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annotate stack.agda @ 575:73fc32092b64

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push local rbtree
author ryokka
date Fri, 01 Nov 2019 17:42:51 +0900
parents 70b09cbefd45
children 0b791ae19543
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1 open import Level renaming (suc to succ ; zero to Zero )
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2 module stack where
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3
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4 open import Relation.Binary.PropositionalEquality
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5 open import Relation.Binary.Core
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6 open import Data.Nat hiding (compare)
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7 open import Data.Maybe
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8
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9 ex : 1 + 2 ≡ 3
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10 ex = refl
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11
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12 -- data Bool {n : Level } : Set n where
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13 -- True : Bool
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14 -- False : Bool
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15
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16 -- record _∧_ {n : Level } (a : Set n) (b : Set n): Set n where
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17 -- field
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18 -- pi1 : a
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19 -- pi2 : b
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20
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21 -- data _∨_ {n : Level } (a : Set n) (b : Set n): Set n where
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22 -- pi1 : a -> a ∨ b
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23 -- pi2 : b -> a ∨ b
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24
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25 -- data Maybe {n : Level } (a : Set n) : Set n where
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26 -- nothing : Maybe a
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27 -- just : a -> Maybe a
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28
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29 record StackMethods {n m : Level } (a : Set n ) {t : Set m } (stackImpl : Set n ) : Set (m Level.⊔ n) where
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30 field
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31 push : stackImpl -> a -> (stackImpl -> t) -> t
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32 pop : stackImpl -> (stackImpl -> Maybe a -> t) -> t
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33 pop2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
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34 get : stackImpl -> (stackImpl -> Maybe a -> t) -> t
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35 get2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
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36 clear : stackImpl -> (stackImpl -> t) -> t
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37 open StackMethods
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38
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39 record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.⊔ n) where
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40 field
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41 stack : si
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42 stackMethods : StackMethods {n} {m} a {t} si
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43 pushStack : a -> (Stack a si -> t) -> t
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44 pushStack d next = push (stackMethods ) (stack ) d (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
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45 popStack : (Stack a si -> Maybe a -> t) -> t
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46 popStack next = pop (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
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47 pop2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
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48 pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
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49 getStack : (Stack a si -> Maybe a -> t) -> t
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50 getStack next = get (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
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51 get2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
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52 get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
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53 clearStack : (Stack a si -> t) -> t
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54 clearStack next = clear (stackMethods ) (stack ) (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
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55
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56 open Stack
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57
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58 {--
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59 data Element {n : Level } (a : Set n) : Set n where
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60 cons : a -> Maybe (Element a) -> Element a
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61
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62
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63 datum : {n : Level } {a : Set n} -> Element a -> a
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64 datum (cons a _) = a
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65
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66 next : {n : Level } {a : Set n} -> Element a -> Maybe (Element a)
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67 next (cons _ n) = n
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68 --}
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69
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70
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71 -- cannot define recrusive record definition. so use linked list with maybe.
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72 record Element {l : Level} (a : Set l) : Set l where
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73 inductive
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74 constructor cons
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75 field
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76 datum : a -- `data` is reserved by Agda.
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77 next : Maybe (Element a)
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78
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79 open Element
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80
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81
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82 record SingleLinkedStack {n : Level } (a : Set n) : Set n where
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83 field
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84 top : Maybe (Element a)
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85 open SingleLinkedStack
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86
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87 pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
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88 pushSingleLinkedStack stack datum next = next stack1
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89 where
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90 element = cons datum (top stack)
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91 stack1 = record {top = just element}
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92
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93
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94 popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
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95 popSingleLinkedStack stack cs with (top stack)
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96 ... | nothing = cs stack nothing
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97 ... | just d = cs stack1 (just data1)
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98 where
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99 data1 = datum d
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100 stack1 = record { top = (next d) }
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101
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102 pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
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103 pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
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104 ... | nothing = cs stack nothing nothing
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105 ... | just d = pop2SingleLinkedStack' {n} {m} stack cs
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106 where
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107 pop2SingleLinkedStack' : {n m : Level } {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
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108 pop2SingleLinkedStack' stack cs with (next d)
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109 ... | nothing = cs stack nothing nothing
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110 ... | just d1 = cs (record {top = (next d1)}) (just (datum d)) (just (datum d1))
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111
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112
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113 getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
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114 getSingleLinkedStack stack cs with (top stack)
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115 ... | nothing = cs stack nothing
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116 ... | just d = cs stack (just data1)
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117 where
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118 data1 = datum d
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119
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120 get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
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121 get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
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122 ... | nothing = cs stack nothing nothing
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123 ... | just d = get2SingleLinkedStack' {n} {m} stack cs
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124 where
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125 get2SingleLinkedStack' : {n m : Level} {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
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126 get2SingleLinkedStack' stack cs with (next d)
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127 ... | nothing = cs stack nothing nothing
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128 ... | just d1 = cs stack (just (datum d)) (just (datum d1))
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129
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130 clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (SingleLinkedStack a -> t) -> t
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131 clearSingleLinkedStack stack next = next (record {top = nothing})
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132
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133
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134 emptySingleLinkedStack : {n : Level } {a : Set n} -> SingleLinkedStack a
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135 emptySingleLinkedStack = record {top = nothing}
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136
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137 -----
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138 -- Basic stack implementations are specifications of a Stack
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139 --
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140 singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} -> StackMethods {n} {m} a {t} (SingleLinkedStack a)
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141 singleLinkedStackSpec = record {
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142 push = pushSingleLinkedStack
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143 ; pop = popSingleLinkedStack
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144 ; pop2 = pop2SingleLinkedStack
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145 ; get = getSingleLinkedStack
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146 ; get2 = get2SingleLinkedStack
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147 ; clear = clearSingleLinkedStack
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148 }
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149
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150 createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> Stack {n} {m} a {t} (SingleLinkedStack a)
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151 createSingleLinkedStack = record {
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152 stack = emptySingleLinkedStack ;
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153 stackMethods = singleLinkedStackSpec
51f0d5e5d1e5 stack proof on indeterminate stack state
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 504
diff changeset
154 }
51f0d5e5d1e5 stack proof on indeterminate stack state
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 504
diff changeset
155