Functional Programming You Already Know

Functional
Programming
You
Already
Know
@KevlinHenney

functional
programming
higher-order functions
recursion
statelessness
first-class functions
immutability
pure functions
unification
declarative
pattern matching
non-strict evaluation
idempotence
lists
mathematics
lambdas
currying
monads

Excel is the world's
most popular
functional language.
Simon Peyton Jones

To iterate is human,
to recurse divine.
L Peter Deutsch

int factorial(int n)
{
int result = 1;
while(n > 1)
result *= n--;
return result;
}

{
if(n > 1)
return n * factorial(n - 1);
else
return 1;
}

{
return
n > 1
? n * factorial(n - 1)
: 1;
}

n! =
1
(n – 1)!  n
if n = 0,
if n > 0.{

#include <stdio.h>
/* printd: print n in decimal */
void printd(int n)
{
if (n < 0) {
putchar('-');
n = -n;
}
if (n / 10)
printd(n / 10);
putchar(n % 10 + '0');
}

/* grep: search for regexp in file */
int grep(char *regexp, FILE *f, char *name)
{
int n, nmatch;
char buf[BUFSIZ];
nmatch = 0;
while (fgets(buf, sizeof buf, f) != NULL) {
n = strlen(buf);
if (n > 0 && buf[n-1] == 'n')
buf[n-1] = '0';
if (match(regexp, buf)) {
nmatch++;
if (name != NULL)
printf("%s:", name);
printf("%sn", buf);
}
}
return nmatch;
}
/* matchhere: search for regexp at beginning of text */
int matchhere(char *regexp, char *text)
{
if (regexp[0] == '0')
return 1;
if (regexp[1] == '*')
return matchstar(regexp[0], regexp+2, text);
if (regexp[0] == '$' && regexp[1] == '0')
return *text == '0';
if (*text!='0' && (regexp[0]=='.' || regexp[0]==*text))
return matchhere(regexp+1, text+1);
return 0;
}
/* match: search for regexp anywhere in text */
int match(char *regexp, char *text)
{
if (regexp[0] == '^')
return matchhere(regexp+1, text);
do { /* must look even if string is empty */
if (matchhere(regexp, text))
return 1;
} while (*text++ != '0');
return 0;
}
/* matchstar: search for c*regexp at beginning of text */
int matchstar(int c, char *regexp, char *text)
{
do { /* a * matches zero or more instances */
if (matchhere(regexp, text))
return 1;
} while (*text != '0' && (*text++ == c || c == '.'));
return 0;
}

http://www.adampetersen.se/articles/fizzbuzz.htm

int atexit(void (*func)(void));

void qsort(
void *base,
size_t nmemb, size_t size,
int (*compar)(
const void *, const void *));

void (*signal(
int sig, void (*func)(int)))(int);

One of the most powerful mechanisms
for program structuring [...] is the block
and procedure concept.
A procedure which is capable of giving
rise to block instances which survive its
call will be known as a class; and the
instances will be known as objects of
that class.
A call of a class generates a new object
of that class.
Ole-Johan Dahl and C A R Hoare
"Hierarchical Program Structures"

public class HeatingSystem {
public void turnOn() 
public void turnOff() 

}
public class Timer {
public Timer(TimeOfDay toExpire, Runnable toDo) 
public void run() 
public void cancel() 

}

Timer on =
new Timer(
timeToTurnOn,
new Runnable() {
public void run() {
heatingSystem.turnOn();
}
});
Timer off =
new Timer(
timeToTurnOff,
new Runnable() {
public void run() {
heatingSystem.turnOff();
}
});

class Timer
{
public:
Timer(TimeOfDay toExpire, function<void()> toDo);
void run();
void cancel();
...
};

Timer on(
timeOn,
bind(&HeatingSystem::turnOn, &heatingSystem));
Timer off(
timeOff,
bind(&HeatingSystem::turnOff, &heatingSystem));

public class Timer
{
public Timer(TimeOfDay toExpire, Action toDo) ...
public void Run() ...
public void Cancel() ...
...
}

Timer on = new Timer(timeOn, heatingSystem.TurnOn);
Timer off = new Timer(timeOff, heatingSystem.TurnOff);

Timer on =
new Timer(timeOn, () => heatingSystem.TurnOn());
Timer off =
new Timer(timeOff, () => heatingSystem.TurnOff());

William Cook, "On Understanding Data Abstraction, Revisited"

newStack =
  (let items = ref() 
{
isEmpty =   #items = 0,
depth =   #items,
push =  x  items := xˆitemsy  y  0...#items,
top =   items0
})

var newStack = function() {
var items = []
return {
isEmpty: function() {
return items.length === 0
},
depth: function() {
return items.length
},
push: function(newTop) {
items = items.unshift(newTop)
},
top: function() {
return items[0]
}
}
}

intension, n. (Logic)
 the set of characteristics or properties by which
the referent or referents of a given expression is
determined; the sense of an expression that
determines its reference in every possible world,
as opposed to its actual reference. For example,
the intension of prime number may be having
non-trivial integral factors, whereas its extension
would be the set {2, 3, 5, 7, ...}.
E J Borowski and J M Borwein
Dictionary of Mathematics

A list comprehension is a syntactic
construct available in some programming
languages for creating a list based on
existing lists. It follows the form of the
mathematical set-builder notation (set
comprehension) as distinct from the use of
map and filter functions.
http://en.wikipedia.org/wiki/List_comprehension

{ 2  x | x  , x > 0 }

(2 * x for x in count() if x > 0)

{ x | x  , x > 0  x mod 2 = 0 }

(x for x in count() if x > 0 and x % 2 == 0)

Concatenative programming is so called
because it uses function composition instead of
function application—a non-concatenative
language is thus called applicative.
Jon Purdy
http://evincarofautumn.blogspot.in/2012/02/
why-concatenative-programming-matters.html

This is the basic reason Unix pipes are so
powerful: they form a rudimentary string-based
concatenative programming language.
Jon Purdy
http://evincarofautumn.blogspot.in/2012/02/
why-concatenative-programming-matters.html

Some people, when confronted with a
problem, think, "I know, I'll use threads,"
and then two they hav erpoblesms.
Ned Batchelder
https://twitter.com/nedbat/status/194873829825327104

public final class Date implements ... {
...
public int getYear() ...
public int getMonth() ...
public int getDayInMonth() ...
public void setYear(int newYear) ...
public void setMonth(int newMonth) ...
public void setDayInMonth(int newDayInMonth) ...
...
}

...
public int getWeekInYear() ...
public int getDayInYear() ...
public int getDayInWeek() ...
public void setYear(int newYear) ...
public void setMonth(int newMonth) ...
public void setWeekInYear(int newWeek) ...
public void setDayInYear(int newDayInYear) ...
public void setDayInMonth(int newDayInMonth) ...
public void setDayInWeek(int newDayInWeek) ...
...
}

...
public int getWeekInYear() ...
public int getDayInYear() ...
public int getDayInWeek() ...
...
}

When it is not
necessary to
change, it is
necessary not to
change.
Lucius Cary

...
public int year() ...
public int month() ...
public int weekInYear() ...
public int dayInYear() ...
public int dayInMonth() ...
public int dayInWeek() ...
...
}

Immutable Value
Define a value object type
whose instances are immutable.
Copied Value
Define a value object type
whose instances are copyable.

Instead of using threads and shared memory
as our programming model, we can use
processes and message passing. Process here
just means a protected independent state
with executing code, not necessarily an
operating system process.
Languages such as Erlang (and occam before
it) have shown that processes are a very
successful mechanism for programming
concurrent and parallel systems. Such
systems do not have all the synchronization
stresses that shared-memory, multithreaded
systems have.
Russel Winder
"Message Passing Leads to Better Scalability in Parallel Systems"

OOP to me means only
messaging, local retention
and protection and hiding of
state-process, and extreme
late-binding of all things.
Alan Kay

The makefile language is similar to
declarative programming. This class
of language, in which necessary end
conditions are described but the
order in which actions are to be
taken is not important, is sometimes
confusing to programmers used to
imperative programming.
http://en.wikipedia.org/wiki/Make_(software)

SELECT time, speaker, title
FROM Sessions
WHERE
date = '2013-06-13' AND
time >= '11:40:00'
ORDER BY time

try {
Integer.parseInt(time.substring(0, 2));
}
catch (Exception x) {
return false;
}
if (Integer.parseInt(time.substring(0, 2)) > 12) {
return false;
}
...
if (!time.substring(9, 11).equals("AM") &
!time.substring(9, 11).equals("PM")) {
return false;
}
Burk Hufnagel
"Put the Mouse Down and Step Away from the Keyboard"

public static boolean validateTime(String time) {
return time.matches("(0[1-9]|1[0-2]):[0-5][0-9]:[0-5][0-9] ([AP]M)");
}
Burk Hufnagel
"Put the Mouse Down and Step Away from the Keyboard"

$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }

echo {1..100} | tr ' ' 'n' | awk '
$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }
'

echo {1..100} | tr ' ' 'n' | awk '
$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }
' | diff - expected && echo Pass

/^1?$|^(11+?)1+$/
http://www.noulakaz.net/weblog/2007/03/18/
a-regular-expression-to-check-for-prime-numbers/
def is_prime(n)
("1" * n) !~ /^1?$|^(11+?)1+$/
end

http://xkcd.com/224/
We lost the documentation on quantum mechanics.
You'll have to decode the regexes yourself.

Functional Programming You Already Know

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