Rainer Grimm, “Functional Programming in C++11”

An Overview
▪ Programming in a
functional style
▪ Why functional
programming?
▪ What is functional
programming?
▪ Characteristics of
functional programming
▪ What's missing?

Functional in C++
▪ Automatic type deduction
for ( auto v: myVec ) std::cout << v << " ";
▪ Lambda-functions
int a= 2000, b= 11;
auto sum= std::async( [=]{return a+b;});
▪ Partial function application
std::function and std::bind
lambda-functions and auto
Haskell Curry Moses Schönfinkel

Functional in C++
▪ Higher-order functions
std::vec<int> vec{1,2,3,4,5,6,7,8,9};
std::for_each(vec.begin(),vec.end(), [ ] (int& v) { v+= 10 });
std::for_each( vec.begin(),vec.end(),
[ ] (int v){ cout << " " << v } );
11 12 13 14 15 16 17 18 19
▪ Generic Programming (Templates)
▪ Standard Template Library
▪ Template Metaprogramming
Alexander Stepanov

Why functional?
▪ More effective use of the Standard Template Library
std::accumulate(vec.begin(),vec.end(),
" "[](int a, int b){return a+b;});
▪ Recognizing functional patterns
template <int N>
struct Fac{ static int const val= N * Fac<N-1>::val; };
template <>
struct Fac<0>{ static int const val= 1; };
▪ Better programming style
▪ reasoning about side effects
▪ more concise

Functional programming?
▪ Functional programming is programming with mathematical
functions.
▪ Mathematical functions are functions that each time return the
same value when given the same arguments (referential
transparency).
▪ Consequences:
▪ Functions are not allowed to have side effects.
▪ The function invocation can be replaced by the result,
rearranged or given to an other thread.
▪ The program flow will be driven by the data dependencies.

Characteristics
Characteristics of
functional
programing
First-class
functions
Higher-order
functions
Immutable data
Pure functionsRecursion
Manipulation
of lists
Lazy evaluation

First-class functions
▪ First-class functions are first-class
citizens.
Functions are like data.
▪ Functions
▪ can be passed as arguments to
other functions.
▪ can be returned from other
functions.
▪ can be assigned to variables or
stored in a data structure.

First-class functions
std::map<const char,function< double(double,double)> > tab;
tab.insert(std::make_pair('+',[](double a,double b){return a + b;}));
tab.insert(std::make_pair('-',[](double a,double b){return a - b;}));
tab.insert(std::make_pair('*',[](double a,double b){return a * b;}));
tab.insert(std::make_pair('/',[](double a,double b){return a / b;}));
cout << "3.5+4.5= " << tab['+'](3.5,4.5) << endl; 8
cout << "3.5*4.5= " << tab['*'](3.5,4.5) << endl; 15.75
tab.insert(std::make_pair('^',
[](double a,double b){return std::pow(a,b);}));
cout << "3.5^4.5= " << tab['^'](3.5,4.5) << endl; 280.741

Higher-order functions
Higher-order functions are functions that accept other functions
as argument or return them as result.
▪ The three classics:
▪ map:
Apply a function to each element of
a list.
▪ filter:
Remove elements from a list.
▪ fold:
Reduce a list to a single value by successively applying a
binary operation.
(source: http://musicantic.blogspot.de, 2012-10-16)

▪ Each programming language supporting programming in a
functional style offers map, filter and fold.
▪ map, filter and fold are 3 powerful functions which are applicable in
many cases.
map + reduce= MapReduce
Haskell Python C++
map map std::transform
filter filter std::remove_if
fold* reduce std::accumulate

▪ Lists and vectors:
▪ Haskell
vec= [1 . . 9]
str= ["Programming","in","a","functional","style."]
▪ Python
vec=range(1,10)
str=["Programming","in","a","functional","style."]
▪ C++
std::vector<int> vec{1,2,3,4,5,6,7,8,9}
std::vector<string>str{"Programming","in","a","functional",
"style."}
The results will be displayed in Haskell or Python notation.

Higher-order functions: map
▪ Haskell
map(a → a^2) vec
map(a -> length a) str
▪ Python
map(lambda x : x*x , vec)
map(lambda x : len(x),str)
▪ C++
std::transform(vec.begin(),vec.end(),vec.begin(),
" "[](int i){ return i*i; });
std::transform(str.begin(),str.end(),back_inserter(vec2),
" "[](std::string s){ return s.length(); });
[1,4,9,16,25,36,49,64,81]
[11,2,1,10,6]

Higher-order functions: filter
▪ Haskell
filter(x-> x<3 || x>8) vec
filter(x → isUpper(head x)) str
▪ Python
filter(lambda x: x<3 or x>8 , vec)
filter(lambda x: x[0].isupper(),str)
▪ C++
auto it= std::remove_if(vec.begin(),vec.end(),
[](int i){ return !((i < 3) or (i > 8)) });
auto it2= std::remove_if(str.begin(),str.end(),
" "[](string s){ return !(isupper(s[0])); });
[1,2,9]
[“Programming”]

Higher-order functions: fold
▪ Haskell:
foldl (a b → a * b) 1 vec
foldl (a b → a ++ ":" ++ b ) "" str
▪ Python:
reduce(lambda a , b: a * b, vec, 1)
reduce(lambda a, b: a + b, str,"")
▪ C++:
std::accumulate(vec.begin(),vec.end(),1,
" " [](int a, int b){ return a*b; });
std::accumulate(str.begin(),str.end(),string(""),
" "[](string a,string b){ return a+":"+b; });
362800
“:Programming:in:a:functional:style.”

Higher-order functions: fold
std::vector<int> v{1,2,3,4};
std::accumulate(v.begin(),v.end(),1,[](int a, int b){return a*b;});
1 * { 1 , 2 , 3 , 4 }
1 * 1
=
1 * 2
=
2 * 3
=
6 * 4 = 24

Immutable data
Data are immutable in pure functional languages.
Distinction between variables and values
▪ Consequences
▪ There is no
▪ Assignment: x= x + 1, ++x
▪ Loops: for, while , until
▪ In case of data modification
▪ changed copies of the data will be generated.
▪ the original data will be shared.
Immutable data are thread safe.

Immutable data
• Haskell
qsort [] = []
qsort (x:xs) = qsort [y | y <- xs, y < x] ++ [x] ++ qsort [y | y <- xs, y >= x]
• C++
void quickSort(int arr[], int left, int right) {
int i = left, j = right;
int tmp;
int pivot = arr[abs((left + right) / 2)];
while (i <= j) {
while (arr[i] < pivot) i++;
while (arr[j] > pivot) j--;
if (i <= j) {
tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
i++; j--;
}
}
if (left < j) quickSort(arr,left,j);
if (i < right) quickSort(arr,i,right);
}

Pure functions
▪ Advantages
▪ Correctness of the code is easier to verify.
▪ Refactor and test is possible
▪ Saving results of pure function invocations.
▪ Reordering pure function invocations or performing them on other
threads.
Pure functions Impure functions
Always produce the same result
when given the same parameters.
May produce different results for the
same parameters.
Never have side effects. May have side effects.
Never alter state. May alter the global state of the
program, system, or world.

Pure functions
▪ Monads are the Haskell solution to deal with the impure world.
▪ A Monad
▪ encapsulates the impure world.
▪ is a imperative subsystem in.
▪ represents a computation structure.
▪ define the composition of computations.
▪ Examples:
▪ I/O monad for input and output
▪ Maybe monad for computations that can fail
▪ List monad for computations with zero or more valid answers
▪ State monad for stateful computation
▪ STM monad for software transactional memory

Recursion
▪ Recursion is the control structure in functional programming.
▪ A loop (for int i=0; i <= 0; ++i) needs a variable i.
Recursion combined with list processing is a powerful pattern in
functional languages.

Recursion
▪ Haskell:
fac 0= 1
fac n= n * fac (n-1)
▪ C++:
template<int N>
struct Fac{
static int const value= N * Fac<N-1>::value;
};
template <>
struct Fac<0>{
static int const value = 1;
};
fac(5) == Fac<5>::value == 120

List processing
▪ LISt Processing is the characteristic for functional programming:
▪ transforming a list into another list
▪ reducing a list to a value
▪ The functional pattern for list processing:
1. Processing the head (x) of the list
2. Recursively processing the tail (xs) of the list => Go to step 1).
mySum [] = 0
mySum (x:xs) = x + mySum xs
mySum [1,2,3,4,5] 15
myMap f [] = []
myMap f (x:xs)= f x: myMap f xs
myMap (x → x*x)[1,2,3] [1,4,9]

List processing
template<int ...> struct mySum;
template<>struct
mySum<>{
static const int value= 0;
};
template<int i, int ... tail> struct
mySum<i,tail...>{
static const int value= i + mySum<tail...>::value;
};
int sum= mySum<1,2,3,4,5>::value; sum == 15

List processing
▪ The key idea behind list processing is pattern matching.
▪ First match in Haskell
mult n 0 = 0
mult n 1 = n
mult n m = (mult n (m – 1)) + n
mult 3 2 = (mult 3 (2 – 1)) + 3
= (mult 3 1 ) + 3
= 3 + 3
= 6
▪ Best match in C++11
template < int N1, int N2 > class Mult { … };
template < int N1 > class Mult <N1,1> { … };
template < int N1 > class Mult <N1,0> { … };

Lazy Evaluation
▪ Evaluate only, if necessary.
▪ Haskell is lazy
length [2+1, 3*2, 1/0, 5-4]
▪ C++ is eager
int onlyFirst(int a, int){ return a; }
onlyFirst(1,1/0);
▪ Advantages:
▪ Saving time and memory usage
▪ Working with infinite data structures

Lazy Evaluation
▪ Haskell
successor i= i: (successor (i+1))
take 5 ( successor 10 ) [10,11,12,13,14]
odds= takeWhile (< 1000) . filter odd . map (^2)
[1..]= [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 ... Control-C
odds [1..] [1,9,25, … , 841,961]
▪ Special case in C++: short circuit evaluation
if ( true or (1/0) ) std::cout << "short circuit evaluation in C++n";

What's missing?
▪ List comprehension: Syntactic sugar for map and filter
▪ Like mathematic
{ n*n | n e N , n mod 2 = 0 } : Mathematik
[n*n | n <- [1..], n `mod` 2 == 0 ] : Haskell
▪ Python
[n for n in range(8)] [0,1,2,3,4,5,6,7]
[n*n for n in range(8)] [0,1,4,9,16,25,36,49]
[n*n for n in range(8) if n%2 == 0] [0,4,16,36]

What's missing?
Function composition: fluent interface
▪ Haskell
(reverse . sort)[10,2,8,1,9,5,3,6,4,7]
[10,9,8,7,6,5,4,3,2,1]
isTit (x:xs)= isUpper x && all isLower xs
sorTitLen= sortBy(comparing length).filter isTit . words
sorTitLen “A Sentence full of Titles .“
[“A“,“Titles“,“Sentence“]

25.10.2014 | Metrax GmbH | Seite 30
Rainer Grimm
www.primedic.com
phone +49 (0)741 257-245
rainer.grimm@primedic.com

Rainer Grimm, “Functional Programming in C++11”

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