Preface ixAbouttheAuthors xiii1 Foundations 1.1 CategoriesofIdeas:Entity,Species,Genus 1.2 Values 1.3 Objects 1.4 rocedures6 1.5 RegularTypes 1.6 RegularProcedures 1.7 Concepts 1.8 Conclusions142 TransformationsandTheirOrbits1 2.1 Transformations 2.2 Orbits 2.3 CollisionPoint 2.4 MeasuringOrbitSizes 2.5 Actions 2.6 Conclusions3 AssociativeOperations 3.1 Associativity 3.2 ComputingPowers 3.3 ProgramTransformations 3.4 Special-CaseProcedures 3.5 ParameterizingAlgorithms 3.6 LinearRecurrences 3.7 AccumulationProcedures 3.8 Conclusions4 LinearOrderings 4.1 Classi?cationofRelations 4.2 TotalandWeakOrderings 4.3 OrderSelection 4.4 NaturalTotalOrdering 4.5 ClustersofDerivedProcedures 4.6 ExtendingOrder-SelectionProcedures 4.7 Conclusions5 OrderedAlgebraicStructures 5.1 BasicAlgebraicStructures 5.2 OrderedAlgebraicStructures 5.3 Remainder 5.4 GreatestCommonDivisor 5.5 Generalizinggcd 5.6 Steingcd 5.7 Quotient 5.8 QuotientandRemainderforNegativeQuantities 5.9 ConceptsandTheirModels 5.10 ComputerIntegerTypes 5.11 Conclusions6 Iterators 6.1 Readability 6.2 Iterators 6.3 Ranges 6.4 ReadableRanges 6.5IncreasingRanges 6.6 ForwardIterators 6.7 IndexedIterators 6.8 BidirectionalIterators 6.9 Random-AccessIterators 6.1 Conclusions7 CoordinateStructures 7.1 ifurcateCoordinates 7.2 BidirectionalBifurcateCoordinates 7.3 CoordinateStructures 7.4 Isomorphism,Equivalence,andOrdering 7.5 Conclusions8 CoordinateswithMutableSuccessors 8.1 LinkedIterators 8.2 LinkRearrangements 8.3 ApplicationsofLinkRearrangements 8.4 LinkedBifurcateCoordinates 8.5 Conclusions9 Copying 9.1 Writability 9.2 Position-BasedCopying 9.3 Predicate-BasedCopying 9.4 SwappingRanges 9.5 Conclusions10 Rearrangements 10.1 Permutations 10.2 Rearrangements 10.3 ReverseAlgorithms 10.4 RotateAlgorithms 10.5 AlgorithmSelection 10.6 Conclusions11 PartitionandMerging 11.1 Partition 11.2 BalancedReduction 11.3 Merging 11.4 Conclusions12 CompositeObjects 12.1 SimpleCompositeObjects 12.2 DynamicSequences 12.3 UnderlyingType 12.4 ConclusionsAfterwordAppendixA MathematicalNotationAppendixB ProgrammingLanguage B.1 LanguageDe?nition B.2 MacrosandTraitStructuresBibliographyIndex
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