Table Of Content·
Tom Addis Jan Addis
Drawing Programs:
The Theory and Practice
of Schematic Functional
Programming
1 3
TomAddis JanAddis
UniversityofPortsmouth ClaritySupport
SchoolofComputing SouthseaPO49QU
PortsmouthP013HE UnitedKingdom
UnitedKingdom
ISBN978-1-84882-617-5 e-ISBN978-1-84882-618-2
DOI10.1007/978-1-84882-618-2
SpringerLondonDordrechtHeidelbergNewYork
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressControlNumber:2009927007
©Springer-VerlagLondonLimited2010
Preface
Drawing programs is a personal response to some very practical problems. To
explain this I need to go back in time to when my greatest toy was the Mechano
set;amechanicalconstructionkitwithinstructionsonhowtobuildyourowntoys.I
soonfoundthatalthoughthekitwasboundlessinonesenseitwasalsoverylimited.
I spent many hours trying to do things that were well beyond the intention of the
kitdesigner.MuchlaterIfoundelectronicswherecircuitsprovidedmewithamuch
widerscopeformodelbuildingbutitstilltookalongtimetomakedevices.Itwas
notuntilprogrammingwasintroducedduringmytimeatUniversitythatthisreally
flexibletoolwasmadeavailable.Nomorebleedingfingersfromtheironworkand
no more burnt ties from soldering irons. Modelling was going to be easy and fun.
However,therewassnag.Ihadanaturalinabilitytospelloreventoconstructcoher-
ent written sentences. It is true that I had evolved many strategies to successfully
overcomethisproblembutthestrategiesonlyworkedwithinalimitedframework.
Theproblemwithprogramsisthattheyarewrittenandinvolvetheaccurateuseof
characters.Mostofmytimewasspentinpursuingtyposandverylittletimeonthe
programming.Sometimesitwasnecessarytoasksomeonetolookformeandusu-
ally they could identify the problem within seconds; natural ability is a wonderful
thing.
FunctionalprogrammingintheformofLISPcamealongandthepowerofthis
language for expressing formal systems in an elegant way was very exciting. It
wasonemoveawayfromhavingtoworryabouttheactualphysicalcomputerwith
all its storage management problems and one step closer to a language designed
specifically for modelling. It was like stepping into an automatic car after years
of struggling with manual gears. Even though practical computer languages had
moved a long way from machine code it was still only a change from the crash
gearboxtosynchromesh.Thecomputerstructurewasstillinthebackgroundinthat
everythingwasforcedintotheframeworkofdataandprocessesthusreflectingthe
fundamentaldualdistinctionwithinthemachineitself.Theproblemwithfunctional
programmingwasthatitwasconstrainedbyitsownformalframeworkandstopped
short of being able to extend itself. LISP overcame this problem, to some extent,
by slipping back into the computer framework by introducing special ‘program’
typefunctions.Italsoovercame another limitationbyallowing thelanguage tobe
extended beyond the original formal functional description. In some cases it was
stillveryclumsyandfrommypointofviewstillrequiredbeingwritten.
As an engineer, electronic circuits had been no problem to read, to find errors
ortoremember.Ifonlyprogrammingcouldbemadethateasy.Itwasthisdriveto
createatoolthatwouldsidestepissuesofspellingandyetstillprovideaprofessional
toolfordevelopingmodelsandotherkindsofprograms.ThisledustocreateClarity,
or rather, led Jan to develop the Clarity environment for me. Also, while we were
at it, we could also eliminate some of the restrictions found in current text-based
languages.
Clarity has been introduced quite slowly in this book simply because it seems
tobeslightlyatoddswiththenormalwindowsapproach.Thisisnottoosurprising
since it was developed well before windows had become generally available and
itwasalsodrivenbydifferentrequirements.Thetheoryrelatedtodesigningmod-
elshasbeenincludedrightfromthebeginningbutforpracticalpurposesitcanbe
skipped.
The justification for Clarity given in Chapter 1 is in response to criticism of
thediagrammaticapproachtoprogramming.Theseotherdiagrammaticapproaches
have usually been stimulated by a desire to make programming available to non-
programmers. This is not the purpose behind Clarity. Clarity has been driven by a
need to provide a sophisticated tool for programmers that would rather work with
diagramsthanwithtext.Projectsaregivenattheendofeachchapter.Thesefollow
thestyleoftheMechanoinstructionbookinthateverystepisdescribed.Thepur-
poseofdoingitthiswayistoshowhowdrawingprogramsshouldbedoneandto
giveanillustrationofgoodtechniques.
Clarity has been developed over the last 23 years for a wide range of different
projects.ItevolvedoutofanIKBSproject(CARDS)in1986–1990withtheGen-
eralElectricCompany,theUniversityofReadingandtheImperialCancerResearch
FundtobuildaspecialhardwaredevicethatwouldallowthoseinvolvedwithDNA
research to create models of DNA behaviour. For this a modelling language was
needed. Originally the researchers had used Prolog. The next SERC/ESRC/MRC
projectin1991–1996waswiththeUniversitiesofBath,withProfessorDavidGood-
ing,andtheUniversityofReadingwithus,toconstructamodelofscientificdiscov-
eryfromthehistoryofscience.Thisworkisstillgoingon.Anotherprojectstarted
in1996andfundedbyShipAnalytics(nowMPRI,partoftheL3consortium)was
anexpertsystemusedasateacherreplacementforMarinerstrainingonashipsim-
ulation for gas and oil management. Work on the automatic assessment of these
studentsisalsoalmostcomplete.Otherworkinvolvingmodellingofthenegotiation
process(BillingeandAddis2008)attheUniversityofPortsmouthhascomeupwith
somesurprisingresultsrequiringustoreconsiderthemotivationbehindreasonsfor
conversation.
WehavealsotakenonsomereallygoodpostgraduatestudentsfromtheTechni-
calUniversityofDelft,TheNetherlands.ThesehavebeenprovidedbyDr,DrsLeon
Rothkrantzalmosteveryyearbetween1996and2006toworkonvariousprojects.
Many of these projects have helped to start new research directions such as those
describedinChapter10.Inparticular,DrBart-FlorisVisscherwasoneofthevisit-
ing students who led a team thatused Claritytoconstruct aplanning systemfor a
multi-leggedrobot(PortechLtd).Hewasanoutstandingstudent.Hecamebackto
PortsmouthtodoresearchwithmeandhisThesis(2005)‘ExploringComplexityin
SoftwareSystems:Fromanirrationalmodelofsoftwareevolutiontoatheoryofpsy-
chologicalcomplexityandcognitivelimitationsbasedonempiricalevidence’went
wellbeyondmyownworkstartedin1977.Itwasthrillingstuff.Healsodesigned
theembellishedClarityicononthefrontcover.
There have been many others that have helped us develop the Clarity Environ-
ment. Simon Gray (Sharp Edge Systems Ltd) was invaluable at the system level
while we working with Apple Macintosh computers and he was always a source
of new ideas. Dr. Carol Small introduced us to the functional database language
(Poulovassilis 1988) during the CARDS project and wrote the core interpreter for
theSunUNIXsystembasedonFieldandHarrisonswork(1988).JohnChewter,an
undergraduate student at the University of Portsmouth, showed considerable pro-
grammingaptitudebyconstructingtheFaithtoClarityinterpreterforhisfinalyear
project in 1995. It has been surprisingly useful. Ray Gillett (Director, MPRI, UK)
hasprovideduswithasetofexcellentpracticalindustrialprojectssince1998.These
projects have not only tested the system to its limits but many of the techniques
developedforthebeliefsystem(modelofscience)havefoundanaturalhome.We
thankhimforhispatienceinallowingustodevelopthesysteminourownway.
TheClarityschemahasallowedustoworkcloselywithmanytechnicallycom-
petent people. This close working with a fast implementation leads directly to
the models needed. Any system that is useful requires to be continually mod-
ified to keep pace with technology and changing perspectives. For this reason
we are giving away Clarity in all its forms with example databases and source
code. At the time of publishing these will be found at the publisher’s web site
http://www.springer.com/978-1-84882-617-5, the University of Portsmouth web
site http://userweb.port.ac.uk/_addist/978-1-84882-617-5.zip andaspecialClarity
communitywebsite http://www.clarity-support.com
Southsea,March2009 TomAddis
References
1. BillingeD.andAddisT.,(2008)‘SeekingAllies:ModellinghowListnersChoosetheirMusical
Friends’, Special issue of Foundations of Science, Vol 13, No1, March, pp 53–66, ISSN
1233–1821.
2. FieldA.J.andHarrisonP.G.,(1998)‘FunctionalProgramming’pubAddis-WesleyLtd,ISBN
0-201-19249-7.
3. PoulovassilisA.,(1988),‘FDL.AnIntegrationofthefunctionaldatabaseModelandtheFunc-
tionalComputerModel’,BNCOD6,CUP,Cambridge,pp215–236.
Contents
1 WhySchematicFunctionalProgramming? . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
TheCollapseofVisualLanguages[→Page12] . . . . . . . . . . . . 3
EngineeringDrawings[→Page12]. . . . . . . . . . . . . . . . . . . 4
EngineeringDrawingsUsedforProgramming[→Page12] . . . . . 6
DifferentTypesofClarity . . . . . . . . . . . . . . . . . . . . . . . . 11
ABriefHistory[→Page12] . . . . . . . . . . . . . . . . . . . . . 11
∗GettingGoing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
ALittleBitAboutFunctions[→Page17] . . . . . . . . . . . . . . . 15
∗“HelloWorld” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Exercise1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
AnExampleSchematic . . . . . . . . . . . . . . . . . . . . . . . . . 18
AFirstAttemptataSchematic . . . . . . . . . . . . . . . . . . . . . 19
Exercise1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
ChangingaFunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
SavingaProgram/Database . . . . . . . . . . . . . . . . . . . . . . . 26
LoadingaProgram/Database . . . . . . . . . . . . . . . . . . . . . . 27
Project:CreatingaSimpleClarityProgramDICE . . . . . . . . . . . 28
Dice:GeneratingaRandomNumber . . . . . . . . . . . . . . . . . 28
Exercises1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Questions1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 MakingChanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
ProblemsofSoftwareDesign[→Page42] . . . . . . . . . . . . . . . 35
ATypicalExample . . . . . . . . . . . . . . . . . . . . . . . . . . 36
TheEngineeringDimensionsofDesign . . . . . . . . . . . . . . . 36
SomeDefinitionsforPracticalResults . . . . . . . . . . . . . . . . 38
ChoiceandRandomSelection . . . . . . . . . . . . . . . . . . . . 40
∗OverYourShoulder . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ListManipulation[→Page44] . . . . . . . . . . . . . . . . . . . . . 43
∗Improving‘Awake’ . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
ALittleBitMoreAboutFunctions[→Page51] . . . . . . . . . . . . 48
Built-InLibraryandFunctionTypes[→Page51] . . . . . . . . . . . 49
Exercise2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Questions2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
∗GreatFunctionsHaveLittleFunctions . . . . . . . . . . . . . . . . . 51
MoreSchemaEditingFeatures . . . . . . . . . . . . . . . . . . . . . 54
Exercise2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Memory,WindowsandYou . . . . . . . . . . . . . . . . . . . . . . . 58
Exercise2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Questions2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Project:ASimpleInteractiveProgram . . . . . . . . . . . . . . . . . 62
Guess:FindingYourNumberwithLeastQuestions . . . . . . . . . 62
Exercise2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Questions2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3 InPursuitofElegance . . . . . . . . . . . . . . . . . . . . . . . . . 73
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
InferringInternalExperience[→Page81] . . . . . . . . . . . . . . . 74
APhilosophicalViewofComputing[→Page81] . . . . . . . . . . . 75
DualSemantics[→Page81] . . . . . . . . . . . . . . . . . . . . . . 78
MoreonFunctions[→Page81] . . . . . . . . . . . . . . . . . . . . 80
∗CreatingComponents . . . . . . . . . . . . . . . . . . . . . . . . . 81
Constructors:ThePackagingofData . . . . . . . . . . . . . . . . . . 86
LookingThroughtheFunctionWindow. . . . . . . . . . . . . . . . . 89
Exercises3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Questions3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
TheNotionofCasting . . . . . . . . . . . . . . . . . . . . . . . . . . 95
AStructureProcessDiagram (SPD) . . . . . . . . . . . . . . . . . . 95
Exercise3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Questions3.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Project:PlayingaSimpleGame . . . . . . . . . . . . . . . . . . . . . 102
Paper:OutGuesstheComputer. . . . . . . . . . . . . . . . . . . . 102
Exercise3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Questions3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4 MindMapsTMandMechanisms . . . . . . . . . . . . . . . . . . . . 111
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Junctions,ColourandOrganisation . . . . . . . . . . . . . . . . . . . 112
Annotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
ListProcessingandConstructors . . . . . . . . . . . . . . . . . . . . 118
DealingwithInput . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
FunctionsasGlobalVariables . . . . . . . . . . . . . . . . . . . . . . 123
Excercises4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Questions4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
DetailsofPattern-Matching[→Page140] . . . . . . . . . . . . . . . 125
DealingwithConditionals(Ifs)[→Page140]. . . . . . . . . . . . . . 126
TheEngineeringCoherencesofDesign[→Page140] . . . . . . . . . 127
Functionalvs.ImperativeProgramming[→Page140] . . . . . . . . . 128
CreatingaSchematicLanguage[→Page140] . . . . . . . . . . . . . 129
TheProblemsofaFunctionalLanguage . . . . . . . . . . . . . . . 129
SolvingtheProblems . . . . . . . . . . . . . . . . . . . . . . . . . 130
DoingWithout‘Ifs’[→Page140] . . . . . . . . . . . . . . . . . . 132
Exploring‘Real’Programs[→Page140] . . . . . . . . . . . . . . . . 135
TheApproach,ResultsandInterpretation . . . . . . . . . . . . . . 135
DiscussiononResults . . . . . . . . . . . . . . . . . . . . . . . . . . 138
ConsequencesoftheExperiments . . . . . . . . . . . . . . . . . . . . 138
*PROJECT:AMinimalistProgram . . . . . . . . . . . . . . . . . . . 140
Digits:DoingWithouttheBuilt-InLibrary . . . . . . . . . . . . . 140
Exercises4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Questions4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5 FunctionalThinking . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
LoopsandRecursion. . . . . . . . . . . . . . . . . . . . . . . . . . . 150
TailRecursionandAuxiliaryFunctions . . . . . . . . . . . . . . . . . 154
Exercise5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Questions5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
FunctionsasMappings[→Page160]. . . . . . . . . . . . . . . . . . 157
∗ProgrammingbyNumbers . . . . . . . . . . . . . . . . . . . . . . . 160
Exercises5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Questions5.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Project:UsingPatternMatching . . . . . . . . . . . . . . . . . . . . . 166
Snake1:SnakesandLadders . . . . . . . . . . . . . . . . . . . . . 166
Snake2:SnakesandLadders . . . . . . . . . . . . . . . . . . . . . 177
Exercise5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
6 ThinkingPractically . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
ConditionalControl . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Higher-OrderFunctions . . . . . . . . . . . . . . . . . . . . . . . . . 191
Non-recursiveApproachtoLoops . . . . . . . . . . . . . . . . . . . . 194
CreatingTwoUsefulFunctions . . . . . . . . . . . . . . . . . . . . . 196
Non-recursiveApproachtoIteration . . . . . . . . . . . . . . . . . . 199
‘Lambda’:ControllingtheParameterAssignment . . . . . . . . . . 200
EditingoutSub-functionstoaNewFunctionWindow . . . . . . . . 202
TheAnnotationWindow . . . . . . . . . . . . . . . . . . . . . . . . . 202
Exercises6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Questions6.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Project:ASimpleLearningStrategy . . . . . . . . . . . . . . . . . . 205
Oxo:TheGamePlayerThatLearns . . . . . . . . . . . . . . . . . 205
7 SideEffectProgrammingandSchematicDesign . . . . . . . . . . 223
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
FunctionsasData . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
FunctionsasRelations . . . . . . . . . . . . . . . . . . . . . . . . 226
StagesofSystemDesign. . . . . . . . . . . . . . . . . . . . . . . . . 227
Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
EvaluationControl . . . . . . . . . . . . . . . . . . . . . . . . . . 233
BenignandMalignantSideEffects . . . . . . . . . . . . . . . . . 234
SchematicDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
AnEmergentDesignTechnique . . . . . . . . . . . . . . . . . . . 235
ArtificialIntelligence . . . . . . . . . . . . . . . . . . . . . . . . . 236
TheGeneralProblemSolver . . . . . . . . . . . . . . . . . . . . . 237
GraphSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
The‘And/Or’Graph . . . . . . . . . . . . . . . . . . . . . . . . . . 239
EmergentAnalysisStage . . . . . . . . . . . . . . . . . . . . . . . 240
ConstructionStage . . . . . . . . . . . . . . . . . . . . . . . . . . 246
InSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Exercises7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Questions7.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Project:LearningfromDefeat . . . . . . . . . . . . . . . . . . . . . . 254
Oxo2:TheGamePlayerThatLearns:AContinuation . . . . . . . . 254
Oxo3:TheGamePlayerThatLearns:AnotherImprovement . . . . 259
Oxo4:TheGamePlayerThatDoesEvenBetter . . . . . . . . . . . 262
Oxo5:HinderingtheOpponent . . . . . . . . . . . . . . . . . . . . 264
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
8 AdultThings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
GraphicsOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
gr_operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
btn_operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Dialog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
NarrativeWindow(nar_) . . . . . . . . . . . . . . . . . . . . . . . . 271
AutomaticJunctionInsertionforDependencyNetworks . . . . . . . . 272
ConvertingFaithCode toClarityDiagrams . . . . . . . . . . . . . . 274
FileOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
ListsandTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
TreesandNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . 279
CastingandCodeGeneration . . . . . . . . . . . . . . . . . . . . . . 281
BayesianDecisionFunctions . . . . . . . . . . . . . . . . . . . . . . 282
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
TheBayesianTheoryofClassification[→Page285] . . . . . . . . 283
*TheBayesianFunctionsinOperation . . . . . . . . . . . . . . . . 285
MatrixOperationsandLinearSimultaneousEquations . . . . . . . . . 287
SetOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Project:UsingFaithwithClarity . . . . . . . . . . . . . . . . . . . . 289
Loans:ALoansCalculationProgram . . . . . . . . . . . . . . . . 289
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
9 Higher-OrderProgrammingandLowerLevelActivity . . . . . . . 301
SpecialFunctionClasses. . . . . . . . . . . . . . . . . . . . . . . . . 301
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
FunctionandConstructorHandling . . . . . . . . . . . . . . . . . . 302
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Client/ServerFacilities. . . . . . . . . . . . . . . . . . . . . . . . . . 309
OverviewofNetworkandMachineOrganisation . . . . . . . . . . 309
ManualNetworking . . . . . . . . . . . . . . . . . . . . . . . . . . 310
NetworkingThroughUserFunctions . . . . . . . . . . . . . . . . . 313
AddingUsers’OwnCode:ExtendingtheLibrary . . . . . . . . . . . 315
ASimpleApproach . . . . . . . . . . . . . . . . . . . . . . . . . . 315
WritingApplicationExtensions:(DLLs) . . . . . . . . . . . . . . . 316
CreatinganInterfacetoClarity . . . . . . . . . . . . . . . . . . . . 319
SomeAdditionalFeatures . . . . . . . . . . . . . . . . . . . . . . . . 322
ImportingandExportingDatabases. . . . . . . . . . . . . . . . . . 322
StackingWindows . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Re-numberingandNamingFunctionComponents . . . . . . . . . 323
TheClaritySourceCode. . . . . . . . . . . . . . . . . . . . . . . . . 324
TheCFilesandHeaderFiles . . . . . . . . . . . . . . . . . . . . . 326
Project:ProblemSolving . . . . . . . . . . . . . . . . . . . . . . . . 327
Sudoku:SearchingforAnswers . . . . . . . . . . . . . . . . . . . 327
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
10 ProgrammingwithUncertainty:Theories,ModelsandPrograms . 343
ModelsandPrograms[→Page349]. . . . . . . . . . . . . . . . . . . 343
TheRoleofaModel . . . . . . . . . . . . . . . . . . . . . . . . . 345
∗SolvingSudoku . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
AnIntroductiontoGameTheory[→Page364] . . . . . . . . . . . . 351
TheProblemofthe‘Best’Choice . . . . . . . . . . . . . . . . . . 351
TheOldShellGame. . . . . . . . . . . . . . . . . . . . . . . . . . 352
PrinciplesofMaximising . . . . . . . . . . . . . . . . . . . . . . . 353
ProbabilisticStrategies . . . . . . . . . . . . . . . . . . . . . . . . 353
ChoosingActions(orCalculatingaHeuristic) . . . . . . . . . . . . . 355
MaximumSecurityLevel(MSL) . . . . . . . . . . . . . . . . . . . 355
GeneralisedMSLforActions . . . . . . . . . . . . . . . . . . . . . 356
MultipleSimultaneousEquationsMatrix . . . . . . . . . . . . . . . 356
ImplementingMSL . . . . . . . . . . . . . . . . . . . . . . . . . . 357
