speakerdeck-june11-fp-pycon2012-gavinbong.pdf

8/13/2019 speakerdeck-june11-fp-pycon2012-gavinbong.pdf

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Functional Programmingfor the Uninitiated

gavin bong

pycon asia 2012, Singaporele 7 juin 2012 2229 jeudi


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2

oadmapfunctional wayhigh order functionsrecursion

foldscurry / partial app.parser combinators

closing

30 mins

mins020208

08mins06mins03

mins

mins

mins

min01


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Purely functional is the right

default. Imperatieconstructs .. must be e!posedthrough e!plicit effects"typing

constructs.

#im $weeney%&PI' games (2006)


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*o matter what language you

wor+ in% programming in afunctional style proidesbenefits. ,ou should do itwheneer it is conenient% andyou should thin+ hard aboutthe decision when it isn-tconenient.

ohn 'armac+% I $oftware26thapril 2012


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The functional way


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$ide effectf eese immutable containe s.

ecu sion oe ite ation

i st"class functions 4 closu es.5ighe "o de functions ee ywhe e

a7y ealuation

Functional way: a cook's tour

Pu efunctions ( efe ential t anspa ency)sin(n), log2(n) 'omposable

&!ecution order insignificant

ata t ansfo mations e.g. $#

etc...


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Is python a functional language?

anonymous functions (a.+.a lambdas)map% filter% reduceite toolsfunctoolslist comp ehensions%gene ato s

It is an impe atielanguage that hasac9ui ed some functional featu es.*o


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Functional aspects #1

Immutable containe s in pythontuplef o7enset

lambdas in python a e limited to a singlee!p ession.#ypes (has+ell as a efe ence)

Patte n matching does not e!ist in python.

nli+e python% has+ell has static typechec+ing with type infe ence.sum :: (Num a) => [a] -> a


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High order functions


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In python 3.!% map etu ns an ite ato .#hus itertools.imapis emoed.

High order functions

:ccept functions as a guments and/oetu n functions.map

map(f, [a, a2]) [f(a), f(a2)]

filtefilter(predicate, [a, a2]) educeetail t eatment in upcoming slides.


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Functional aspects #2

[(!, ") for ! in !range(, #)for " in !range(#, )if "-! == $]

ist comp ehension in python

[(!, ") % ! &- [..'], " &- [#..], "-! == $]is inspi ed by has+ell;s synta!

ist comp ehension has la gelysupe ceded the utility of the filter5


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Recursion


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ecu sionunctional languages do *+ntegersum [] =sum (!:!s) =! sum !s

> has+ell


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defsum(se): ifnotse: return

else: returnse[] sum(se[:])

> python

nave sum function

#his does not wo + if you pass in anite ato (e.g. gene ato e!p ession) as thea gument. ?e will fi! this in upcomingslides.


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*


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+nteger ->+ntegersum [] acc =accsum (!:!s) acc =sum !s (! acc) > has+ell


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Bany functional languages (li+e $cheme) cansuppo t an unboundednumbe of actie tailcalls ( ecu sie o othe wise).

5as+ell being a la7y language has adiffe ent app oach.

tail ecu sion elimination

defsum(se): deftailsum(se, acc):ifnotse: returnacc else: returntailsum(se[:], se[]acc) returntailsum(se, )

Python does not perform #ail 'all 4()


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ecu sion in PythonEIn 'Python%

P efe ite ation oe ecu sion.

:oid the python stac+.# ampoline techni9ue

se co e python featu es. e.g.uiltins.sum

: t ampoline is a function e!ecuto .?o +s fo tail" ecu sie functions(and also co outines with tail"calls).:oids stac+ oe flow.


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Trampolines


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t ampoline >1t*un5 = lamdafn: lamda3args: lamda: fn(3args)

deftailsum(se, acc): it = iter(se) tr": first, rest = (ne!t(it), list(it)) e!cept 6top+teration: returnacc else: returnt*un5(tailsum)(rest, first acc)

elayed computation

#rampoline code is based on e!ample by

ames #auber FDtauber


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t ampoline >2In python 3.! (see P&P3132)% we can simplifythe code that e!t acts the head 4 tail of theite ato .deftailsum(se, acc): it = iter(se) tr": first, 3rest = it e!cept 7alue1rror: returnacc else: returnt*un5(tailsum)(rest, first acc)

>python 3


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t ampoline >3deftrampoline(ouncer): *ilecallale(ouncer): 8 s*ould e land "et9 ouncer = ouncer() returnouncer

defsum(se): returntrampoline(t*un5(tailsum)(se, ))

#rampoline code is based on e!ample by FDtauber

bounce

land

>>>sum(i fori in range(2))


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t ampoline >G

# ampoline e sion highly inefficient.

H8G secs>>>sum( i fori in!range() );'

'ompa isons of benchma +s using timeit>>>sum( i fori in!range() );'

1.66 secs

>>>sum( i fori in!range());'>>sum( i for i in!range());' has+ell

It encapsulates the ecu sie patte nofp ocessing data st uctu es (listsfo simplicity).


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fold

sum [] =sum (!:!s) =()!(sum !s) > has+ell

It encapsulates the ecu sie patte nofp ocessing data st uctu es (listsfo simplicity).

K2LMraham 5utton N : tutorial on the uniersality 4

e!pressieness of fold% 1JJJ

nie salp ope tyK2Lof thef ldope ato g [] =g (!:!s) =f!(g !s) fold f #hus% sumsimplifies to

relude>foldl () [..$]#

a ity 2initelists

It educes a list to a single alue.


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left s ight foldIn has+ell% use foldlfor folding from the left (the

start) and foldrfor folding from the right (the end).

relude> let f = (?acc ! -> acc)relude>foldl f [..$];

&!ample finding the length

f

f

f

2

f

$ left fold


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left s ight fold >2relude> let g = (?! acc -> acc)relude>foldr g [..$];

&!ample finding the length

$ g

g

2

g

g

ight fold


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fold in pythonIn python 2.!% uiltins.reduce is thepython e sion of the fold ope ato .eft 4 ight folds a e handled by same function.defre@erse(se):

defr(acc, !): acc.insert(, !) returnacc returnreduce(r, se, [])

&!ample reerse a list

et;s implement has+ell;selemusing ight fold.relude>elem 2 [..$]Aruerelude>elem [..$]Balse


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defelem(item, se):

se = re@erse(se) defmatc*(!, acc): if! == item: returnArue else:

returnacc returnreduce(lamda a, : matc*(, a), se, Balse)

&!ample has+ell;selemusing ight fold.

#he initial alue is set to Balse.#he accumulato emains Balseuntil amatch is found.


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H8G secs>>>sum(i fori in!range() )

'ompa isons of benchma +s using timeit

>>> reduce(operator.add,i fori in!range(), )

1.38msecs

>>> reduce(operator.add,i fori in!range(), )

13.6msecsH.HJmsecs

>>>sum(i for i in!range())

$imple benchma + of educe>>> importoperator


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In python 3.!% uiltins.reducehasbeen moed to functools.reduce

$ee al p ope ties of educe

reduce( lamdaa, : a % , [Arue, Balse, Balse], Balse ) 8 an"

reducedoes not sho t"ci cuitO which woulde!plain why it is slowe than the builtin an"oallfo use cases below

reduce( lamdaa, : a C , [Balse, Balse, Arue], Balse ) 8 all

5omewo +Implement map4 filterusing reduce.


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Currying &

partial application


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'u ied functions'u yingis the techni9ue of t ansfo ming afunction that ta+es multiplea guments into ..a chain of una yfunctions.&!ample cu ying functions of a ity2>>> importoperator>>> assertoperator.su(, 2)== -operator

>>> defcurr"2(f): returnlamdaa: lamda: f(a, )

>>> curriedsu = curr"2(operator.su)>>> assertcurriedsu()(2) ==-


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&!ample uncu ying functions of a ity2uncu y

>>> defuncurr"2(f): return lamda a, : f(a)()

>>> originalsu = uncurr"2(curriedsu)

>>> assertoriginalsu(, 2) ==-

:ll functions a e cu iedin 5as+ell.K1Lsutract :: (Num a) => a -> a -> a

as oppose to the uncu iedfo msutract :: (Num a) => (a, a) -> a


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Cenefits of cu ied functions?hat is the point of this E

#heo etical N able to t eat functions unifo mly.P actical N aids in the c eation of pa tiallyapplied functions.

Cind somealues to some (but not all) of thea guments of a cu ied function.Pa tial application

> has+ellg*ci> map (23) [, , 2][, 2, ;]

g*ci> map (sutract ) [, , 2][-, , ]

P&P 30J standa di7es a pa tialobDect(since python 2.).


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functools.pa tial in action>>> operator.su.docDsu(a, ) E same as a - .D>>> sutract = partial(operator.su, )>>> sutract(2) 8 e@aluat ng - 2-

>>> sutract.5e"ordsFG

>>> sutract.args(,)

'aeat $ince pe at is a ' module% you cannotbind alues to specific positionala guments.


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functools.pa tial in action >2#he limitation desc ibed in the last slide doesnot apply to use defined functions. #hus%>>> defminus(a, ): Dclone of operator.suD returna - >>> sutract2 = partial(minus, =2)>>> sutract2.5e"ordsFDD: 2G>>> sutract2.docDpartial(func, 3args, 335e"ords) ...D>>> fromfunctools importupdaterapper>>> updaterapper(sutract2, minus)>>> sutract2.docDclone of operator.suD


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miscpa tialcan be applied to classes% classmethods and instance methods.pa tialcan be used to c eate thun+s (asopposed to hand"c afted lambdas)It is o+ to imagine pe at .itemgette 4pe at .att gette as cu ied functions(although thei implementation does notmatch that mental model).


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functools.w apsP o!ying to callables fo c eating deco ato s.

In conDunction with functools.updateQw appe4 functools.pa tial% the w apped function;sQQnameQQ% QQmoduleQQandQQdocQQa ep ese ed.

e.g. Dango iew deco ato Fcs fQe!empt

&!ample deco ato to measu e unning timedefueue(fn, duration): 8 send timings as"nc*ronousl" pass


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importtimefromfunctools importrapsdeftimer(f): Hraps(f) defrapper(3args, 335args): start = time.time() f(3args, 335args) end = time.time() ueue(f.name, end E start) return rapperHtimerdefuserfunction(a, , c): pass


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functools in python 3.!functools.l uQcacheBemoi7ation deco ato that caches esultsof the w appe function.Imp oes pe fo mance of t ee ecu siefunctions e.g. fibonacci.


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Parser combinators:

a case study


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Pa se combinato s: eal wo ld application of highe o de functions.: pa se is built up f om smalle p imitie pa se s.Pa se combinato s a e Dust highe "o defunctions.

arser :: 6tring I6AJominator :: arser arser arser#hus% g amma const uction fo things li+eepetition % se9uencing o choice is modelled usingcombinato s.&!ample t iial ma athon unning timepa seusing funcpa selib.

parse(2:':2')==(2,',2')


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Pa se combinato s >2to5enie: 6tring [Ao5en]

parse: [Ao5en] tuple

>>> to5enie(D2:':2'D)[Ao5en(Dositi@e+ntegerD, D2D),Ao5en(DJolonD, D:D),

Ao5en(Dositi@e+ntegerD, D'D),Ao5en(DJolonD, D:D),Ao5en(Dositi@e+ntegerD, D2'D)]

>>> parse(to5enie(D2:':2'D))(2, ', 2')


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Pa se combinato s >3grammar = (*our colon minute colon second s5ip(finis*ed))grammar.parse(se) 8se is [Ao5en]

'omplete code at http//pastebin.com/+1Bd5$i

ma5enum = lamdan: int(n)to5@al = lamda!: !.@alue*our = some(lamda !: posint(!) and it*in(!.@alue,K))>> to5@al>> ma5enum
http://pastebin.com/k1MdUHSihttp://pastebin.com/k1MdUHSi


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#he endea ning P will ma+e you a bette(python) p og amme .#heo y$tudy 'atego y theo y4 #ype theo y.

Play with othe P languages5as+ell%

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