Introduc)ontoRacket,adialectofLISP:ExpressionsandDeclara)ons

CS251ProgrammingLanguagesSpring2018,LynTurbak

DepartmentofComputerScienceWellesleyCollege

TheseslidesbuildonBenWood’sFall‘15slides

LISP:designedbyJohnMcCarthy,1958published1960

2Expr/decl

LISP:implementedbySteveRussell,early1960s

3Expr/decl

LISP:LIStProcessing

•  McCarthy,MITarNficialintelligence,1950s-60s– AdviceTaker:representlogicasdata,notjustprogram

•  Neededalanguagefor:–  SymboliccomputaNon–  Programmingwithlogic– ArNficialintelligence–  Experimentalprogramming

•  Somakeone!

i.e.,notjustnumbercrunching

Emacs:M-xdoctor

4Expr/decl

Scheme•  GeraldJaySussmanand

GuyLewisSteele(mid1970s)•  Lexically-scopeddialectofLISP

thatarosefromtryingtomakean“actor”language.

•  Describedinamazing“LambdatheUlNmate”papers(hap://library.readscheme.org/page1.html)–  LambdatheUlNmatePLbloginspiredbythese:

hap://lambda-the-ulNmate.org

•  LedtoStructureandInterpretaNonofComputerPrograms(SICP)andMIT6.001(haps://mitpress.mit.edu/sicp/)

5Expr/decl

•  GrandchildofLISP(variantofScheme)–  Somechanges/improvements,quitesimilar

•  DevelopedbythePLTgroup(haps://racket-lang.org/people.html),thesamefolkswhocreatedDrJava.

•  WhystudyRacketinCS251?–  Cleanslate,unfamiliar–  CarefulstudyofPLfoundaNons(“PLmindset”)–  FuncNonalprogrammingparadigm

•  EmphasisonfuncNonsandtheircomposiNon•  Immutabledata(lists)

–  Beautyofminimalism–  Observedesignconstraints/historicalcontext

6Expr/decl

Expressions,Values,andDeclaraNons

•  EnNrelanguage:thesethreethings

•  Expressionshaveevalua6onrules:– Howtodeterminethevaluedenotedbyanexpression.

•  Foreachstructureweaddtothelanguage:– Whatisitssyntax?Howisitwriaen?– Whatisitsevalua)onrule?Howisitevaluatedtoavalue(expressionthatcannotbeevaluatedfurther)?

7Expr/decl

Values

•  Valuesareexpressionsthatcannotbeevaluatedfurther.

•  Syntax:– Numbers:251, 240, 301–  Booleans:#t, #f –  Therearemorevalueswewillmeetsoon(strings,symbols,lists,funcNons,…)

•  EvaluaNonrule:–  Valuesevaluatetothemselves.

8Expr/decl

AddiNonexpression:syntax

Addstwonumberstogether. Syntax: (+ E1 E2)

Everyparenthesisrequired;nonemaybeomiaed.E1andE2 standinforanyexpression.NoteprefixnotaNon.

Examples:(+ 251 240) (+ (+ 251 240) 301) (+ #t 251)

Noterecursivestructure!

9Expr/decl

AddiNonexpression:evaluaNon

Syntax: (+ E1 E2) EvaluaNonrule:

1.  EvaluateE1toavalueV12.  EvaluateE2toavalueV23.  ReturnthearithmeNcsumofV1 + V2.

Noterecursivestructure!

Notquite!10Expr/decl

AddiNon:dynamictypecheckingSyntax: (+ E1 E2)

EvaluaNonrule:1.  evaluateE1toavalueV12.  EvaluateE2toavalueV23.  IfV1andV2arebothnumbersthen

returnthearithmeNcsumofV1 + V2.4.  Otherwise,atypeerroroccurs.

Dynamictype-checking

S)llnotquite!Morelater…

11Expr/decl

EvaluaNonAsserNonsFormalizeEvaluaNon

Theevalua)onasser)onnotaNonE↓ Vmeans``EevaluatestoV’’.

OurevaluaNonrulessofar:

•  valuerule:V↓ V(whereVisanumberorboolean)

•  addi6onrule:ifE1↓ V1andE2↓ V2andV1andV2arebothnumbersandVisthesumofV1andV2then(+ E1 E2) ↓ V

12Expr/decl

EvaluaNonDerivaNoninEnglishAnevalua)onderiva)onisa``proof’’thatanexpressionevaluatestoavalueusingtheevaluaNonrules.(+ 3 (+ 5 4)) ↓ 12 bytheaddiNonrulebecause:

•  3 ↓ 3 bythevaluerule

•  (+ 5 4) ↓ 9 bytheaddiNonrulebecause:

–  5 ↓ 5 bythevaluerule

–  4 ↓ 4 bythevaluerule

–  5and4arebothnumbers

–  9isthesumof5and4

•  3and9arebothnumbers

•  12isthesumof3and9

13Expr/decl

MoreCompactDerivaNonNotaNon

V↓ V

whereVisavalue(number,boolean,etc.)

[valuerule] E1↓ V1E2↓ V2(+ E1E2)↓ V

[addiNonrule]

WhereV1andV2arenumbersandVisthesumofV1andV2.

3 ↓ 3 [value]5 ↓ 5 [value] 4 ↓ 4 [value](+ 5 4)↓9 (+ 3 (+ 5 4))↓12

[addiNon]

sidecondiNonsofrules

[addiNon]

14Expr/decl

ErrorsAreModeledby“Stuck”DerivaNons

#t ↓ #t [value]5 ↓ 5 [value]

4 ↓ 4 [value]

(+ 5 4)↓9

[addiNon]

Stuckhere.Can’tapply(addiNon)rulebecause#tisnotanumberin(+#t9)

Howtoevaluate(+ #t (+ 5 4))?

Howtoevaluate(+ (+ 1 2) (+ 5 #f))?

1 ↓ 1 [value] 2 ↓ 2 [value]

(+ 1 2) ↓ 3 [addiNon]

5 ↓ 5 [value]

#f ↓ #f [value]

Stuckhere.Can’tapply(addiNon)rulebecause#fisnotanumberin(+5#f)

15Expr/decl

SyntacNcSugarforAddiNonTheaddiNonoperator+cantakeanynumberofoperands.

•  Fornow,treat(+ E1 E2 … En)as(+ (+ E1 E2) … En) E.g.,treat(+ 7 2 -5 8)as(+ (+ (+ 7 2) -5) 8)

•  Treat(+ E)asE(orsayifE↓Vthen(+ E)↓V)

•  Treat(+)as0(orsay(+)↓ 0 )

•  Thisapproachisknownassyntac)csugar:introducenewsyntacNcformsthat“desugar”intoexisNngones.

•  Inthiscase,analternaNveapproachwouldbetointroducemorecomplexevaluaNonruleswhen+hasanumberofargumentsdifferentfrom2.

16Expr/decl

OtherArithmeNcOperatorsSimilarsyntaxandevaluaNonfor

-  * / quotient remainder min max except:•  Secondargumentof/,quotient,remainder

mustbenonzero•  Resultof/isaraNonalnumber(fracNon)whenbothvaluesare

integers.(ItisafloaNngpointnumberifatleastonevalueisafloat.)

•  quotientandremaindertakeexactlytwoarguments;anythingelseisanerror.

•  (- E)istreatedas(- 0 E)•  (/ E)istreatedas(/ 1 E)•  (min E)and(max E)treatedasE•  (*)evaluatesto1.•  (/),(-),(min),(max)areerrors(i.e.,stuck)

17Expr/decl

RelaNonOperatorsThefollowingrelaNonaloperatorsonnumbersreturnbooleans:< <= = >= > Forexample:

E1↓ V1E2↓ V2(< E1E2)↓ V

[lessthan]

WhereV1andV2arenumbersandVis#tifV1islessthanV2or#fifV1isnotlessthanV2

18Expr/decl

CondiNonal(if)expressions

Syntax: (if Etest Ethen Eelse)EvaluaNonrule:

1.  EvaluateEtest toavalueVtest.2.  IfVtestisnotthevalue#fthen

returntheresultofevaluaNngEthenotherwise

returntheresultofevaluaNngEelse

19Expr/decl

DerivaNon-stylerulesforCondiNonals

Etest↓ VtestEthen↓ Vthen(if EtestEthenEelse)↓ Vthen

[ifnonfalse]

WhereVtestisnot#f

Etest↓ #f Eelse↓ Velse(if EtestEthenEelse)↓ Velse

[iffalse]

Eelseisnotevaluated!

Ethenisnotevaluated!

20Expr/decl

YourturnUseevaluaNonderivaNonstoevaluatethefollowingexpressions

(if (< 8 2) (+ #f 5) (+ 3 4))

(if (+ 1 2) (- 3 7) (/ 9 0))

(+ (if (< 1 2) (* 3 4) (/ 5 6)) 7)

(+ (if 1 2 3) #t)

21Expr/decl

Expressionsvs.statementsCondiNonalexpressionscangoanywhereanexpressionisexpected:

(+ 4 (* (if (< 9 (- 251 240)) 2 3) 5))

(if (if (< 1 2) (> 4 3) (> 5 6))

(+ 7 8)

(* 9 10)

Note:ifisanexpression,notastatement.DootherlanguagesyouknowhavecondiNonalexpressionsinaddiNontocondiNonalstatements?(Manydo!Java,JavaScript,Python,…)

22Expr/decl

CondiNonalexpressions:careful!

Unlikeearlierexpressions,notallsubexpressionsofifexpressionsareevaluated!(if (> 251 240) 251 (/ 251 0))

(if #f (+ #t 240) 251)

23Expr/decl

DesignchoiceincondiNonalsemanNcs

Etest↓ VtestEthen↓ Vthen

(if EtestEthenEelse)↓ Vthen

[ifnonfalse]

WhereVtestisnot#f

Inthe[ifnonfalse]rule,Vtestisnotrequiredtobeaboolean!

Etest↓ #tEthen↓ Vthen

(if EtestEthenEelse)↓ Vthen

Thisisadesignchoiceforthelanguagedesigner.Whatwouldhappenifwereplacetheaboveruleby

[iftrue]

ThisdesignchoiceisrelatedtonoNonsof“truthiness”and“falsiness”thatyouwillexploreinPS2.

24Expr/decl

Environments:MoNvaNonWanttobeabletonamevaluessocanrefertothemlaterbyname.E.g.;

(define x (+ 1 2))

(define y (* 4 x))

(define diff (- y x))

(define test (< x diff))

(if test (+ (* x y) diff) 17)

25Expr/decl

Environments:DefiniNon•  AnenvironmentisasequenceofbindingsthatassociateidenNfiers(variablenames)withvalues.–  Concreteexample:num ⟼ 17, absoluteZero ⟼ -273, true ⟼#t

–  AbstractExample(useIdtorangeoveridenNfiers=names): Id1 ⟼ V1, Id2 ⟼ V2, …, Idn ⟼ Vn

–  Emptyenvironment:∅•  AnenvironmentservesasacontextforevaluaNngexpressionsthatcontainidenNfiers.

•  SecondargumenttoevaluaNon,whichtakesbothanexpressionandanenvironment.

26Expr/decl

AddiNon:evaluaNonwithenvironment

Syntax: (+ E1 E2)

EvaluaNonrule:1.  evaluateE1inthecurrentenvironmenttoavalueV12.  EvaluateE2inthecurrentenvironmenttoavalueV23.  IfV1andV2arebothnumbersthen

returnthearithmeNcsumofV1 + V2.4.  Otherwise,atypeerroroccurs.

27Expr/decl

VariablereferencesSyntax:Id

Id:anyiden6fier

EvaluaNonrule:LookupandreturnthevaluetowhichIdisboundinthecurrentenvironment.

•  Look-upproceedsbysearchingfromthemost-recentlyaddedbindingstotheleast-recentlyaddedbindings(fronttobackinourrepresentaNon)

•  IfIdisnotboundinthecurrentenvironment,evaluaNngitis“stuck”atanunboundvariableerror.

Examples:•  Supposeenvisnum ⟼ 17, absZero ⟼ -273, true ⟼ #t, num ⟼ 5

•  Inenv,numevaluatesto17(morerecentthan5),absZeroevaluatesto-273, andtrueevaluatesto#t.Anyothernameisstuck.

28Expr/decl

defineDeclaraNonsSyntax:(define Id E)

define:keywordId:anyiden6fierE:anyexpression

Thisisadeclara)on,notanexpression!Wewillsayadeclara)onsareprocessed,notevaluated Processingrule:

1.  EvaluateE toavalueV inthecurrentenvironment2.  ProduceanewenvironmentthatisidenNcaltothe

currentenvironment,withtheaddiNonalbindingId→Vatthefront.Usethisnewenvironmentasthecurrentenvironmentgoingforward.

29Expr/decl

Environments:Exampleenv0=∅ (canwriteas.intext)

(define x (+ 1 2))

env1=x⟼ 3, ∅ (abbreviated x⟼ 3;canwriteasx -> 3intext)

(define y (* 4 x))

env2=y ⟼ 12, x ⟼ 3 (most recent binding 2irst) (define diff (- y x))

env3=diff ⟼ 9, y ⟼ 12, x ⟼ 3

(define test (< x diff))

env4=test ⟼ #t, diff ⟼ 9, y ⟼ 12, x ⟼ 3

(if test (+ (* x 5) diff) 17)

environmenthereissNllenv4(define x (* x y))

env5=x ⟼ 36, test ⟼ #t, diff ⟼ 9, y ⟼ 12, x ⟼ 3 Notethatbindingx ⟼ 36“shadows”x ⟼ 3,makingitinaccessible

30Expr/decl

EvaluaNonAsserNons&RuleswithEnvironments

V#env↓ V

whereVisavalue(number,boolean,etc.)

[value]

E1#env↓ V1E2#env↓ V2

(+ E1E2)#env↓ V

[addiNon]

WhereV1andV2arenumbersandVisthesumofV1andV2.RulesforotherarithmeNcandrelaNonalopsaresimilar.

Theevalua)onasser)onnotaNonE#env↓ Vmeans``EvaluaNngexpressionEinenvironmentenvyieldsvalueV’’.

Id#env↓ V

WhereIdisanidenNfierandId⟼ VisthefirstbindinginenvforId

[varref]

E1#env↓ V1E2#env↓ V2

(if E1E2E3)#env↓ V2

[ifnonfalse]

WhereV1isnot#f

E1#env↓ #f E3#env↓ V3

(if E1E2E3)#env↓ V3

[iffalse]

Onlythisruleactuallyusesenv;othersjustpassitalong

31Expr/decl

ExampleDerivaNonwithEnvironments

test #env4↓#t[varref] x#env4↓3[varref] 5#env4↓5[value] (* x 5)#env4↓15 diff#env4↓9[varref](+ (* x 5) diff)#env4↓24(if test (+ (* x 5) diff) 17)#env4↓24

Supposeenv4=test ⟼ #t, diff ⟼ 9, y ⟼ 12, x ⟼ 3

[mulNplicaNon]

[addiNon]

[ifnonfalse]

32Expr/decl

Conclusion-below-subderivaNons,intext

| test # env4 ↓ #t [varref] | | | x # env4 ↓ 3 [varref] | | | 5 # env4 ↓ 5 [value] | | -------------------- [multiplication]

| | (* x 5) # env4 ↓ 15 | | diff # env4 ↓ 9 [varref] | | ------------------------- [addition]

| (+ (* x 5) diff)# env4 ↓ 24 ---------------------------------------- [if nonfalse]

(if test (+ (* x 5) diff) 17)# env4 ↓ 24

Suppose env4 = test -> #t, diff -> 9, y -> 12, x -> 3

33Expr/decl

Conclusion-above-subderivaNons,withbullets

(if test (+ (* x 5) diff) 17)# env4 ↓ 24 [if nonfalse] q  test # env4 ↓ #t [varref] q  (+ (* x 5) diff)# env4 ↓ 24 [addition]

o  (* x 5) # env4 ↓ 15 [multiplication] §  x # env4 ↓ 3 [varref] §  5 # env4 ↓ 5 [value]

o  diff # env4 ↓ 9 [multiplication]

Suppose env4 = test -> #t, diff -> 9, y -> 12, x -> 3

34Expr/decl

FormalizingdefiniNons

E # env ↓ V (define Id E)# env ⇓ Id ⟼ V, env

[define]

Thedeclara)onasser)onnotaNon(define Id E)#env⇓ env’means``ProcessingthedefiniNon(define Id E)inenvironmentenvyieldsanewenvironmentenv’’’.Weuseadifferentarrow,⇓, toemphasizethatdefiniNonsarenotevaluatedtovalues,butprocessedtoenvironments.

35Expr/decl

ThreadingenvironmentsthroughdefiniNons 2 # � ↓ 2 [value]

3 # � ↓ 3 [value]

(+ 2 3)# � ↓ 5

(define a (+ 2 3))# � ⇓ a ⟼ 5

[define]

[addiNon]

a # a ⟼ 5 ↓ 5 [varref]

a # a ⟼ 5 ↓ 5 [varref]

(* a a)# a ⟼ 5 ↓ 25

(define b (* a a))# a ⟼ 5 ⇓ b ⟼ 25, a ⟼ 5

[define]

[mulNplicaNon]

b # b ⟼ 25, a ⟼ 5 ↓ 25 [varref]

a # b ⟼ 25, a ⟼ 5 ↓ 5 [varref]

(- b a)# b ⟼ 25, a ⟼ 5 ↓ 20

[subtracNon]

36Expr/decl

RacketIdenNfiers•  RacketidenNfiersarecasesensiNve.Thefollowingarefourdifferent

idenNfiers:ABC,Abc,aBc,abc •  Unlikemostlanguages,RacketisveryliberalwithitsdefiniNonoflegal

idenNfers.PreaymuchanycharactersequenceisallowedasidenNfierwiththefollowingexcepNons:–  Can’tcontainwhitespace–  Can’tcontainspecialcharacters()[]{}”,’`;#|\ –  Can’thavesamesyntaxasanumber

•  Thismeansvariablenamescanuse(andevenbeginwith)digitsandcharacterslike!@$%^&*.-+_:<=>?/ E.g.:–  myLongName, my_long__name, my-long-name–  is_a+b<c*d-e? –  76Trombones

•  WhyareotherlanguageslessliberalwithlegalidenNfiers?

37Expr/decl

Small-stepvs.big-stepsemanNcsTheevaluaNonderivaNonswe’veseensofararecalledabig-stepseman)csbecausethederivaNone#env2↓vexplainstheevaluaNonofetovasone“bigstep”jusNfiedbytheevaluaNonofitssubexpressions.

AnalternaNvewaytoexpressevaluaNonisasmall-stepseman)csinwhichanexpressionissimplifiedtoavalueinasequenceofstepsthatsimplifiessubexpressions.YoudothisalltheNmewhensimplifyingmathexpressions,andwecandoitinRacket,too.E.g;

(- (* (+ 2 3) 9) (/ 18 6))

⇒ (- (* 5 9) (/ 18 6))

⇒ (- 45 (/ 18 6))

⇒ (- 45 3)

⇒ 42

38Expr/decl

Small-stepsemanNcs:intuiNon

Scanlewtorighttofindthefirstredex(nonvaluesubexpressionthatcanbereducedtoavalue)andreduceit:

(- (* (+ 2 3) 9) (/ 18 6))

⇒ (- (* 5 9) (/ 18 6))

⇒ (- 45 (/ 18 6))

⇒ (- 45 3)

⇒ 42

39Expr/decl

[addition]

[multiplication]

[division] [subtraction]

Small-stepsemanNcs:reducNonrulesThereareasmallnumberofreducNonrulesforRacket.Thesespecifytheredexesofthelanguageandhowtoreducethem.

Therulesowenrequirecertainsubpartsofaredextobe(parNcularkindsof)valuesinordertobeapplicable.

Id⇒V,whereId⟼VisthefirstbindingforIdinthecurrentenvironment*[varref]

(+ V1V2)⇒V,whereVisthesumofnumbersV1andV2[addiNon]

TherearesimilarrulesforotherarithmeNc/relaNonaloperators

(if Vtest EthenEelse) ⇒ Ethen,ifVtestisnot#f[ifnonfalse]

(if #f EthenEelse) ⇒ Eelse[iffalse]

*Inamoreformalapproach,thenotaNonwouldmaketheenvironmentexplicit.E.g.,E#env⇒V

40Expr/decl

Small-stepsemanNcs:condiNonalexample(+ (if {(< 1 2)} (* 3 4) (/ 5 6)) 7)

=> (+ {(if #t (* 3 4) (/ 5 6))} 7) [less than]

⇒ (+ {(* 3 4)} 7) [if nonfalse]

⇒ {(+ 12 7)} [multiplication]

⇒ 19 [addition]

41Expr/decl

NotesforwriNngderivaNonsintext:

o  Youcanuse=>for⇒

o  Usecurlybraces{…}tomarktheredex

o  Usesquarebracketstonametheruleusedtoreducetheredexfromthepreviouslinetothecurrentline.

Small-stepsemanNcs:errorsasstuckexpressions

Similartobig-stepsemanNcs,wemodelerrors(dynamictypeerrors,dividebyzero,etc.)insmall-stepsemanNcsasexpressionsinwhichtheevaluaNonprocessisstuckbecausenoreducNonruleismatched.Forexample:

(- (* (+ 2 3) #t) (/ 18 6))

⇒ (- (* 5 #t) (/ 18 6))

(if (= 2 (/ (+ 3 4) (- 5 5))) 8 9)

⇒ (if (= 2 (/ 7 (- 5 5))) 8 9)

⇒ (if (= 2 (/ 7 0)) 8 9)

42Expr/decl

Small-stepsemanNcs:yourturnUsesmall-stepsemanNcstoevaluatethefollowingexpressions:

(if (< 8 2) (+ #f 5) (+ 3 4))

(if (+ 1 2) (- 3 7) (/ 9 0))

(+ (if (< 1 2) (* 3 4) (/ 5 6)) 7)

(+ (if 1 2 3) #t)

43Expr/decl

RacketDocumentaNon

RacketGuide:haps://docs.racket-lang.org/guide/RacketReference:haps://docs.racket-lang.org/reference

44Expr/decl