Concepts and Semantics of Programming Languages 1
A Semantical Approach with OCaml and Python
Thérèse Hardin
Mathieu Jaume
François Pessaux
Véronique Viguié Donzeau-Gouge
First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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Library of Congress Control Number: 2021930488
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ISBN 978-1-78630-530-5
Foreword .......................................xi
Preface
Chapter1.FromHardwaretoSoftware ...................1
1.1.Computers:alow-levelview........................1
1.1.1.Informationprocessing.........................1
1.1.2.Memories.................................2
1.1.3.CPUs...................................3
1.1.4.Peripheraldevices............................7
1.2.Computers:ahigh-levelview.......................8
1.2.1.Modelingcomputations.........................9
1.2.2.High-levellanguages..........................9
1.2.3.Fromsourcecodetoexecutableprograms..............10
Chapter2.IntroductiontoSemanticsofProgrammingLanguages 15
2.1.Environment,memoryandstate......................16
2.1.1.Evaluationenvironment.........................16
2.1.2.Memory.................................18
2.1.3.State....................................20
2.2.Evaluationofexpressions..........................21
2.2.1.Syntax..................................21
2.2.2.Values...................................22
2.2.3.Evaluationsemantics..........................24
2.3.Definitionandassignment.........................26
2.3.1.Defininganidentifier..........................26
2.3.2.Assignment................................29
2.4.Exercises...................................31
Chapter3.SemanticsofFunctionalFeatures
3.1.Syntacticaspects...............................35
3.1.1.Syntaxofafunctionalkernel......................35
3.1.2.Abstractsyntaxtree...........................36
3.1.3.Reasoningbyinductionoverexpressions...............39
3.1.4.Declarationofvariables,boundandfreevariables..........39
3.2.Executionsemantics:evaluationfunctions................42
3.2.1.Evaluationerrors.............................42
3.2.2.Values...................................43
3.2.3.Interpretationofoperators.......................45
3.2.4.Closures.................................46
3.2.5.Evaluationofexpressions........................47
3.3.Executionsemantics:operationalsemantics...............54
3.3.1.Simpleexpressions...........................55
3.3.2.Call-by-value...............................56
3.3.3.Recursiveandmutuallyrecursivefunctions..............60
3.3.4.Call-by-name...............................61
3.3.5.Call-by-valueversuscall-by-name...................62
3.4.Evaluationfunctionsversusevaluationrelations.............64
3.4.1.Statusoftheevaluationfunction....................64
3.4.2.Inductionoverevaluationtrees.....................65
3.5.Semanticproperties.............................69
3.5.1.Equivalentexpressions.........................69
3.5.2.Equivalentenvironments........................71
4.1.Syntaxofakernelofanimperativelanguage...............77 4.2.Evaluationofexpressions..........................81 4.3.Evaluationofdefinitions..........................86 4.4.Operationalsemantics............................89
4.4.1.Big-stepsemantics............................89
4.4.2.Small-stepsemantics..........................93
4.4.3.Expressivenessofoperationalsemantics...............95 4.5.Semanticproperties.............................96 4.5.1.Equivalentprograms..........................96
4.5.2.Programtermination..........................98
4.5.3.Determinismofprogramexecution..................100
4.5.4.Bigstepsversussmallsteps......................103
4.6.Procedures..................................109
4.6.1.Blocks..................................109
4.6.2.Procedures................................112
4.7.Otherapproaches..............................118
4.7.1.Denotationalsemantics.........................118
4.7.2.Axiomaticsemantics,Hoarelogic...................129
4.8.Exercises...................................134
Chapter5.Types ..................................137
5.1.Typechecking:whenandhow?......................139
5.1.1.Whentoverifytypes?..........................139
5.1.2.Howtoverifytypes?..........................140
5.2.Informaltypingofaprogram Exp2 ....................141
5.2.1.Afirstexample..............................141
5.2.2.Typingaconditionalexpression....................142
5.2.3.Typingwithouttypeconstraints....................142
5.2.4.Polymorphism..............................143
5.3.Typingrulesin Exp2 ............................143
5.3.1.Types,typeschemesandtypingenvironments............143
5.3.2.Generalization,substitutionandinstantiation.............146
5.3.3.Typingrulesandtypingtrees......................151
5.4.Typeinferencealgorithmin Exp2 .....................154
5.4.1.Principaltype..............................154
5.4.2.Setsofconstraintsandunification...................155
5.4.3.Typeinferencealgorithm........................159
5.5.Properties...................................167
5.5.1.Propertiesoftypechecking.......................167
5.5.2.Propertiesoftheinferencealgorithm.................167
5.6.Typecheckingofimperativeconstructs..................168
5.6.1.Typealgebra...............................168
5.6.2.Typingrules...............................169
5.6.3.Typingpolymorphicdefinitions....................171
5.7.Subtypingandoverloading.........................172
5.7.1.Subtyping.................................173
5.7.2.Overloading...............................175
Chapter6.DataTypes
..............................179
6.1.Basictypes..................................179
6.1.1.Booleans.................................179
6.1.2.Integers..................................181
6.1.3.Characters................................186
6.1.4.Floatingpointnumbers.........................187
6.2.Arrays.....................................191
6.3.Strings....................................194
6.4.Typedefinitions...............................194
6.4.1.Typeabbreviations............................195
6.4.2.Records..................................196
6.4.3.Enumeratedtypes............................200
6.4.4.Sumtypes................................202
6.5.Generalizedconditional...........................205
6.5.1.Cstyle switch/case ...........................205
6.5.2.Patternmatching.............................208
6.6.Equality....................................216
6.6.1.Physicalequality.............................217
6.6.2.Structuralequality............................218
6.6.3.Equalitybetweenfunctions.......................220
Chapter7.PointersandMemoryManagement ..............223
7.1.Addressesandpointers...........................223
7.2.Endianness..................................225
7.3.Pointersandarrays.............................225
7.4.Passingparametersbyaddress.......................226
7.5.References..................................229
7.5.1.ReferencesinC++............................229
7.5.2.ReferencesinJava............................233
7.6.Memorymanagement............................234
7.6.1.Memoryallocation...........................234
7.6.2.Freeingmemory.............................237
7.6.3.Automaticmemorymanagement...................239
Chapter8.Exceptions ..............................243
8.1.Errors:notificationandpropagation....................243
8.1.1.Globalvariable..............................245
8.1.2.Recorddefinition............................245
8.1.3.Passingbyaddress............................245
8.1.4.Introducingexceptions.........................246
8.2.Asimpleformalization:ML-styleexceptions..............247
8.2.1.Abstractsyntax.............................247
8.2.2.Values...................................248
8.2.3.Typealgebra...............................248
8.2.4.Operationalsemantics..........................248
8.2.5.Typing..................................250
8.3.Exceptionsinotherlanguages.......................250
8.3.1.ExceptionsinOCaml..........................251
8.3.2.ExceptionsinPython..........................251
8.3.3.ExceptionsinJava............................253
8.3.4.ExceptionsinC++............................254
Foreword
Computerprogramshaveplayedanincreasinglycentralroleinourlivessincethe 1940s,andthequalityoftheseprogramshasthusbecomeacrucialquestion.Writing ahigh-qualityprogram–aprogramthatperformstherequiredtaskandisefficient, robust,easytomodify,easytoextend,etc.–isanintellectuallychallengingtask, requiringtheuseofrigorousdevelopmentmethods.Firstandforemost,however,the creationofsuchaprogramisdependentonanin-depthknowledgeofthe programminglanguageused,itssyntaxand,crucially,itssemantics,i.e.what happenswhenaprogramisexecuted.
Thedescriptionofthissemanticsputsthemostfundamentalconceptsintolight, includingthoseofvalue,reference,exceptionorobject.Theseconceptsarethe foundationsofprogramminglanguagetheory.Masteringtheseconceptsiswhatsets experiencedprogrammersapartfrombeginners.Certainconcepts–likethatofvalue –arecommontoallprogramminglanguages;others–suchasthenotionoffunctions –operatedifferentlyindifferentlanguages;finally,otherconcepts–suchasthatof objects–onlyexistincertainlanguages.Computerscientistsoftenreferto “programmingparadigms”toconsidersetsofconceptssharedbyafamilyof languages,whichimplyacertainprogrammingstyle:imperative,functional, object-oriented,logical,concurrent,etc.Nevertheless,anunderstandingofthe conceptsthemselvesisessential,asseveralparadigmsmaybeinterwovenwithinthe samelanguage.
Introductorytextsonprogramminginanygivenlanguagearenotdifficulttofind, andanumberofpublishedbooksaddressthefundamentalconceptsoflanguage semantics.Muchrarerarethose,likethepresentvolume,whichestablishand examinethelinksbetweenconceptsandtheirimplementationinlanguagesusedby programmersonadailybasis,suchasC,C++,Ada,Java,OCamlandPython.The authorsprovideawealthofexamplesintheselanguages,illustratingandgivinglife tothenotionsthattheypresent.Theyproposegeneralmodels,suchasthe kit
presentedinVolume2,permittingaunifiedviewofdifferentnotions;thismakesit easierforreaderstounderstandtheconstructsusedinpopularprogramming languagesandfacilitatescomparison.Thisthoroughanddetailedworkprovides readerswithanunderstandingofthesenotionsand,aboveall,anunderstandingof thewaysofusingthelattertocreatehigh-qualityprograms,buildingasaferand morereliablefutureincomputing.
GillesD OWEK ResearchDirector,Inria ProfessorattheÉcolenormalesupérieure,Paris-Saclay
CatherineD UBOIS ProfessorattheÉcolenationalesupérieure d’informatiquepourl’industrieetl’entreprise
January2021
Preface
Thistwo-volumeworkrelatestothefieldofprogramming.Firstandforemost,it isintendedtogivereadersasolidgroundinginthebasesoffunctionalorimperative programming,alongwithathoroughknowledgeofthemoduleandclassmechanisms involved.Inourview,thesemanticsapproachismostappropriatewhenstudying programming,astheimpactofinterlanguagesyntaxdifferencesislimited.Practical considerations,determinedbythematerialcharacteristicsofcomputersand/or “smart”devices,willalsobeaddressed.Thesameapproachwillbetakeninboth volumes,usingbothmathematicalformulasandmemorystatediagrams.Withthis book,wehopetohelpreadersunderstandthemeaningoftheconstructsdescribedin thereferencemanualsofprogramminglanguagesandtoestablishsolidfoundations forreasoningandassessingthecorrectnessoftheirownprogramsthroughcritical review.Inshort,ouraimistofacilitatethedevelopmentofsafeandreliable programs.
Volume1beginswithapresentationofthecomputer,inChapter1,firstatthe materiallevel–asanassemblageofcomponents–thenasatoolforexecuting programs.Chapter2isanintuitive,step-by-stepintroductiontolanguagesemantics, intendedtofamiliarizereaderswiththisapproachtoprogramming.InChapter3,we provideadetaileddiscussiononthesubject,withaformalpresentationofthe executionsemanticsoffunctionalfeatures.Chapter4continueswiththesametopic, lookingattheexecutionsemanticsofimperativefeatures.Inthesetwochapters,a clearmathematicalframeworkisusedtosupportourpresentation.Also,allofthe notionswhichweintroduceinthesechaptersareimplementedinbothPythonand OCamltoassistreaderslearningaboutthesemanticconceptsinquestionforthefirst time.Multipleexercises,withdetailedsolutions,areprovidedinbothcases.Chapter 5,onthesubjectoftyping,beginsbyaddressingtypingrules,whichareusedto checkprograms;wethenpresentthealgorithmusedtoinferpolymorphictypes, alongwiththeassociatedmathematicalnotions,allimplementedinbothlanguages. Finally,theextensionoftypingtoimperativefeaturesisaddressed.InChapter6,we
presentthemaindatatypesandmethodsofpatternmatching,usingarangeof examplesexpressedindifferentprogramminglanguages.Chapter7focuseson low-levelprogrammingfeatures:endianness,pointersandmemorymanagement; thesenotionsaremostlypresentedusingCandC++.Volume1endswitha discussionoferrorprocessingusingexceptions,theirsemanticsispresentedin OCaml,andtheexceptionmanagementmechanismsusedinPython,JavaandC++ arealsodescribed(seeChapter8).
Thus,Volume1isintendedtogiveabroadoverviewofthefunctionaland imperativefeaturesofprogramming,fromnotionsthatcanbemodeled mathematicallytonotionsthatarelinkedtothehardwareconfigurationofcomputers themselves.Volume2focusesonmodularandobjectprogramming,buildingonthe foundationslaiddowninVolume1sincemodules,classesandobjectsare,in essence,themeansoforganizingfunctionalorimperativeconstructs.Volume2first analyzestheneedsofdevelopersintermsoftoolsforsoftwarearchitecture.Basedon thisstudy,anoriginalsemanticmodel,calleda kit,isdrawnup,jointlypresentingall thefeaturesofthemodulesandobjectsthatcanmeettheseneeds.Thesemanticsof thesekitsaredefinedinaratherinformalway,asresearchinthisfieldhasnotyetled toamathematicalmodelofthissetoffeatures,whileremainingrelativelysimple. Fromthismodel,weconsiderasetofemergingquestions,theobjectiveofwhichis toguidetheacquisitionofalanguage.Thisapproachisthenexemplifiedbythestudy ofthemodulesystemsofAda,OCamlandC.Finally,thesameapproachwillbeused todeduceasemanticmodelofclassandobjectfeatures,whichwillservetopresent classesinJava,C++,OCamlandPythonfromaunifiedperspective.
Thisworkisaimedatarelativelywideaudience,fromexperienceddevelopers–whowillfindvaluableadditionalinformationonlanguagesemantics–tobeginners whohaveonlywrittenshortprograms.Forbeginners,werecommendworkingonthe semanticconceptsdescribedinVolume1usingtheimplementationsinOCamlor Pythontoeaseassimilation.Allreadersmaybenefitfromstudyingthereference manualofaprogramminglanguage,whilecomparingthepresentationsofconstructs giveninthemanualwiththosegivenhere,guidedbythequestionsmentionedin Volume2.
Notethatwedonotdiscussthealgorithmicaspectofdataprocessinghere. However,choosingthealgorithmandthedatarepresentationthatfittherequirements ofthespecificationisanessentialstepinprogramdevelopment.Manyexcellent workshavebeenpublishedonthissubject,andweencouragereaderstoexplorethe subjectfurther.Wealsorecommendusingthestandardlibrariesprovidedbythe chosenprogramminglanguage.Theselibrariesincludetriedandtested implementationsformanydifferentalgorithms,whichmaygenerallybeassumedto becorrect.
Thisfirstchapterprovidesabriefoverviewofthecomponentsfoundinall computers,frommainframestotheprocessingchipsintablets,smartphonesand smartobjectsviadesktoporlaptopcomputers.Buildingonthishardware-centric presentation,weshallthengiveamoreabstractdescriptionoftheactionscarriedout bycomputers,leadingtoauniformdefinitionoftheterms“program”and “execution”,aboveandbeyondthevariouscharacteristicsofso-calledelectronic devices.
1.1.Computers:alow-levelview
Computerscienceisthescienceofrationalprocessingofinformationby computers.Computershavethecapacitytocarryoutavarietyofprocesses, dependingontheinstructionsgiventothem.Eachitemof information isanelement ofknowledgethatmaybetransmittedusingasignalandencodedusingasequenceof symbolsinconjunctionwithasetofrulesusedtodecodethem,i.e.toreconstructthe signalfromthesequenceofsymbols.Computersusebinaryencoding,involvingtwo symbols;thesemaybereferredtoas“true”/“false”,“0”/“1”or“high”/“low”;these termsareinterchangeable,andallrepresentthetwostablestatesoftheelectrical potentialofdigitalelectroniccircuits.
1.1.1. Informationprocessing
Schematically,acomputerismadeupofthreefamiliesofcomponentsasfollows: –memories:storedata(information)andexecutablecode(theso-calledvon Neumannarchitecture);
–oneormoremicroprocessors,knownasCPUs(centralprocessingunits),which processinformationbyapplyingelementaryoperations;
–peripherals:theseenableinformationtobeexchangedbetweenthe CPU/memorycoupleandtheoutside.
Informationprocessingbyacomputer–inotherterms,theexecutionofa program–canbesummarizedasasequenceofthreesteps:fetchingdata,computing theresultsandreturningthem.Eachelementaryprocessingoperationcorrespondsto aconfigurationofthelogicalcircuitsoftheCPU,knownasa logicfunction.Ifthe resultofthisfunctionissolelydependentoninput,andifnonotionof“time”is involvedinthecomputations,thenthefunctionissaidtobe combinatorial; otherwise,itissaidtobe sequential.
Forexample,abinaryhalf-adder,asshowninFigure1.1,isacircuitthat computesthesumoftwobinarydigits(input),alongwiththepossiblecarryvalue.It thusimplementsacombinatoriallogicfunction.
Theessentialcharacterofacombinatorialfunctionisthat,forthesameinput,the functionalwaysproducesthesameoutput,nomatterwhatthecircumstances.Thisis nottrueofsequentiallogicfunctions.
Forexample,alogicfunctionthatcountsthenumberoftimesitsinputchanges reliesonanotionof“time”(changestakeplaceintime),andapersistentstatebetween twoinputsisrequiredinordertorecordthepreviousvalueofthecounter.Thisstateis savedina memory.Forsequentialfunctions,asameinputvaluecanresultindifferent outputvalues,aseveryoutputdependsnotonlyontheinput,butalsoonthestateof thememoryatthemomentofreadingthenewinput.
1.1.2. Memories
Computersusememorytosaveprogramsanddata.Thereareseveraldifferent technologiesusedinmemorycomponents,andasimplifiedpresentationisasfollows: –RAM(RandomAccessMemory):RAMmemoryisbothreadableandwriteable. RAMcomponentsaregenerallyfast,butalsovolatile:ifelectricpowerfallsdown, theircontentislost;
Figure1.1. Binaryhalf-adder
–ROM(ReadOnlyMemory):informationstoredinaROMiswrittenatthetime ofmanufacturing,anditisread-only.ROMisslowerthanRAM,butisnon-volatile, like,forexample,aburnedDVD;
–EPROM(ErasableProgrammableReadOnlyMemory):thismemoryis non-volatile,butcanbewrittenusingaspecificdevice,throughexposuretoultravioletlight,orbymodifyingthepowervoltage,etc.ItisslowerthanRAM,forboth readingandwriting.EPROMmaybeconsideredequivalenttoarewritableDVD.
Computersusethememorycomponentsofseveraltechnologies.Storagesize diminishesasaccessspeedincreases,asfast-accessmemoryismorecostly.A distinctionisgenerallymadebetweenfourdifferenttypesofmemory:
–massstorageismeasuredinterabytesandismadeeitherofmechanicaldisks (withanaccesstimeof ∼ 10 ms)or–increasingly–ofsolid-statedrive(SSD)blocks. TheseblocksuseanEEPROMvariant(electricallyerasable)withanaccesstimeof ∼ 0 1 0 3 ms,knownas flashmemory.Massstorageisnon-volatileandisprincipally usedforthefilesystem;
–RAM,whichisexternaltothemicroprocessor.Recenthomecomputersand smartphonesgenerallypossesslargeRAMcapacities(measuredingigabytes). Embeddedsystemsorconsumerdevelopmentelectronicboardsmayhaveamuch lowerRAMcapacity.Theaccesstimeisaround40–50 η s;
–the cache isgenerallyincludedintheCPUofmodernmachines.Thisisasmall RAMmemoryofafewkilobytes(ormegabytes),withanaccesstimeofaround 5 10 η s.Thereareoftenmultiplelevelsofcache,andaccesstimedecreaseswithsize. Thecacheisusedtosavefrequentlyusedand/orconsecutivedataand/orinstructions, reducingtheneedtoaccessslowerRAMbyretaininginformationlocally.Cache managementiscomplex:itisimportanttoensureconsistencybetweenthedatain themainmemoryandthecache,betweendifferentCPUsordifferentcores(full, independentprocessingunitswithinthesameCPU)andtodecidewhichdatato discardtofreeupspace,etc.;
– registers arethefastestmemoryunitsandarelocatedinthecenterofthe microprocessoritself.Themicroprocessorcontainsalimitednumber(afewdozen) ofthesestoragezones,useddirectlybyCPUinstructions.Accesstimeisaroundone processorcycle,i.e.around1ns.
1.1.3. CPUs
TheCPU,asitsnamesuggests,istheunitresponsibleforprocessinginformation, viatheexecutionof elementaryinstructions,whichcanberoughlygroupedintofive categories:
–datatransferinstructions(copybetweenregistersorbetweenmemoryand registers);
–arithmeticinstructions(additionoftwointegervaluescontainedintworegisters, multiplicationbyaconstant,etc.);
–logicalinstructions(bit-wiseand/or/not,shift,rotate,etc.);
–branchingoperations(conditional,non-conditional,tosubroutines,etc.);
–otherinstructions(halttheprocessor,reset,interruptrequests, test-and-set, compare-and-swap,etc.).
Instructionsarecodedbybinarywordsinaformatspecifictoeachmicroprocessor. Aprogramofafewlinesinahigh-levelprogramminglanguageistranslatedintotens orevenhundredsofelementaryinstructions,whichwouldbedifficult,errorprone andtimeconsumingtowriteoutmanually.ThisisillustratedinFigure1.2,wherea “HelloWorld!”programwritteninCisshownalongsideitscounterpartinx86-64 instructions,generatedbythe gcc compiler.
.section__TEXT .globl_main .align4,0x90 _main:
#include<stdio.h> intmain(){ printf("Hellow orld!\n"); return(0); }
.cfi_startproc ##BB#0: pushq%rbp Ltmp0: .cfi_def_cfa_offset16 Ltmp1: .cfi_offset%rbp, 16 movq%rsp,%rbp Ltmp2:
.cfi_def_cfa_register%rbp subq$16,%rsp leaqL_.str(%rip),%rdi movl$0, 4(%rbp) movb$0,%al callq_p rintf xorl%ecx,%ecx movl%eax, 8(%rbp) movl%ecx,%eax addq$16,%rsp popq%rbp retq .cfi_endproc .section__TEXT L_.str: .asciz"Helloworld!\n"
Putsimply,amicroprocessorissplitintotwoparts:acontrolunit,whichdecodes andsequencestheinstructionstoexecute,andoneormorearithmeticandlogicunits (ALUs),whichcarryouttheoperationsstipulatedbytheinstructions.TheCPUruns permanentlythroughathree-stagecycle:
Figure1.2. “Helloworld!”inCandinx86-64instructions
1)fetchingthenextinstructiontobeexecutedfromthememory:every microprocessorcontainsaspecialregister,theProgramCounter(PC),whichrecords thelocation(address)ofthisinstruction.ThePCisthenincremented,i.e.thesizeof thefetchedinstructionisaddedtoit;
2)decodingofthefetchedinstruction;
3)executionofthisinstruction.
However,thenextinstructionisnotalwaystheonelocatednexttothecurrent instruction.Considerthefunction min inexample1.1,writteninC,whichreturnsthe smallestofitstwoarguments.
E XAMPLE 1.1.–
C intmin(inta,intb){ if(a<b)return(a); elsereturn(b); }
Thisfunctionmaybetranslated,intuitivelyandnaively,intoelementary instructions,byfirstplacing a and b intoregisters,thencomparingthem:
min: loada,reg0 loadb,reg1 comparereg0,reg1
Dependingontheresultofthetest–trueorfalse–differentcontinuationsare considered.Executioncontinuesusinginstructionsforoneortheotherofthese continuations:wethereforehavetwopossiblecontrolpaths.Inthiscase,a conditionaljump instructionmustbeusedtomodifythePCvalue,whenrequired,to selectthefirstinstructionofoneofthetwopossiblepaths.
branchgta_gt_b loadreg0,reg2 jumpend
a_gt_b: loadreg1,reg2 end: returnreg2
The branchgt instructionloadsthelocationoftheinstructionatlabel a_gt_b into thePC.Iftheresultofthe compare instructionisthat reg0 > reg1,thenextinstruction istheonefoundatthisaddress: loadreg1,reg2.Otherwise,thenextinstructionis theonefollowing branchgt: loadreg0,reg2.Thisisfollowedbythe unconditional
jump instruction, jump,enablingunconditionalmodificationofthePC,loadingitwith theaddressofthe end label.Thus,whatevertheresultofthecomparison,execution finisheswiththeinstruction returnreg2.
Conditionalbranchingrequirestheuseofaspecificmemorytodetermine whethercertainconditionshavebeensatisfiedbytheexecutionoftheprevious instruction(overflow,positiveresult,nullresult,superiority,etc.).EveryCPU containsadedicatedregister,theStateRegister(SR),inwhicheverybitisassigned tosignalingoneoftheseconditions.Executingmostinstructionsmaymodifyallor someofthebitsintheregister.Conditionalinstructions(bothjumpsandmore “exotic”variants)usetheappropriatebitvaluesforexecution.CertainARM ® architectures[ARM10]evenpermitallinstructionstobeintrinsicallyconditional.
Everyprogramismadeupoffunctionsthatcanbecalledatdifferentpointsinthe programandthesecallscanbenested.Whenafunctioniscalled,thepointwhere executionshouldresumeoncetheexecutionofthefunctioniscompleted–the return address –mustberecorded.Consideraprogrammadeupofthefunctions g ()= k ()+ h() and f ()= g ()+ h(),featuringseveralfunctioncalls,someofwhich arenested.
g()= t11=k() t12=h() returnt11+t12
f()= v11=g() v12=h() returnv11+v12
Asingleregisterisnotsufficienttorecordthereturnaddressesofthedifferent calls.Calling k from g mustbefollowedbycalling h toevaluate t12.Butthiscall of g wasdoneby f,thusitsreturnaddressin f shouldalsobememorizedtofurther evaluationof v12.Thenumberofreturnaddressestorecordincreaseswiththenumber ofnestedcalls,anddecreasesasweleavethesecalls,suggestingverynaturallytosave theseaddressesina stack.Figure1.3showstheevolutionofastackstructureduring successivefunctioncalls,demonstratingtheneedtorecordmultiplereturnaddresses. Thestateofthestackisshownateverystepoftheexecution,atthemomentwherethe lineintheprogramisbeingexecuted.
Adedicatedregister,theStackPointer(SP),alwayscontainstheaddressofthe nextfreeslotinthestack(or,alternatively,theaddressofthelastslotused).Thus, inthecaseofnestedcalls,thereturnaddressissavedattheaddressindicatedbythe SP,andtheSPisincrementedbythesizeofthisaddress.Whenthefunctionreturns, thePCisloadedwiththesavedaddressfromthestack,andtheSPisdecremented accordingly.
Insummary,theinternalstateofamicroprocessorismadeupofitsgeneral registers,theprogramcounter,thestateregisterandthestackpointer.Note,however, thatthisisahighlysimplifiedvision.Therearemanydifferentvarietiesof microprocessorswithdifferentinternalarchitecturesand/orinstructionsets(for example,somedonotpossessanintegerdivisioninstruction).Thus,aprogram writtendirectlyusingtheinstructionsetofamicroprocessorwillnotbeexecutable usinganothermodelofmicroprocessor,anditwillneedtoberewritten.The portabilityofprogramswrittenintheassemblylanguageofagivenmicroprocessoris practicallynull.High-levellanguagesrespondtothisproblembyprovidingsyntactic constructs,whichareindependentofthetargetmicroprocessors.Thecompilerorthe interpreterhavetotranslatetheseconstructsintothelanguageusedbythe microprocessor.
1.1.4. Peripheraldevices
Aswesawinsection1.1.3,processorsexecuteaconstantcycleoffetching, decodingandexecutinginstructions.Computationsarecarriedoutusingdatastored inthememory,eitherbytheprogramitselforbyaninput/outputmechanism.The resultsofcomputationsarealsostoredinthememory,andmaybereturnedtousers usingthisinput/outputmechanism.
Theinterestofanyprogrammablesystemisinherentlydependentoninput/output capacitiesthroughwhichthesystemreactstotheexternalenvironmentandmayact onthisenvironment.Evenanassemblyrobotinacarfactory,whichrepeatsthesame actionsagainandagain,mustreacttodatainputfromtheenvironment.Forexample, thepressureofthegripmechanismmuststopincreasingonceithascaughtabolt,and thetimeittakestodothiswilldifferdependingontheexactpositionofthebolt.
Input/outputsystemsoperateusing peripherals,ancillarydevicesthatmaybe electronic,mechanicaloracombinationofthetwo.Theseallowthemicroprocessor toacquireexternalinformation,andtotransmitinformationtotheexterior.Computer
mice,screensandkeyboardsareperipheralsusedwithdesktopcomputers,butother elementssuchasmotors,analog/digitalacquisitioncards,etc.arealsoperipherals.
Ifperipheralsarepresent,themicroprocessorneedstodevotepartofits processingtimetodataacquisitionandtothetransmissionofcomputedresults.This interactionwithperipheralsmaybedirectlyintegratedintoprograms.Butinthis case,theprogramshavetointegrateregularcheckingofinputperipheralstoseeif newinformationisavailable.Itistechnicallydifficult(ifnotimpossible)toinclude suchamonitoringineveryprogram.Furthermore,regularperipheralchecksarea wasteoftimeandenergyifnonewdataisavailable.Finally,thereisnoguarantee thatinformationwouldarriveexactlyatthemomentofchecking,asdatamaybe asynchronously emitted.
Thisproblemcanbeavoidedbyrelyingonthehardwaretoindicatethe occurrenceofnewexternalevents,insteadofusingsoftwaretocheckforthese events.The interrupt mechanismisusedtointerrupttheexecutionofthecurrentcode andtolaunchtheinterrupthandlerassociatedwiththeexternalevent.Thishandleris asectionofcode,whichisnotexplicitlycalledbytheprogrambeingexecuted;itis locatedatanaddressknownbythemicroprocessor.Asanyprogrammaybe interruptedatanypoint,theprocessorstate,andnotablytheregisters,mustbesaved beforeprocessingtheinterrupt.Thecodethatisexecutedtoprocesstheinterruptwill indeedusetheregistersandmodifytheSR,SPandPC.Therefore,previousvaluesof registersmustberestoredinordertoresumeexecutionoftheinterruptedcode.This contextsavingiscarriedoutpartiallybythehardwareandpartiallybythesoftware.
1.2.Computers:ahigh-levelview
Thelow-levelvisionofavonNeumannmachinepresentedinsection1.1 providesagoodoverviewofthecomponentsofacomputerandofprogram execution,withoutgoingintodetailconcerningtheoperationsofelectronic components.However,thisviewisnotparticularlyhelpfulinthecontextofeveryday programmingactivity.Programsinbinarycode,orevenassemblycode,aredifficult towriteastheyneedtotakeaccountofeverydetailofexecution;theyare,bynature, longandhardtoreview,understandanddebug.Thefirst“high-level”programming languagesemergedveryshortlyafterthefirstcomputers.Theselanguagesassign namestocertainvaluesandaddressesinthememory,providingasetofinstructions thatcanbesplitintolow-levelmachineinstructions.Inotherterms,programming languagesofferanabstractvisionofthecomputer,enablinguserstoignorelow-level detailswhilewritingaprogram.The“helloworld”programinFigure1.2clearly demonstratesthepowerofabstractionofCcomparedtotheX86assemblylanguage.
1.2.1. Modelingcomputations
Anyprogramissimplyadescription,initsownprogramminglanguage,ofa seriesofcomputations(includingreadingandwriting),whicharetheonlyoperations thatacomputercancarryout.Anabstractviewofacomputerrequiresanabstract view–wecallita model –ofthenotionofcomputation.Thissubjectwasfirst addressedwellbeforetheemergenceofcomputers,inthelate19thcentury,by logicians,mathematiciansandphilosophers,whointroducedarangeofdifferent approachestothetheoryofcalculability.
TheTuringmachine[TUR95]isamathematicalmodelofcomputationintroduced in1936.Thismachineoperatesonaninfinitememorytapedividedintocellsandhas threeinstructions:moveonecellofthetaperightorleft,writeorreadasymbolin thecellorcomparethecontentsoftwocells.Ithasbeenformallyproventhatany “imperative”programminglanguage,featuringassignment,aconditionalinstruction anda while loop,hasthesamepowerofexpressionasthisTuringmachine.
Severalothermodelsofthenotionofalgorithmiccomputationwereintroduced overthecourseofthe20thcentury,andhavebeenformallyproventobeequivalent totheTuringmachine.OnenotableexampleisKleene’srecursiontheory[KLE52], thebasisforthe“purefunctional”languages,basedonthenotionof(potentially) recursivefunctions;hence,theselanguagesalsohavethesamepowerofexpression astheTuringmachine.Purefunctionalandimperativelanguageshavedevelopedin parallelthroughoutthehistoryofhigh-levelprogramming,leadingtodifferent programmingstyles.
1.2.2. High-levellanguages
Broadlyspeaking,theexecutionofafunctionalprogramcarriesoutaseriesof functioncallsthatleadtotheresult,withintermediatevaluesstoredexclusivelyin theregisters.Theexecutionofanimperativeprogramcarriesoutasequenceof modificationsofmemorycellsnamedbyidentifiers,thevaluesinthecellsbeing computedduringexecution.Themostwidespreadhigh-levellanguagesincludeboth functionalandimperativefeatures,alongwithvariouspossibilities(modules,object features,etc.)todividesourcecodeintopiecesthatcanbereused.
Whateverthestyleofprogrammingused,anyprogramwritteninahigh-level languageneedstobetranslatedintobinarylanguagetobeexecuted.These translationsareexecutedeithereverytimetheprogramisexecuted–inwhichcase thetranslationprogramisknownasan interpreter orjustonce,storingtheproduced binarycode–inwhichcasethetranslatorisknownasa compiler.
Aswehaveseen,high-levellanguagesfacilitatethecodingofalgorithms.They easereviewingofthesourcecodeofaprogram,asthetextismoreconcisethanit
10ConceptsandSemanticsofProgrammingLanguages1
wouldbeforthesamealgorithminassemblycode.Thisdoesnot,however,implythat usersgainabetterunderstandingofthewaytheprogramworks.Towriteaprogram, apreciseknowledgeoftheconstructsused–inotherterms,their semantics,what theydoandwhattheymean–iscrucialtounderstandthesourcecode.Bugsarenot alwaystheresultofalgorithmcodingerrors,andareoftencausedbyanerroneous interpretationofelementsofthelanguage.Forexample,theincrementationoperator ++ inCexistsintwoforms(i++ or ++i),anditsunderstandingisnotassimpleasit mayseem.Forexample,theprogram:
C #include<stdio.h>
intmain(){ inti=0; printf("%d\n",i++); return(0); } willprint0,butif i++ isreplacedwith ++i,thesameprogramwillprint1.
Thereareanumberofconceptsthatarecommontoallhigh-levellanguages:value naming,organizationofnamespaces,explicitmemorymanagement,etc.However, theseconceptsmaybeexpressedusingdifferentsyntacticconstructs.Thefieldof languagesemanticscoversasetoflogico-mathematicaltheories,whichdescribethese conceptsandtheirproperties.Constructingthesemanticsofaprogramallowstothe formalverificationofwhethertheprogrampossessesalloftherequiredproperties.
1.2.3. Fromsourcecodetoexecutableprograms
Thetransitionfromtheprogramsourcetoitsexecutionisamultistepprocess. Someofthesestepsmaydifferindifferentlanguages.Inthissection,weshallgive anoverviewofthemainstepsinvolvedinanalyzingandtransformingsourcecode, applicabletomostprogramminglanguages.
Thesourcecodeofaprogramismadeupofoneormoretextfiles.Indeed,toease softwarearchitecture,mostlanguagesallowsourcecodetobesplitacrossseveralfiles, knownas compilationunits.Eachfileisprocessedseparatelypriortothefinalphase, inwhichtheresultsofprocessingarecombinedintoonesingle executable file.
1.2.3.1. Lexicalanalysis
Lexicalanalysis isthefirstphaseoftranslation:itconvertsthesequenceof charactersthatisindeedthesourcefileintoasequenceof words,assigningeachtoa category.Commentsaregenerallydeletedatthisstage.Thus,inthefollowingtext presumedtobewritteninC
/*Thisisacomment.*/ if[x==3int+)cos($v)
lexicalanalysiswillrecognizethekeyword if,theopeningbracket,theidentifier x, theoperator ==,theintegerconstant 3,thetypeidentifier int,etc.NowordinCcan containthecharacter $,soalexicalerrorwillbehighlightedwhen $v isencountered.
Lexicalanalysismaybeseenasaformof“spellcheck”,inwhicheachrecognized wordisassignedtoacategory(keyword,constant,identifier).Thesewordsarereferred toas tokens
1.2.3.2.
Syntacticanalysis
Everylanguagefollows grammar.Forexample,inEnglish,asentenceis generallyconsideredtobecorrectlyformedifitcontainsasubject,verband complementinanunderstandableorder.Programminglanguagesarenoexception: syntacticanalysis verifiesthatthephrasesofasourcefileconformwiththegrammar oftheirlanguage.Forexample,inC,thekeyword if mustbefollowedbya bracketedexpression,aninstructionmustendwithasemicolon,etc.Clearly,the sourcetextgivenintheexampleaboveinthecontextoflexicalanalysisdoesnot respectthesyntaxofC.
Technically,thesyntacticanalyzerisinchargeofthecompletegrammatical analysisofthesourcefile.Itcallsthelexicalanalyzereverytimeitrequiresatokento progressthroughtheanalyzedsource.Syntacticanalysisisthusaformofgrammar verification,anditalsobuildsarepresentationofthesourcefilebyadatastructure, whichisoftenatree,calledthe abstractsyntaxtree (AST).Thisdatastructurewill beusedbyallthefollowingphasesofcompilation,uptothepointofexecutionbyan interpreterorthecreationofanexecutablefile.
1.2.3.3. Semanticanalyses
Thefirsttwoanalysisphasesofcompilationonlyconcernthetextualstructureof thesource.Theydonotconcernthe meaning oftheprogram,i.e.its semantics.Source textsthatpassthesyntacticanalysisphasedonotalwayshavemeaning.Thephrase “theseaeatsaderivablerabbit”isgrammaticallycorrect,butisevidentlynonsense.
Thebest-knownsemanticanalysisisthetypinganalysis,whichprohibitsthe combinationofelementsthatareincompatibleinnature.Thus,inthepreviousphase, “derivable”couldbeapplicabletoafunction,butcertainlynottoa“rabbit”.
Semanticanalysesdonotreducetoaformoftypinganalysisbuttheyallinterpret theconstructsofaprogramaccordingtothesemanticsofthechosenlanguage. Semanticanalysesmaybeusedtoeliminateprograms,whichleadstoexecution errors.Theymayalsoapplysometransformationstoprogramcodeinordertogetan
executablefile(dependencyanalysis,closureelimination,etc.).Thesesemantic analysesmaybecarriedoutduringsubsequentpassesofsourcecodeprocessing, evenafterthecodegenerationphasedescribedinthefollowingsection.
1.2.3.4. Codeinterpretation/generation
Oncetheabstractsyntaxtree(oraderivedtree)hasbeencreated,therearetwo options.Eitherthetreemaybeexecuteddirectlyviaan interpreter,whichisaprogram suppliedbytheprogramminglanguage,ortheASTisusedtogenerate object code files,withtheaimofcreatinganexecutablefilethatcanberunindependently.Letus firstfocusonthesecondapproach.Theinterpretationmechanismwillbediscussed later.
CompilationusestheASTgeneratedfromthesourcefiletoproduceasequence ofinstructionstobeexecutedeitherbytheCPUorbyavirtualmachine(VM).The compilationiscorrectiftheexecutionofthissequenceofinstructionsgivesaresult, whichconformstotheprogram’ssemantics.
Optimizationphasesmaytakeplaceduringorafterobjectcodegeneration,with theaimofimprovingitscompactnessoritsexecutionspeed.Moderncompilers implementarangeofoptimizations,whichstudyliesoutsidethescopeofthisbook. Certainoptimizationsare“universal”,whileothersmaybespecifictotheCPUfor whichthecodeisgenerated.
Theobjectcodeproducedbythecompilermaybeeitherbinarycodeencoding instructionsdirectlyorsourcetextinassemblycode.Inthelattercase,aprogram–knownasthe assembler –mustbecalledtotransformthislow-levelsourcecodeinto binarycode.Generallyspeaking,assemblerssimplyproduceamechanical translationofinstructionswrittenmnemonically(mov, add, jmp,etc.)intobinary representations.However,certainmoresophisticatedassemblersmayalsocarryout optimizationoperationsatthislevel.
Assemblingmnemoniccodeintobinarycodeisaverysimpleoperation,which doesnotalterthestructureoftheprogram.ThereferencemanualofthetargetCPU provides,foreachinstruction,themeaningofthebitsofthecorrespondingbinary word.Forexample,thereferencemanualfortheMIPS32®architecture[MIP13] describesthe32-bitbinaryformatoftheinstruction ADDrd,rs,rt (withtheeffect rd ← rs+rt ontheregisters)as:
Figure1.4. CodingtheADDinstructioninMIPS32®
Threepacketsof6bitsarereservedforencodingtheregisternumbers;theother bitsinthiswordarefixedandencodetheinstruction.Thetaskoftheassembleris togeneratesuchbitpatternsaccordingtotheinstructionsencounteredinthesource code.
1.2.3.5. Linking
Asingleprogrammaybemadeupofseveralsourcefiles,compiledseparately. Oncetheobjectcodefromeachsourcefilehasbeenproduced,allthesecodesmust becollectedintoasingleexecutablefile.Eachobjectfileincludes“holes”,indicating unknowninformationatthemomentofproductionofthisobjectcode.Itisimportant toknowwheretofindthismissingcode,whencallingfunctionsdefinedinadifferent compilationunit,orwheretofindvariablesdefinedinalocationoutsideofthecurrent unit.
The linker hastogatheralltheobjectfilesandfillalltheholes.Evidently,fora setofobjectfilestoleadtoanexecutablefile,allholesmustbefilled;sothecode ofeveryfunctioncalledinthesourcemustbeavailable.Thelinkingprocessalso hastointegratetheneededcode,ifitcomesfromsomelibraries,whetherfromthe standardlanguagelibraryorathird-partylibrary.Thereisonefinalquestiontoanswer, concerningthepointatwhichexecutionshouldbegin.Incertainlanguages(suchasC, C++andJava),thesourcecodemustcontainone,andonlyone,specialfunction,often named main,whichiscalledtostarttheexecution.Inotherlanguages(suchasPython andOCaml),definitionsareexecutedintheorderinwhichtheyappear,definedbythe fileorderingduringthelinkingprocess.Thus,“executing”thedefinitionofafunction doesnotcallthefunction:instead,the“value”ofthisfunctioniscreatedandstored tobeusedlaterwhenthefunctioniscalled.Thismeansthatprogrammershaveto insertintothesourcefileacalltothefunctionwhichtheyconsidertobethe“starting point”oftheexecution.Thiscallisusuallythefinalinstructionofthelastsourcefile processedbythelinker.
Asimplifiedillustrationofthedifferenttransformationpassesinvolvedinsource codecompilationisshowninFigure1.5. generation
1.2.3.6.
Interpretationandvirtualmachines
Aswehaveseen,informallyspeaking,aninterpreter“executes”aprogramdirectly fromtheAST.Furthermore,itwassaidthatthecodegenerationprocessmaygenerate
Figure1.5. Compilationprocess
codeforavirtualmachine.Inreality,interpretersrarelyworkdirectlyonthetree; compilationtoavirtualmachineisoftencarriedoutasanintermediatestage.A virtual machine (VM)maybeseenasapseudo-microprocessor,withoneormorestacks, registersandfairlyhigh-levelinstructions.ThecodeforaVMisoftenreferredtoas bytecode.Inthiscase,compilationdoesnotgenerateafiledirectlyexecutablebythe CPU.Executioniscarriedoutbythe virtualmachineinterpreter,aprogramsupplied bytheprogramminglanguageenvironment.So,thedifferencebetweeninterpretation andcompilationisnotclear-cut.
ThereareseveraladvantagesofusingaVM:thecompilernolongerneedstotake thespecificitiesoftheCPUintoaccount,thecodeisoftenmorecompactand portabilityishigher.Aslongastheexecutablefileforthevirtualmachineinterpreter isavailableonacomputer,itwillbepossibletogenerateabinaryfileforthe computerinquestion.Thedrawbacktothisapproachisthattheprogramsobtainedin thiswayareoftenslowerthanprogramscompiledas“native”machinecode.
