Download Principles of Programming Languages - 815338A

PrinciplesofProgramming
Languages- 815338A
FunctionalProgramming
1-1
Introduction
• Thedesignoftheimperativelanguagesisbaseddirectlyonthevon
Neumannarchitecture
• Efficiencyistheprimaryconcern,ratherthanthesuitabilityofthelanguage
forsoftwaredevelopment
• Thedesignofthefunctionallanguagesisbasedonmathematical
functions
• Asolidtheoreticalbasisthatisalsoclosertotheuser,butrelatively
unconcernedwiththearchitectureofthemachinesonwhichprogramswill
run
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1-2
MathematicalFunctions
• Amathematicalfunctionisamapping ofmembersofoneset,called
thedomainset,toanotherset,calledtherangeset
• Alambdaexpression specifiestheparameter(s)andthemappingofa
functioninthefollowingform
l(x) x * x * x
forthefunctioncube(x) = x * x * x
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1-3
LambdaExpressions
• Lambdaexpressionsdescribenamelessfunctions
• Lambdaexpressionsareappliedtoparameter(s)byplacingthe
parameter(s)aftertheexpression
e.g.,(l(x) x * x * x)(2)
whichevaluatesto8
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1-4
FunctionalForms
• Ahigher-orderfunction,orfunctionalform,isonethateithertakes
functionsasparametersoryieldsafunctionasitsresult,orboth
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1-5
FunctionComposition
• Afunctionalformthattakestwofunctionsasparametersandyieldsa
functionwhosevalueisthefirstactualparameterfunctionappliedto
theapplicationofthesecond
Form:h º f ° g
whichmeansh (x) º f ( g ( x))
Forf (x) º x + 2 andg (x) º 3 * x,
h º f ° g yields(3 * x)+ 2
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1-6
Apply-to-all
• Afunctionalformthattakesasinglefunctionasaparameterandyields
alistofvaluesobtainedbyapplyingthegivenfunctiontoeachelement
ofalistofparameters
Form:a
Forh(x) º x * x
a(h, (2, 3, 4)) yields(4, 9, 16)
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1-7
FundamentalsofFunctionalProgramming
Languages
• TheobjectiveofthedesignofaFPListomimicmathematical
functionstothegreatestextentpossible
• ThebasicprocessofcomputationisfundamentallydifferentinaFPL
thaninanimperativelanguage
• Inanimperativelanguage,operationsaredoneandtheresultsare
storedinvariablesforlateruse
• Managementofvariablesisaconstantconcernandsourceof
complexityforimperativeprogramming
• InanFPL,variablesarenotnecessary,asisthecaseinmathematics
• ReferentialTransparency- InanFPL,theevaluationofafunction
alwaysproducesthesameresultgiventhesameparameters
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1-8
LISPDataTypesandStructures
• Dataobjecttypes:originallyonlyatomsandlists
• Listform:parenthesizedcollectionsofsublistsand/oratoms
e.g.,(A B (C D) E)
• Originally,LISPwasatypelesslanguage
• LISPlistsarestoredinternallyassingle-linkedlists
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1-9
LISPInterpretation
• Lambdanotationisusedtospecifyfunctionsandfunction
definitions.Functionapplicationsanddatahavethesameform.
e.g.,Ifthelist(A B C) isinterpretedasdataitis
asimplelistofthreeatoms,A,B,andC
Ifitisinterpretedasafunctionapplication,
itmeansthatthefunctionnamedA is
appliedtothetwoparameters,B andC
• ThefirstLISPinterpreterappearedonlyasademonstrationofthe
universalityofthecomputationalcapabilitiesofthenotation
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1-10
OriginsofScheme
• Amid-1970sdialectofLISP,designedtobeacleaner,moremodern,
andsimplerversionthanthecontemporarydialectsofLISP
• Usesonlystaticscoping
• Functionsarefirst-classentities
• Theycanbethevaluesofexpressionsandelementsoflists
• Theycanbeassignedtovariables,passedasparameters,andreturnedfrom
functions
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1-11
TheSchemeInterpreter
• Ininteractivemode,theSchemeinterpreterisaninfinitereadevaluate-printloop(REPL)
• ThisformofinterpreterisalsousedbyPythonandRuby
• ExpressionsareinterpretedbythefunctionEVAL
• Literalsevaluatetothemselves
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1-12
PrimitiveFunctionEvaluation
•
•
•
•
Parametersareevaluated,innoparticularorder
Thevaluesoftheparametersaresubstitutedintothefunction
body
Thefunctionbodyisevaluated
Thevalueofthelastexpressioninthebodyisthevalueofthe
function
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1-13
PrimitiveFunctions&LAMBDA Expressions
•
PrimitiveArithmeticFunctions:+,-,*,/,ABS,SQRT,REMAINDER,
MIN,MAX
e.g.,(+ 5 2) yields7
• LambdaExpressions
• Formisbasedonl notation
e.g.,(LAMBDA (x) (* x x)
x iscalledaboundvariable
• Lambdaexpressionscanbeappliedtoparameters
e.g.,((LAMBDA (x) (* x x)) 7)
• LAMBDA expressionscanhaveanynumberofparameters
(LAMBDA (a b x) (+ (* a x x) (* b x)))
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1-14
SpecialFormFunction:DEFINE
•
DEFINE - Twoforms:
1.
Tobindasymboltoanexpression
e.g.,(DEFINE pi 3.141593)
Exampleuse:(DEFINE two_pi (* 2 pi))
Thesesymbolsarenotvariables– theyarelikethenamesboundbyJava’s
final declarations
2.
Tobindnamestolambdaexpressions(LAMBDA isimplicit)
e.g.,(DEFINE (square x) (* x x))
Exampleuse:(square 5)
- TheevaluationprocessforDEFINE isdifferent!Thefirstparameter
isneverevaluated.Thesecondparameterisevaluatedandboundto
thefirstparameter.
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1-15
OutputFunctions
• Usuallynotneeded,becausetheinterpreteralwaysdisplaysthe
resultofafunctionevaluatedatthetoplevel(notnested)
• SchemehasPRINTF,whichissimilartotheprintf functionof
C
• Note:explicitinputandoutputarenotpartofthepurefunctional
programmingmodel,becauseinputoperationschangethestateof
theprogramandoutputoperationsaresideeffects
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1-16
NumericPredicateFunctions
• #T (or#t)istrueand#F (or#f)isfalse(sometimes() isusedfor
false)
• =,<>,>,<,>=,<=
• EVEN?,ODD?,ZERO?,NEGATIVE?
• TheNOT functioninvertsthelogicofaBooleanexpression
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1-17
ControlFlow
• Selection- thespecialform,IF
(IF predicatethen_expelse_exp)
(IF (<> count 0)
(/ sum count)
)
• RecallfromChapter8theCOND function:
(DEFINE (leap? year)
(COND
((ZERO? (MODULO year 400)) #T)
((ZERO? (MODULO year 100)) #F)
(ELSE (ZERO? (MODULO year 4)))
))
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1-18
ListFunctions
QUOTE - takesoneparameter;returnstheparameter
•
•
•
withoutevaluation
QUOTE isrequiredbecausetheSchemeinterpreter,namedEVAL,
alwaysevaluatesparameterstofunctionapplicationsbefore
applyingthefunction.QUOTE isusedtoavoidparameter
evaluationwhenitisnotappropriate
QUOTE canbeabbreviatedwiththeapostropheprefixoperator
'(A B) isequivalentto(QUOTE (A B))
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1-19
ExampleSchemeFunction:member
• member takesanatomandasimplelist;returns#T iftheatomis
inthelist;#F otherwise
DEFINE (member atm a_list)
(COND
((NULL? a_list) #F)
((EQ? atm (CAR lis)) #T)
((ELSE (member atm (CDR a_list)))
))
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1-20
ExampleSchemeFunction:equalsimp
• equalsimp takestwosimplelistsasparameters;returns#T if
thetwosimplelistsareequal;#F otherwise
(DEFINE (equalsimp list1 list2)
(COND
((NULL? list1) (NULL? list2))
((NULL? list2) #F)
((EQ? (CAR list1) (CAR list2))
(equalsimp(CDR list1)(CDR list2)))
(ELSE #F)
))
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1-21
ExampleSchemeFunction:equal
• equal takestwogenerallistsasparameters;returns#T ifthe
twolistsareequal;#F otherwise
(DEFINE (equal list1 list2)
(COND
((NOT (LIST? list1))(EQ? list1 list2))
((NOT (LIST? lis2)) #F)
((NULL? list1) (NULL? list2))
((NULL? list2) #F)
((equal (CAR list1) (CAR list2))
(equal (CDR list1) (CDR list2)))
(ELSE #F)
))
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1-22
ExampleSchemeFunction:append
• append takestwolistsasparameters;returnsthefirst
parameterlistwiththeelementsofthesecondparameter
listappendedattheend
(DEFINE (append list1 list2)
(COND
((NULL? list1) list2)
(ELSE (CONS (CAR list1)
(append (CDR list1) list2)))
))
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1-23
ExampleSchemeFunction:LET
• RecallthatLET wasdiscussedinChapter5
• LET isactuallyshorthandforaLAMBDA expressionappliedtoa
parameter
(LET ((alpha 7))(* 5 alpha))
isthesameas:
((LAMBDA (alpha) (* 5 alpha)) 7)
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1-24
LET Example
(DEFINE (quadratic_roots a b c)
(LET (
(root_part_over_2a
(/ (SQRT (- (* b b) (* 4 a c)))(* 2 a)))
(minus_b_over_2a (/ (- 0 b) (* 2 a)))
(LIST (+ minus_b_over_2a root_part_over_2a))
(- minus_b_over_2a root_part_over_2a))
))
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1-25
TailRecursioninScheme
• Definition:Afunctionistailrecursiveifitsrecursivecallisthelast
operationinthefunction
• Atailrecursivefunctioncanbeautomaticallyconvertedbyacompiler
touseiteration,makingitfaster
• SchemelanguagedefinitionrequiresthatSchemelanguagesystems
convertalltailrecursivefunctionstouseiteration
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1-26
TailRecursioninScheme- continued
• Exampleofrewritingafunctiontomakeittailrecursive,usinghelperafunction
Original:(DEFINE (factorial n)
(IF (<= n 0)
1
(* n (factorial (- n 1)))
))
Tailrecursive:
(DEFINE (facthelper n factpartial)
(IF (<= n 0)
factpartial
facthelper((- n 1) (* n factpartial)))
))
(DEFINE (factorial n)
(facthelper n 1))
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1-27
FunctionalForm- Composition
• Composition
• Ifh isthecompositionoff andg,h(x) = f(g(x))
(DEFINE (g x) (* 3 x))
(DEFINE (f x) (+ 2 x))
(DEFINE h x) (+ 2 (* 3 x))) (Thecomposition)
• InScheme,thefunctionalcompositionfunctioncompose canbe
written:
(DEFINE (compose f g) (LAMBDA (x) (f (g x))))
((compose CAR CDR) '((a b) c d)) yieldsc
(DEFINE (third a_list)
((compose CAR (compose CDR CDR)) a_list))
isequivalenttoCADDR
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1-28
FunctionalForm– Apply-to-All
• ApplytoAll- oneforminSchemeismap
• Appliesthegivenfunctiontoallelementsofthegivenlist;
(DEFINE (map fun a_list)
(COND
((NULL? a_list) '())
(ELSE (CONS (fun (CAR a_list))
(map fun (CDR a_list))))
))
(map (LAMBDA (num) (* num num num)) '(3 4 2 6)) yields
(27 64 8 216)
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1-29
FunctionsThatBuildCode
• ItispossibleinSchemetodefineafunctionthatbuildsSchemecode
andrequestsitsinterpretation
• Thisispossiblebecausetheinterpreterisauser-availablefunction,
EVAL
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1-30
AddingaListofNumbers
((DEFINE (adder a_list)
(COND
((NULL? a_list) 0)
(ELSE (EVAL (CONS '+ a_list)))
))
• Theparameterisalistofnumberstobeadded;adder
insertsa+ operatorandevaluatestheresultinglist
• UseCONS toinserttheatom+ intothelistofnumbers.
• Besurethat+ isquotedtopreventevaluation
• SubmitthenewlisttoEVAL forevaluation
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1-31
CommonLISP
• Acombinationofmanyofthefeaturesofthepopular
dialectsofLISParoundintheearly1980s
• Alargeandcomplexlanguage--theoppositeofScheme
• Featuresinclude:
•
•
•
•
•
•
•
records
arrays
complexnumbers
characterstrings
powerfulI/Ocapabilities
packageswithaccesscontrol
iterativecontrolstatements
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1-32
CommonLISP(continued)
• Macros
• Createtheireffectintwosteps:
• Expandthemacro
• Evaluatetheexpandedmacro
• SomeofthepredefinedfunctionsofCommonLISPareactually
macros
• UserscandefinetheirownmacroswithDEFMACRO
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1-33
CommonLISP(continued)
• Backquoteoperator(`)
• SimilartotheScheme’sQUOTE,exceptthatsomepartsoftheparameter
canbeunquotedbyprecedingthemwithcommas
`(a (* 3 4) c) evaluatesto(a (* 3 4) c)
`(a ,(* 3 4) c) evaluatesto(a 12 c)
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1-34
CommonLISP(continued)
• ReaderMacros
• LISPimplementationshaveafrontendcalledthereader thattransforms
LISPintoacoderepresentation.Thenmacrocallsareexpandedintothe
coderepresentation.
• Areadermacroisaspecialkindofmacrothatisexpandedduringthe
readerphase
• Areadermacroisadefinitionofasinglecharacter,whichisexpanded
intoitsLISPdefinition
• Anexampleofareadermacroisanapostrophecharacter,whichis
expandedintoacalltoQUOTE
• Userscandefinetheirownreadermacrosasakindofshorthand
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1-35
CommonLISP(continued)
• CommonLISPhasasymboldatatype(similartothatofRuby)
• Thereservedwordsaresymbolsthatevaluatetothemselves
• Symbolsareeitherboundorunbound
• Parametersymbolsareboundwhilethefunctionisbeingevaluated
• Symbolsthatarethenamesofimperativestylevariablesthathavebeenassignedvalues
arebound
• Allothersymbolsareunbound
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1-36
ML
• Astatic-scopedfunctionallanguagewithsyntaxthatiscloserto
PascalthantoLISP
• Usestypedeclarations,butalsodoestypeinferencing to
determinethetypesofundeclaredvariables
• Itisstronglytyped(whereasSchemeisessentiallytypeless)and
hasnotypecoercions
• Doesnothaveimperative-stylevariables
• Itsidentifiersareuntypednamesforvalues
• Includesexceptionhandlingandamodulefacilityfor
implementingabstractdatatypes
• Includeslistsandlistoperations
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1-37
MLSpecifics
• Atablecalledtheevaluationenvironmentstoresthenamesof
allidentifiersinaprogram,alongwiththeirtypes(likearuntimesymboltable)
• Functiondeclarationform:
fun name (formalparameters) = expression;
e.g.,fun cube(x : int) = x * x * x;
- Thetypecouldbeattachedtoreturnvalue,asin
fun cube(x) : int = x * x * x;
- Withnotypespecified,itwoulddefaultto
int (thedefaultfornumericvalues)
- User-definedoverloadedfunctionsarenotallowed,soifwe
wantedacube functionforrealparameters,itwouldneedto
haveadifferentname
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1-38
MLSpecifics(continued)
• MLselection
if expression then then_expression
else else_expression
wherethefirstexpressionmustevaluatetoaBooleanvalue
• Patternmatchingisusedtoallowafunctiontooperateondifferent
parameterforms
fun fact(0) = 1
|
fact(1) = 1
|
fact(n : int) : int = n * fact(n – 1)
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1-39
MLSpecifics(continued)
• Lists
Literallistsarespecifiedinbrackets
[3, 5, 7]
[] istheemptylist
CONS isthebinaryinfixoperator,::
4 :: [3, 5, 7],whichevaluatesto[4, 3, 5, 7]
CAR istheunaryoperatorhd
CDR istheunaryoperatortl
fun length([]) = 0
|
length(h :: t) = 1 + length(t);
fun append([], lis2) = lis2
|
append(h :: t, lis2) = h :: append(t, lis2);
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1-40
MLSpecifics(continued)
• Theval statementbindsanametoavalue(similartoDEFINE in
Scheme)
val distance = time * speed;
• AsisthecasewithDEFINE,val isnothinglikeanassignment
statementinanimperativelanguage
• Iftherearetwoval statementsforthesameidentifier,thefirstis
hiddenbythesecond
• val statementsareoftenusedinlet constructs
let
val radius = 2.7
val pi = 3.14159
in
pi * radius * radius
end;
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1-41
MLSpecifics(continued)
• filter
• Ahigher-orderfilteringfunctionforlists
• Takesapredicatefunctionasitsparameter,oftenintheformofalambda
expression
• Lambdaexpressionsaredefinedlikefunctions,exceptwiththereserved
wordfn
filter(fn(x) => x < 100, [25, 1, 711, 50,
100]);
Thisreturns[25, 1, 50]
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1-42
MLSpecifics(continued)
• map
• Ahigher-orderfunctionthattakesasingleparameter,afunction
• Appliestheparameterfunctiontoeachelementofalistandreturnsalistof
results
fun cube x = x * x * x;
val cubeList = map cube;
val newList = cubeList [1, 3, 5];
ThissetsnewList to[1, 27, 125]
- Alternative:usealambdaexpression
val newList = map (fn x => x * x * x, [1, 3,
5]);
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1-43
MLSpecifics(continued)
• FunctionComposition
• Usetheunaryoperator,o
val h = g o f;
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1-44
MLSpecifics(continued)
• Currying
• MLfunctionsactuallytakejustoneparameter—ifmorearegiven,it
considerstheparametersatuple(commasrequired)
• Processofcurrying replacesafunctionwithmorethanoneparameter
withafunctionwithoneparameterthatreturnsafunctionthattakes
theotherparametersoftheoriginalfunction
• AnMLfunctionthattakesmorethanoneparametercanbedefinedin
curriedformbyleavingoutthecommasintheparameters
fun add a b = a + b;
Afunctionwithoneparameter,a.Returnsafunctionthattakesb asa
parameter.Call:add 3 5;
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1-45
MLSpecifics(continued)
• PartialEvaluation
• Curriedfunctionscanbeusedtocreatenewfunctionsbypartialevaluation
• Partialevaluationmeansthatthefunctionisevaluatedwithactualparameters
foroneormoreoftheleftmostactualparameters
fun add5 x add 5 x;
Takestheactualparameter5 andevaluatestheadd functionwith5 asthe
valueofitsfirstformalparameter.Returnsafunctionthatadds5 toitssingle
parameter
val num = add5 10;
(* sets num to 15 *)
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1-46
Haskell
• SimilartoML(syntax,staticscoped,stronglytyped,typeinferencing,pattern
matching)
• DifferentfromML(andmostotherfunctionallanguages)inthatitispurely
functional(e.g.,novariables,noassignmentstatements,andnosideeffects
ofanykind)
SyntaxdifferencesfromML
fact 0 = 1
fact 1 = 1
fact n = n * fact (n – 1)
fib 0 = 1
fib 1 = 1
fib (n + 2) = fib (n + 1) + fib n
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1-47
FunctionDefinitionswithDifferentParameter
Ranges
fact
|
|
|
sub
|
|
|
n
n == 0 = 1
n == 1 = 1
n > 0 = n * fact(n – 1)
n
n < 10 = 0
n > 100 = 2
otherwise
= 1
square x = x * x
- BecauseHaskellsupportpolymorphism,this
worksforanynumerictypeofx
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1-48
HaskellLists
• Listnotation:Putelementsinbrackets
e.g.,directions = ["north", "south", "east",
"west"]
• Length:#
e.g.,#directions is 4
• Arithmeticserieswiththe.. operator
e.g.,[2, 4..10] is [2, 4, 6, 8, 10]
• Catenationiswith++
e.g.,[1, 3] ++ [5, 7] resultsin[1, 3, 5, 7]
• CONS,CAR,CDR viathecolonoperator
e.g.,1:[3, 5, 7] resultsin[1, 3, 5, 7]
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1-49
Haskell(continued)
• PatternParameters
product [] = 1
product (a:x) = a * product x
• Factorial:
fact n = product [1..n]
• ListComprehensions(Chapter6)
[n * n * n | n <- [1..50]]
Thequalifierinthisexamplehastheformofagenerator.It
couldbeintheformofatest
factors n = [i | i <- [1..n `div` 2], n `mod` i == 0]
Thebackticksspecifythefunctionisusedasabinaryoperator
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1-50
Quicksort
sort [] = []
sort (h:t) =
sort [b | b ← t; b <= h]
++ [h] ++
sort [b | b ← t; b > h]
IllustratestheconcisionofHaskell
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1-51
LazyEvaluation
• Alanguageisstrict ifitrequiresallactualparameterstobefully
evaluated
• Alanguageisnonstrict ifitdoesnothavethestrictrequirement
• Nonstrictlanguagesaremoreefficientandallowsomeinteresting
capabilities– infinitelists
• Lazyevaluation- Onlycomputethosevaluesthatarenecessary
• Positivenumbers
positives = [0..]
• Determiningif16 isasquarenumber
member [] b = False
member(a:x) b=(a == b)||member x b
squares = [n * n | n ← [0..]]
member squares 16
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1-52
MemberRevisited
• Thememberfunctioncouldbewrittenas:
member b [] = False
member b (a:x)=(a == b) || member b x
• However,thiswouldonlyworkiftheparametertosquares
wasaperfectsquare;ifnot,itwillkeepgeneratingthem
forever.Thefollowingversionwillalwayswork:
member2 n (m:x)
| m < n = member2 n x
| m == n = True
| otherwise = False
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1-53
F#
• BasedonOcaml,whichisadescendantofMLandHaskell
• Fundamentallyafunctionallanguage,butwithimperative
featuresandsupportsOOP
• Hasafull-featuredIDE,anextensivelibraryofutilities,and
interoperateswithother.NETlanguages
• Includestuples,lists,discriminatedunions,records,and
bothmutableandimmutablearrays
• Supportsgenericsequences,whosevaluescanbecreated
withgeneratorsandthroughiteration
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1-54
F#(continued)
• Sequences
let x = seq {1..4};;
• Generationofsequencevaluesislazy
let y = seq {0..10000000};;
Setsy to[0; 1; 2; 3;…]
• Defaultstepsizeis1,butitcanbeanynumber
let seq1 = seq {1..2..7}
Sets seq1 to[1; 3; 5; 7]
• Iterators– notlazyforlistsandarrays
let cubes = seq {for i in 1..4 -> (i, i * i * i)};;
Setscubesto[(1, 1); (2, 8); (3, 27); (4, 64)]
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1-55
F#(continued)
• Functions
• Ifnamed,definedwithlet;iflambdaexpressions,definedwithfun
(fun a b -> a / b)
• Nodifferencebetweenanamedefinedwithlet andafunctionwithout
parameters
• Theextentofafunctionisdefinedbyindentation
let f =
let pi = 3.14159
let twoPi = 2.0 * pi;;
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1-56
F#(continued)
• Functions(continued)
• Ifafunctionisrecursive,itsdefinitionmustincludetherec reservedword
• Namesinfunctionscanbeoutscoped,whichendstheirscope
let x4 =
let x = x * x
let x = x * x
Thefirstlet inthebodyofthefunctioncreatesanewversionofx;this
terminatesthescopeoftheparameter;Thesecondlet inthebodycreates
anotherx,terminatingthescopeofthesecondx
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1-57
F#(continued)
• FunctionalOperators
• Pipeline(|>)
• Abinaryoperatorthatsendsthevalueofitsleftoperandtothelast
parameterofthecall(therightoperand)
let myNums = [1; 2; 3; 4; 5]
let evensTimesFive = myNums
|> List.filter (fun n -> n % 2 = 0)
|> List.map (fun n -> 5 * n)
Thereturnvalueis[10; 20]
ll
• ;lkj;
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1-58
F#(continued)
• FunctionalOperators(continued)
• Composition(>>)
• Buildsafunctionthatappliesitsleftoperandtoagivenparameter(afunction)andthen
passestheresultreturnedfromthefunctiontoitsrightoperand(anotherfunction)
TheF#expression(f >> g) x isequivalenttothemathematicalexpressiong(f(x))
• CurriedFunctions
let add a b = a + b;;
let add5 = add 5;;
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F#(continued)
• WhyF#isInteresting:
• Itbuildsonpreviousfunctionallanguages
• Itsupportsvirtuallyallprogrammingmethodologiesinwidespreadusetoday
• Itisthefirstfunctionallanguagethatisdesignedforinteroperabilitywith
otherwidelyusedlanguages
• Atitsrelease,ithadanelaborateandwell-developedIDEandlibraryofutility
software
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SupportforFunctionalProgramminginPrimarily
ImperativeLanguages
• Supportforfunctionalprogrammingisincreasinglycreepinginto
imperativelanguages
• Anonymousfunctions(lambdaexpressions)
• JavaScript:leavethenameoutofafunctiondefinition
• C#:i => (i % 2) == 0 (returnstrueorfalsedependingonwhetherthe
parameterisevenorodd)
• Python:lambda
a, b : 2 * a
- b
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SupportforFunctionalProgramminginPrimarily
ImperativeLanguages(continued)
• Pythonsupportsthehigher-orderfunctionsfilterandmap
(oftenuselambdaexpressionsastheirfirstparameters)
map(lambda x : x ** 3, [2, 4, 6, 8])
Returns[8, 64, 216, 512]
• Pythonsupportspartialfunctionapplications
from operator import add
add5 = partial (add, 5)
(thefirstlineimportsadd asafunction)
Use:add5(15)
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SupportforFunctionalProgramminginPrimarily
ImperativeLanguages(continued)
• RubyBlocks
• Areeffectivelysubprogramsthataresenttomethods,whichmakesthe
methodahigher-ordersubprogram
• Ablockcanbeconvertedtoasubprogramobjectwithlambda
times = lambda {|a, b| a * b}
Use:x = times.(3, 4) (setsx to12)
• Timescanbecurriedwith
times5 = times.curry.(5)
Use:x5 = times5.(3) (setsx5 to15)
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ComparingFunctionalandImperativeLanguages
• ImperativeLanguages:
•
•
•
•
Efficientexecution
Complexsemantics
Complexsyntax
Concurrencyisprogrammerdesigned
• FunctionalLanguages:
•
•
•
•
Simplesemantics
Simplesyntax
Lessefficientexecution
Programscanautomaticallybemadeconcurrent
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Summary
• Functionalprogramminglanguagesusefunctionapplication,conditional
expressions,recursion,andfunctionalformstocontrolprogramexecution
• LISPbeganasapurelyfunctionallanguageandlaterincludedimperative
features
• SchemeisarelativelysimpledialectofLISPthatusesstaticscoping
exclusively
• CommonLISPisalargeLISP-basedlanguage
• MLisastatic-scopedandstronglytypedfunctionallanguagethatusestype
inference
• Haskellisalazyfunctionallanguagesupportinginfinitelistsandset
comprehension.
• F#isa.NETfunctionallanguagethatalsosupportsimperativeandobjectorientedprogramming
• Someprimarilyimperativelanguagesnowincorporatesomesupportfor
functionalprogramming
• Purelyfunctionallanguageshaveadvantagesoverimperativealternatives,
butstillarenotverywidelyused
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