Functional Structures in PHP

{unctionalStructures
byMarcelloDuarte
@_md
f inPHP

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Expressinganything

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categorytheory
somecoolstructures
somearrows
somelaws
{

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A B
"PHPBenelux" 10

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A B
"PHPBenelux"
f
10

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github.com/phunkie/phunkie

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SEMIGROUPS
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https://upload.wikimedia.org/wikipedia/commons/c/c2/Falkland_Islands_Penguins_40.jpg

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combine(1, 2) == 3;
combine("a", "b") == "ab";
combine(true, false) == false;

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$f = function(string $a): int {
return strlen($a);
};

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return strlen($a);
};
$g = function(int $b): bool {
return $b % 2 === 0;
};

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return strlen($a);
};
$g = function(int $b): bool {
return $b % 2 === 0;
};
$h = combine($f, g);
$h("PHPBenelux") == true;

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combine($f, g) == compose ($f, $g)
// if $f and $g are functions

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compose ("strlen", odd, Option, ...)

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combine(combine(1, 2), 3) == combine(1, combine(2, 3))
associativity

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MONOIDS
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$identity = function ($x) {
return $x;
};
A
"PHPBenelux"
i

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zero(42) == 0;
zero("any string") == "";
zero(true, false) == true;

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combine(combine(1, 2), 3) == combine(1, combine(2, 3))
combine(zero($x), $x) == $x
combine($x, zero($x)) == $x
associativity
(left and right) identity

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interface Monoid extends Semigroup { 
public function zero();
// inherited from Semigroup
public function combine($another);
}

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interface Monoid extends Semigroup { 
public function zero();
// inherited from Semigroup
public function combine($another);
}
class Balance implements Monoid { // ... }

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$deposit100bucks = function(Balance $b) {
return $b->plus(100);
} 
 
$listOfBalances->foldMap($deposit100bucks);

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FUNCTORS
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https://upload.wikimedia.org/wikipedia/commons/3/3b/World_Map_1689.JPG

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givemeaword "cabuzle"

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proper
first-order{

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givemealist alistofwhat?

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ImmList(1,2,3)
// List<Int> 
ImmList("a thing", "another thing")
// List<String>

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abstract class Option {}
class Some extends Option {}
class None extends Option {}

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phunkie > Option(42)
$var0: Option<Int> = Some(42)
phunkie > Option(null)
$var1: None = None

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phunkie > $f = compose(mayBeRubish, Option) 
phunkie > $f(42)
$var0: None = None

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proper
first-order
higherorder
{

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function fmap(Mappable $mappable, callable $f) {
return $mappable->map($f);
}

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$listOfWords = ImmList("guacamole", "nose", "penguin");
$lengths = fmap ("strlen") ($listOfWords);
// List (9, 4, 7)

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$maybeSomeGuaca = Option("guacamole");
$length = fmap ("strlen") ($maybeSomeGuaca);
// Some (9)

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$maybeSomeGuaca = Option("guacamole");
$length = fmap ("strlen") ($maybeSomeGuaca);
// Some (9)
$maybeSomeGuaca = Option(null);
$length = fmap ("strlen") ($maybeSomeGuaca); 
 
// None

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// Already Mappable in Phunkie
ImmList
Option
Function1
Validations (Either)
// Planned
ImmMap
ImmSet
Tuples (inc. Pair)

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$fa == fmap(identity)($fa)
fmap(compose($f, $g))($fa) == fmap($g)(fmap($f)($fa))
covariant identity
covariant composition

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APPLICATIVE
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https://upload.wikimedia.org/wikipedia/commons/5/5c/Brick_and_block_laying.jpg

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interface Apply extends Functor 
{
public function apply($ff); 
public function map2($fb, callable $f); 
}
interface Applicative extends Apply 
{ 
public function pure($a); 
}

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/**
* @param A $a
* @return FirstOrderKind<A>
*/
function pure($a)

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/**
* @param A $a
*/
function pure($a)
Option()->pure(42);
// Some(42)

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/**
* @param A $a
*/
function pure($a)
Option()->pure(42);
// Some(42)
ImmList()->pure(42);
// ImmList(42)

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/**
* @param FirstOrderKind<callable<A,B>> $ff
* @return FirstOrderKind
*/
function apply($ff)

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/**
*/
function apply($ff)
$increment = function($x){ return $x + 1;};

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/**
*/
function apply($ff)
Some(1)->apply(Some($increment));

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/**
*/
function apply($ff)
// Some(2)

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/**
*/
function apply($ff)
// Some(2) 
None()->apply(Some($increment));

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/**
*/
function apply($ff)
// Some(2) 
None()->apply(Some($increment)); 
// None

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/**
*/
function apply($ff)
// Some(2) 
// None
ImmList(1,2,3)->apply(ImmList($increment));

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/**
*/
function apply($ff)
// Some(2) 
// None
ImmList(1,2,3)->apply(ImmList($increment)); 
// ImmList(2,3,4)

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/**
* @param FirstOrderKind $fb
* @param (A, B) => C $
* @return FirstOrderKind<C>
*/
function map2($fb, callable $f)

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/**
* @param (A, B) => C $
*/
Some(1)->map2(Some(2), function($x, $y) { return $x + $y; });;

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/**
* @param (A, B) => C $
*/
// Some(3)

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/**
* @param (A, B) => C $
*/
// Some(3) 
ImmList(1,2)->map2(ImmList(4,5),
function($x, $y) { return $x + $y; });

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/**
* @param (A, B) => C $
*/
// Some(3) 
ImmList(1,2)->map2(ImmList(4,5),
function($x, $y) { return $x + $y; }); 
// ImmList(5,6,6,7)

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$fa->apply($fa->pure(identity)) == $fa
$fa->pure($a)->fa->apply($fa->pure($f)) == 
$fa->pure($f($a))
identity
homomorphism

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$fa->pure($a)->apply == 
$fab->apply($fa->pure(function($f)use($a){return $f($a)}))
$fa->map($f) == $fa->apply($fa->pure($f))
interchange
map

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whywouldyoueveruseafunctor?

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weakertypesaremorepredictable

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$xs = fmap (ImmList(1,2,3)) ($f);
echo $xs->length;

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MONADS
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https://upload.wikimedia.org/wikipedia/commons/b/bd/Golden_tabby_and_white_kitten_n01.jpg

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interface FlatMap extends Functor 
{
public function flatMap(callable $f); 
}
interface Monad extends FlatMap 
{ 
public function flatten(); 
}

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/**
* @param (A) -> FirstOrderKind $a
*/
function flatMap($a)

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/**
*/
Option(42)->flatMap(function($x) { return Some($x + 1); });

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/**
*/
// Some(43)

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/**
*/
// Some(43)
ImmList(1,2,3)->flatMap(function($x) {
return Option($x % 2 === 0 ? null : $x); });
// ImmList(1,3)

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/**
*/
function flatten()
Some(Some(42))->flatten();
// Some(42)

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$fa->flatMap($f)->flatMap($g) == $fa->flatMap(function($a) use ($f,$g) {
return $f($a)->flatMap( function($b) use ($g) { return $g($b); } ) ;})
$fa->pure($a)->flatMap($f) == $f($a)
associativity
right and left identity
$fa->flatMap(function($a) use ($fa) { return $fa-
>pure($a); }) == $fa;

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monadsyntaxsugar

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function repl($state) 
{ 
return read()-> 
flatMap(evaluate)-> 
flatMap(andPrint)-> 
flatMap(loop) 
->run($state); 
}
def repl(state) = 
for {
(s,input) <- read 
(s,result)<- evaluate 
s <- andPrint 
s <- loop 
} yield s

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monadcomposability

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f(A $a): M 
 
g(B $b): M<C>

f(a) ~= M 
f(a) map g ~= M<M<C>>

f(a) ~= M 
f(a) map g ~= M<M<C>>
 
urgh!

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butyoucancomposethemonad’sfunctions!

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VALIDATIONS
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http://www.sbs.com.au/topics/sites/sbs.com.au.topics/ﬁles/gettyimages-470309868.jpg

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abstract class Validation {}
class Success extends Validation {}
class Failure extends Validation {}

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phunkie > Success(42)
$var0: Validation<E, Int> = Success(42)
phunkie > Failure("nay")
$var0: Validation<String, A> = Failure("nay")

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phunkie > Either("nay")(42)
$var0: Validation<E, Int> = Success(42)
phunkie > Either("nay")(null)
$var0: Validation<String, A> = Failure("nay")

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marcelloduarte
@PhunkiePhp
{

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thanks
{bit.ly/inviqa-contact bit.ly/inviqa-careers
you!

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credits
{https://upload.wikimedia.org/wikipedia/commons/3/3b/World_Map_1689.JPG
https://upload.wikimedia.org/wikipedia/commons/5/5c/Brick_and_block_laying.jpg
https://upload.wikimedia.org/wikipedia/commons/b/bd/Golden_tabby_and_white_kitten_n01.jpg

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Questions?
 
joind.in/talk/75f65
?

Functional Structures in PHP

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