A Func’onal Introduc’on · • good but not great support for OCaml. • on the other hand,...

AFunc'onalIntroduc'on

COS326DavidWalker

PrincetonUniversityslidescopyright2013-2015DavidWalkerandAndrewW.Appel

permissiongrantedtoreusetheseslidesfornon-commercialeduca'onalpurposes

ThinkingFunc'onallyInJavaorC,youget(most)workdonebychangingsomethingInML,youget(most)workdonebyproducingsomethingnew

temp=pair.x;pair.x=pair.y;pair.y=temp; commandsmodifyorchangean

exis'ngdatastructure(likepair)

let(x,y)=pairin(y,x)

youanalyzeexis'ngdata(likepair)andyouproducenewdata(y,x)

2

Thissimpleswitchinperspec'vecanchangethewayyouthink

aboutprogrammingandproblemsolving.

3

ThinkingFunc'onally

impera'vecode:•  outputsareirrelevant!•  outputisnotfunc9onofinput•  vola9le•  unrepeatable•  parallelismhidden•  hardertotest•  hardertocompose

pure,func'onalcode:•  outputsareeverything!•  outputisfunc9onofinput•  persistent•  repeatable•  parallelismapparent•  easiertotest•  easiertocompose

temp=pair.x;pair.x=pair.y;pair.y=temp;

let(x,y)=pairin(y,x)

4

WhyOCaml?5

Small,orthogonalcorebasedonthelambdacalculus.–  Controlisbasedon(recursive)func'ons.–  Insteadoffor-loops,while-loops,do-loops,iterators,etc.

•  canbedefinedaslibraryfunc'ons.–  Makesiteasytodefineseman'cs

Supportsfirst-class,lexically-scoped,higher-orderprocedures–  a.k.a.first-classfunc'onsorclosuresorlambdas.–  first-class:func'onsaredatavalueslikeanyotherdatavalue

•  likenumbers,theycanbestored,definedanonymously,...–  lexically-scoped:meaningofvariablesdeterminedsta'cally.–  higher-order:func'onsasargumentsandresults

•  programspassedtoprograms;generatedfromprograms

ThesefeaturesalsofoundinRacket,Haskell,SML,F#,Clojure,....

WhyOCaml?6

Sta'callytyped:debuggingandtes'ngaid–  compilercatchesmanysillyerrorsbeforeyoucanrunthecode.

•  Atypeisworthathousandtests(startat6:20):–  h]ps://www.youtube.com/watch?v=q1Yi-WM7XqQ

–  Javaisalsostrongly,sta'callytyped.–  Scheme,Python,Javascript,etc.areallstrongly,dynamicallytyped–typeerrorsarediscoveredwhilethecodeisrunning.

Stronglytyped:compilerenforcestypeabstrac'on.–  cannotcastanintegertoarecord,func'on,string,etc.

•  sowecanu'lizetypesascapabili9es;crucialforlocalreasoning–  C/C++areweakly-typed(sta'callytyped)languages.Thecompilerwillhappilyletyoudosomethingsmart(moreo?enstupid).

Typeinference:compilerfillsintypesforyou

Installing,runningOcaml7

•  OCamlcomeswithcompilers:–  “ocamlc”–fastbytecodecompiler–  “ocamlopt”–op'mizing,na'vecodecompiler–  “ocamlbuild–anicewrapperthatcomputesdependencies

•  Andaninterac've,top-levelshell:–  occasionallyusefulfortryingsomethingout.–  “ocaml”attheprompt.

•  Andmanyothertools–  e.g.,debugger,dependencygenerator,profiler,etc.

•  Seethecoursewebpagesforinstalla'onpointers–  alsoOCaml.org

Edi'ngOcamlPrograms8

•  Manyop'ons:pickyourownpoison–  Emacs

•  whatI’llbeusinginclass.•  goodbutnotgreatsupportforOCaml.•  ontheotherhand,it’ss'llthebestcodeeditorI’veused

–  thatmaybebecauseI'moldandstuckinmyways:-)•  (extensionswri]eninelisp–afunc'onallanguage!)

–  OCamlIDE•  integrateddevelopmentenvironmentwri]eninOcaml.•  haven’tuseditmuch,socan’tcomment.

–  Eclipse•  I’veputupalinktoanOcamlplugin•  Ihaven'ttrieditbutothersrecommendit

–  Sublime•  Alotofstudentsseemtogravitatetothis

XKCDonEditors

9

ANINTRODUCTORYEXAMPLE(ORTWO)

10

OCamlCompilerandInterpreter•  Demo:

–  emacs–  mlfiles–  wri'ngsimpleprograms:hello.ml,sum.ml–  simpledebuggingandunittests–  ocamlccompiler

11

AFirstOCamlProgram

hello.ml:

print_string “Hello COS 326!!\n";;

12


AFirstOCamlProgram

hello.ml:

afunc'on itsstringargumentenclosedin"..."

top-levelexpressionsterminatedby;;

13

AFirstOCamlProgram


$ ocamlbuild hello.d.byte $ ./hello.d.byte Hello COS 326!! $

hello.ml:

compiling and running hello.ml:

.dfordebugging(otherchoices.pforprofiled;ornone)

.byteforinterpretedbytecode(otherchoices.na'veformachinecode)

14

AFirstOCamlProgram

$ ocaml Objective Caml Version 3.12.0

#

hello.ml:

interpreting and playing with hello.ml:


15

AFirstOCamlProgram


# 3 + 1;; -  : int = 4 #

hello.ml:



16

AFirstOCamlProgram


# 3 + 1;; -  : int = 4 # #use "hello.ml";; hello cos326!! -  : unit = () #

hello.ml:



17

AFirstOCamlProgram


# 3 + 1;; -  : int = 4 # #use "hello.ml";; hello cos326!! -  : unit = () # #quit;; $

hello.ml:



18

ASecondOCamlProgram

(* sum the numbers from 0 to n precondition: n must be a natural number *) let rec sumTo (n:int) : int = match n with 0 -> 0 | n -> n + sumTo (n-1) ;; print_int (sumTo 8);; print_newline();;

acomment(*...*)sumTo8.ml:

19


ASecondOCamlProgram

thenameofthefunc'onbeingdefined

thekeyword“let”beginsadefini'onthekeyword“rec”indicatesthedefini'onisrecursive

top-leveldeclara'onendswith“;;”

sumTo8.ml:

20


ASecondOCamlProgram

resulttypeint

argumentnamednwithtypeint

sumTo8.ml:

21


ASecondOCamlProgram

deconstructthevaluenusingpa]ernmatching

datatobedeconstructedappearsbetweenkeywords“match”and“with”

sumTo8.ml:

22


ASecondOCamlProgram

deconstructeddatamatchesoneof2cases:(i)thedatamatchesthepa]ern0,or(ii)thedatamatchesthevariablepa]ernn

ver'calbar"|"separatesthealterna'vepa]erns

sumTo8.ml:

23


ASecondOCamlProgram

Eachbranchofthematchstatementconstructsaresult

constructtheresult0

constructaresultusingarecursivecalltosumTo

sumTo8.ml:

24


ASecondOCamlProgram

printtheresultofcallingsumToon8

printanewline

sumTo8.ml:

25

OCAMLBASICS:EXPRESSIONS,VALUES,SIMPLETYPES

26

Expressions,Values,Types•  Expressionsarecomputa'ons

–  2+3isacomputa'on

•  Valuesaretheresultsofcomputa'ons–  5isavalue

•  Typesdescribecollec'onsofvaluesandthecomputa'onsthatgeneratethosevalues–  intisatype

–  valuesoftypeintinclude•  0,1,2,3,…,max_int•  -1,-2,…,min_int

27

Moresimpletypes,values,opera'ons28

Type: Values: Expressions:int -2, 0, 42 42 * (13 + 1) float 3.14, -1., 2e12 (3.14 +. 12.0) *. 10e6

char ’a’, ’b’, ’&’ int_of_char ’a’

string "moo", "cow" "moo" ^ "cow" bool true, false if true then 3 else 4

unit () print_int 3

Formoreprimi'vetypesandfunc'onsoverthem,seetheOCamlReferenceManualhere:

h]p://caml.inria.fr/pub/docs/manual-ocaml/libref/Pervasives.html

Noteveryexpressionhasavalue29

Expression:42 * (13 + 1) evaluates to 588 (3.14 +. 12.0) *. 10e6 ↦ 151400000.

int_of_char ’a’ ↦ 97

"moo" ^ "cow" ↦ “moocow" if true then 3 else 4 ↦ 3 print_int 3 ↦ ()

1 + "hello" does not evaluate!

LanguageDefini'on•  Thereareanumberofwaystodefineaprogramminglanguage•  Inthisclass,wewillbrieflyinves'gate:

–  Syntax–  Evalua'on–  Typechecking

•  StandardML,averycloserela'veofOCaml,hasafulldefini'onofeachofthesepartsandanumberofproofsofcorrectness–  Formoreonthistheme,seeCOS441/510

•  TheOCamlManualfleshesoutthesyntax,evalua'onandtypecheckingrulesinformally

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OCAMLBASICS:COREEXPRESSIONSYNTAX

31

CoreExpressionSyntax32

ThesimplestOCamlexpressionseare:•  values numbers,strings,bools,...•  id variables(x,foo,...)•  e1ope2 operators(x+3,...)•  ide1e2…en func9oncall(foo342)•  letid=e1ine2 localvariabledecl.•  ife1thene2elsee3 acondi9onal•  (e) aparenthesizedexpression•  (e:t) anexpressionwithitstype

Anoteonparentheses33

Inmostlanguages,argumentsareparenthesized&separatedbycommas: f(x,y,z) sum(3,4,5)

InOCaml,wedon’twritetheparenthesesorthecommas:

f x y z sum 3 4 5

Butwedohavetoworryaboutgrouping.Forexample, f x y z f x (y z)

Thefirstonepassesthreeargumentstof(x,y,andz)Thesecondpassestwoargumentstof(x,andtheresultofapplyingthe

func'onytoz.)

OCAMLBASICS:TYPECHECKING

34

TypeChecking•  Everyvaluehasatypeandsodoeseveryexpression•  ThisisaconceptthatisfamiliarfromJavabutitbecomes

moreimportantwhenprogramminginafunc'onallanguage•  Thetypeofanexpressionisdeterminedbythetypeofits

subexpressions•  Wewrite(e:t)tosaythatexpressionehastypet.eg:

2:int "hello":string2+2:int "Isay"^"hello":string

35

TypeCheckingRules•  Thereareasetofsimplerulesthatgoverntypechecking

–  programsthatdonotfollowtheruleswillnottypecheckandO’Camlwillrefusetocompilethemforyou(thenerve!)

–  atfirstyoumayfindthistobeapain…

•  Buttypesareagreatthing:–  theyhelpusthinkabouthowtoconstructourprograms–  theyhelpusfindstupidprogrammingerrors–  theyhelpustrackdowncompa'bilityerrorsquicklywhenweeditandmaintainourcode

–  theyallowustoenforcepowerfulinvariantsaboutourdatastructures

36

TypeCheckingRules•  Examplerules:

0:int (andsimilarlyforanyotherintegerconstantn)

"abc":string (andsimilarlyforanyotherstringconstant"…")(2)

(1)

37


ife1:intande2:intthene1+e2:int

ife1:intande2:intthene1*e2:int



(1)

(3) (4)

38




ife1:stringande2:stringthene1^e2:string

ife:intthenstring_of_inte:string



(1)

(3)

(5)

(4)

(6)

39


•  Usingtherules:





2:intand3:int. (Byrule1)



(1)

(3)

(5)

(4)

(6)

40







2:intand3:int. (Byrule1)Therefore,(2+3):int (Byrule3)



(1)

(3)

(5)

(4)

(6)

41







2:intand3:int. (Byrule1)Therefore,(2+3):int (Byrule3)5:int (Byrule1)



(1)

(3)

(5)

(4)

(6)

42







2:intand3:int. (Byrule1)Therefore,(2+3):int (Byrule3)5:int (Byrule1)Therefore,(2+3)*5:int (Byrule4andourpreviouswork)



(1)

(3)

(5)

(4)

(6)

FYI:Thisisaformalproofthattheexpressioniswell-

typed!

43


•  Anotherperspec've:





????*????:int



(1)

(3)

(5)

(4)

(6)

rule(4)fortypingexpressionssaysIcanputanyexpressionwithtypeintinplaceofthe????

44







7*????:int



(1)

(3)

(5)

(4)

(6)


45







7*(add_one17):int



(1)

(3)

(5)

(4)

(6)


46

TypeCheckingRules•  YoucanalwaysstartuptheOCamlinterpretertofindouta

typeofasimpleexpression:


#

47




# 3 + 1;;

48




# 3 + 1;; -  : int = 4 #

pressreturnandyoufindoutthetypeandthevalue

49




# 3 + 1;; -  : int = 4 # “hello ” ^ “world”;; - : string = “hello world” #

pressreturnandyoufindoutthetypeandthevalue

50




# 3 + 1;; -  : int = 4 # “hello ” ^ “world”;; - : string = “hello world” # #quit;; $

51


•  Viola'ngtherules:





"hello":string (Byrule2)1:int (Byrule1)1+"hello":?? (NOTYPE!Rule3doesnotapply!)



(1)

(3)

(5)

(4)

(6)

52

•  Viola'ngtherules:

•  Thetypeerrormessagetellsyouthetypethatwasexpectedandthetypethatitinferredforyoursubexpression

•  Bytheway,thiswasoneofthenonsensicalexpressionsthatdidnotevaluatetoavalue

•  Itisagoodthingthatthisexpressiondoesnottypecheck!“Welltypedprogramsdonotgowrong”

RobinMilner,1978

TypeCheckingRules•  Viola'ngtherules:

•  Thetypeerrormessagetellsyouthetypethatwasexpectedandthetypethatitinferredforyoursubexpression

•  Bytheway,thiswasoneofthenonsensicalexpressionsthatdidnotevaluatetoavalue

•  Itisagoodthingthatthisexpressiondoesnottypecheck!

# "hello" + 1;; Error: This expression has type string but an expression was expected of type int

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TypeCheckingRules•  Viola'ngtherules:

•  Apossiblefix:

•  OneofthekeystobecomingagoodMLprogrammeristounderstandtypeerrormessages.

# "hello" + 1;; Error: This expression has type string but an expression was expected of type int

# "hello" ^ (string_of_int 1);; - : string = "hello1"

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OVERALLSUMMARY:ASHORTINTRODUCTIONTOFUNCTIONALPROGRAMMING

55

OCamlOCamlisafunc9onalprogramminglanguage

–  Javagetsmostworkdonebymodifyingdata

–  OCamlgetsmostworkdonebyproducingnew,immutabledata

OCamlisatypedprogramminglanguage

–  thetypeofanexpressioncorrectlypredictsthekindofvaluetheexpressionwillgeneratewhenitisexecuted

–  typeshelpusunderstandandwriteourprograms–  thetypesystemissound;thelanguageissafe

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A Func’onal Introduc’on · • good but not great support for OCaml. • on the other hand,...

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