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| Bird R., de Moor O. — Algebra of programming |
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| Предметный указатель |
 problem 62 259
 -calculus$ 161
Absorption law for A 105
Absorption law for products 41 114
Accumulation parameter 7 12 74 77 139
Ackermann's function 6
Addition modulo p 45
Algebra 46
Allegory 81—85
Anti-symmetry 86
Arrows of a category 25
ASCII 1
bags 130
Banana-split law 55 56 78
Base functor 52
Bifunctor 31 40 50
Bijection 29 75
Binary thinning theorem 202
Bitonic tours problem 212
Boolean allegory 101 122
Boolean operators 67
Bottom element 43
Branch-and-bound 243
Bus-stop problem 217
Cancellation law for coproducts 42 118
Cancellation law for division 99
Cancellation law for power transpose 104
Cancellation law for products 39 41 43 116
Carrier (of an algebra) 45
Cartesian closed category 72 75 78
Cartesian product function 125
Case operator 41 42 122
Catamorphism 46
Category 25—30
Closure 157—162
Co-algebra 52
combinatorial functions 123
Company party problem 175
Concatenation 8 70
conditionals 21 66 122
Connected relation 151
Cons-lists 7
Constant arrow 38
Constant functor 31
constructor 1
Constructor classes 23
Context condition 167 223
Continuous mapping 141
contravariance 83
Converse function theorem 128
Coproduct 41—42
Coreflexive 86 122
Currying 2—3 16 44 70 71
Data compression problem 238
datatype 1—3 36—38
Datatype, parameterised 3 49
Datatype, with laws 53
De Morgan's law 101
Decimal representation 11 17 62 137
Dedekinds rule see "Modular law"
Detab-entab problem 246
Diagonal rule 161
Diagram 27—28
Diagram, commuting 27
Diagram, pasting 35
Diagrammatic form 2
Difunctional arrow 142
Difunctional closure 142
Disjoint union 1 38 42
Distributive category 67
Distributivity 172
Divide and conquer 137 144 146
Domain 26 86
Dominance relation 217
Duality 28—30 41 52 118
Dynamic programming 219
Dynamic programming theorem 220
Eilenberg-Wright Lemma 122
Empty object 38
Entire arrow 88
Epi-monic factorisation 96
Epic arrow 28
EQUIVALENCE 86
Evaluating polynomials 58 62
Exchange law 45
Existential image functor 32 35 105
Existential quantification 102
Exponential 44 72 117
Exponential functor 113
exponentiation 144
F-algebra 45
Factorial function 4 5 57
fibonacci function 4 5
Fixed point induction 141 259
Fixed point, greatest 140
Fixed point, least 140 142
Fixed point, unique 140 146 221
fixpoint 49
FLOOR 65
Fokkinga's Theorem 58
Fold operator 5
Font conventions for datatypes 3
Font conventions for identifiers 30
Forest 15
Function space see "Exponential"
Functional application 2
Functional composition 2
functor 30—33
Fusion (with the power functor) 168
Fusion law for catamorphisms 48 141
Fusion law for coproducts 42
Fusion law for exponentials 72
Fusion law for power transpose 104
Fusion law for products 39
Fusion law for terminal objects 37 40
Fusion law for type functors 51
Galois connection 100 109
Gofer, xii 1 23 165
Graph algorithms 157
Graph functor 32
Greedoids 191
Greedy theorem 173 245
Haskell 1 22
Hom sentence 95
Homomorphism 5 30 45—46
HOPE 1
Horners rule 58
Horners rule, generalisation of 62
Hylomorphism 142 162
Hylomorphism theorem 144
Hyperproduct 62
Idempotent arrow 90
Identity functor 31 49
Iinjection 17 28 65 68
IMP see "Simple arrow"
Inclusion functor 32 35
Indirect equality 65 107
Indirect proof 82 102
Induction 147
Inductive relation 147—151 158
Inequation 82
Infinite lists 52
Initial algebra 45—49
Initial object 37—38
Initial type 51
Insertion sort 157
Inverse 16—18 29
Involution 83 101
Isomorphism 29 33 48
Iterative definition 12 14
| Jointly monic arrows 92
Kleene's theorem 141
Knapsack problem 205
Knaster-Tarski Theorem 140
Lambek's Lemma 49 142
Large category 31
Lawvere's Recursion Theorem 78
Lax natural transformation 132 148 182
Layered network problem 196
Lazy functional programming 43 45
Lexical ordering 98 175
Linear functor 202
Linear order 152
List comprehension 13
Locale 91
Locally complete allegory 96
Longest upsequence problem 217
Loops 12 264
Lower adjoint 101
Maximum 166
Maximum segment sum problem 174
Membership relation 32 34 103 147—151
Memoisation 219
Mergesort 156
Merging loops 56
Minimal elements 170
Minimum tardiness problem 253
Miranda 1
Modular identity 88
Modular law 84
Modulus computation 145
Monad 52
Monic arrow 28
Monotonic algebra 172
Monotonic functor see "Relator"
Monotonicity of composition 82
Monotonicity of division 99
Natural isomorphism 34 67
Natural transformation 19 33—35
Naturality condition 34 133
negation operator 2
Non-empty lists 13
Non-empty power object 107
Non-strict constructor 43
Non-strict semantics 22
Nondeterminism 81
Objects of a category 25
One-pass program 56
Opposite category 28
Optimal bracketing problem 230
Orwell 1
Pair operator 39 43
Paragraph problem 190 207
Parallel loop fusion 78
Partial function 26 30 88
Partial order 44 86 108
Partitions 128
Pattern matching 2 66
permutations 130
Ping-pong argument 82
Point-free 19—22
Pointwise 19—22
Polymorphism 18—19 34 35
Polynomial functor 44—45
Power allegory 103 117
Power functor 105
Power object 103
Power relator 119
Power transpose 103
Powerset functor 32
Predicate calculus 28
Predicate transformer 108
Prefix 126
Preorder 30 33 38 75 86 98 108 170
Principle of optimality 219
Problem reduction generator 217
PRODUCT 38—41
Product category 27 40
Projection function 6 39 40 45
Quicksort 154
Rally driver's problem 217
RANGE 26 86
Reciprocal see "Relational converse"
Recursion 4 137
Recursion, mutual 15
Recursion, non-structural 139
Recursion, primitive 5 6
Recursion, structural 5 10 56
refinement 18 138 194
Reflection law for catamorphisms 48
Reflection law for coprodcuts 42
Reflection law for exponentials 72
Reflection law for products 39
Reflection law for terminal objects 37 40
Reflexivity 86
Regular category 108
Relational algebra 121
Relational catamorphism 121
Relational converse 43 83
Relational coproduct 117
Relational difference 100 159
relational division 98
Relational implication 97
Relational inclusion 82
Relational join 96
Relational meet 83
Relational negation 101
Relational product 114
Relations (as data) 161
Relator 111 134
Retraction 30
Rolling rule 159 161
Ruby 58 78 135
Ruby triangles 58
Rule of floors 63 65
Schroder's rule 103
Security van problem 184
Selection sort 152
Semi-commuting diagram 82
Sequential decision process 217
Set comprehension 104
Set theory 95 104 162 169
Shortest paths problem 179
Shunting rules 89
Simple arrow 88
singleton set 36 37 106
SmL 1
Snoc-lists 7
Sorting 151—157
Sorting sets 200
Source operator 25
Source type 2
spans 40
Squaring functor 31
Strict functional programming 22
String edit problem 225
strings 47
Strong functor 76
Structural recursion theorem 73
Subcategory 26 32 88
Subsequences 123
Substitution rule 162
Suffix 126
Supersequences 132
Supremum operator 170
Surjection 17 28
Surjective relation 149
Symmetry 28 86
Tabulation (of an arrow) 91
Tabulation scheme 6 219 227 233
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