x: not(x < x)

Irreflexive

for all x, y, z: x < y & y < z implies x < z

Transitive

Strict Partial Order

Strict Weak Order

Functor

IrreflexiveTransitiveTransitive[E/<]E(x,y) not(x<y) & not(y<x)

Strict Weak Order

for all x, y: x < y | y < x | x = y

Trichotomy

TotalOrder

Sufficient for all STL sorting-relatedgeneric algorithms

Not needed!

vector<int> v;// Put some elements in v: ... ... // Sort v into descending order:sort(v.begin(), v.end(), greater_equal<int>());

// Why doesn’t the above call// terminate?

vector<int> v;// Put some elements in v: ... ...// Sort v into descending order:sort(v.begin(), v.end(), greater<int>());

// Now we get here - that’s better!

vector<int> v;// Put some elements in v: ...// Sort v into descending order:assert greater<int> models Strict Weak Order;sort(v.begin(), v.end(), greater<int>());

Container Iterator Algorithm Functor Adaptor Allocator

STL Concepts

Container Iterator Algorithm Functor Adaptor Allocator

Boost Graph Library Concepts

Graph Visitor

BFS Visitor

DFS Visitor

Uniform Cost Visitor

See http://www.boost.org

Graph Algorithm

Graph Algorithm + Visitor = More Specialized Algorithm

Visitor

BFS Visitor

DFS Visitor

Uniform Cost Visitor

Algorithm

DFS+ topological_sort_visitor =

TopologicalSort

+ cycle_detection_visitor = Cycle Detector

Let’s summarize

Lift

Concrete algorithms

A 0

A1

Lift

Lift

Am

Generic algorithms

. .

Concept Taxonomy

Useful Data and Algorithm Abstractions – a Generic Library

C requires . . .

template <typename T models C>. . .assert T models C

Making Concepts First Class Constructs

. . . for formal checking of

syntactic and semantic

properties and using

them in software

engineering

Algorithms, Concepts & Challenges

generic programming in the stl and beyond david r. musser rensselaer polytechnic institute

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