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| preface ix abouttheauthors xiii 1 foundations 1 1.1 categoriesofideas:entity,species,genus 1 1.2 values 2 1.3 objects 4 1.4 rocedures6 1.5 regulartypes 6 1.6 regularprocedures 8 1.7 concepts 10 1.8 conclusions14 2 transformationsandtheirorbits1 5 2.1 transformations 15 2.2 orbits 18 2.3 collisionpoint 21 2.4 measuringorbitsizes 27 2.5 actions 28 2.6 conclusions 29 3 associativeoperations 31 3.1 associativity 31 .3.2 computingpowers 33 3.3 programtransformations 35 3.4 special-caseprocedures 39 3.5 parameterizingalgorithms 42 3.6 linearrecurrences 43 3.7 accumulationprocedures 46 3.8 conclusions 47 4 linearorderings 49 4.1 classi?cationofrelations 49 4.2 totalandweakorderings 51 4.3 orderselection 52 4.4 naturaltotalordering 61 4.5 clustersofderivedprocedures 62 4.6 extendingorder-selectionprocedures 63 4.7 conclusions 63 5 orderedalgebraicstructures 65 5.1 basicalgebraicstructures 65 5.2 orderedalgebraicstructures 70 5.3 remainder 71 5.4 greatestcommondivisor 76 5.5 generalizinggcd 79 5.6 steingcd 81 5.7 quotient 81 5.8 quotientandremainderfornegativequantities 83 5.9 conceptsandtheirmodels 85 5.10 computerintegertypes 87 5.11 conclusions 88 6 iterators 89 6.1 readability 89 6.2 iterators 90 6.3 ranges 92 6.4 readableranges 95 6.5increasingranges 103 6.6 forwarditerators 106 6.7 indexediterators 110 6.8 bidirectionaliterators 111 6.9 random-accessiterators 113 6.1 0conclusions 114 7 coordinatestructures 115 7.1 ifurcatecoordinates 115 7.2 bidirectionalbifurcatecoordinates 119 7.3 coordinatestructures 124 7.4 isomorphism,equivalence,andordering 124 7.5 conclusions 131 8 coordinateswithmutablesuccessors 133 8.1 linkediterators 133 8.2 linkrearrangements 134 8.3 applicationsoflinkrearrangements 140 8.4 linkedbifurcatecoordinates 143 8.5 conclusions1489copying 149 9.1 writability 149 9.2 position-basedcopying 151 9.3 predicate-basedcopying 157 9.4 swappingranges 164 9.5 conclusions 168 10 rearrangements 169 10.1 permutations 169 10.2 rearrangements 172 10.3 reversealgorithms 174 10.4 rotatealgorithms 178 10.5 algorithmselection 186 10.6 conclusions 189 11 partitionandmerging 191 11.1 partition 191 11.2 balancedreduction 198 11.3 merging 202 11.4 conclusions 208 12 compositeobjects 209 12.1 simplecompositeobjects 209 12.2 dynamicsequences 216 12.3 underlyingtype 222 12.4 conclusions 225 afterword 227 appendixa mathematicalnotation 231 appendixb programminglanguage 233 b.1 languagede?nition 233 b.2 macrosandtraitstructures 240 bibliography 243 index 247 |
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