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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
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7
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8 ex : 1 + 2 @$\equiv$@ 3
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9 ex = refl
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10
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11 data Bool {n : Level } : Set n where
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12 True : Bool
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13 False : Bool
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14
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15 record _@$\wedge$@_ {n : Level } (a : Set n) (b : Set n): Set n where
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16 field
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17 pi1 : a
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18 pi2 : b
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19
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20 data Maybe {n : Level } (a : Set n) : Set n where
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21 Nothing : Maybe a
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22 Just : a @$\rightarrow$@ Maybe a
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23
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24 record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
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25 field
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26 push : stackImpl @$\rightarrow$@ a @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
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27 pop : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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28 pop2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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29 get : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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30 get2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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31 clear : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
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32 open StackMethods
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33
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34 record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.@$\sqcup$@ n) where
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35 field
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36 stack : si
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37 stackMethods : StackMethods {n} {m} a {t} si
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38 pushStack : a @$\rightarrow$@ (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
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39 pushStack d next = push (stackMethods ) (stack ) d (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
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40 popStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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41 popStack next = pop (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
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42 pop2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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43 pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
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44 getStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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45 getStack next = get (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
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46 get2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
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47 get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
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48 clearStack : (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
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49 clearStack next = clear (stackMethods ) (stack ) (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
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50
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51 open Stack
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52
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53 {--
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54 data Element {n : Level } (a : Set n) : Set n where
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55 cons : a @$\rightarrow$@ Maybe (Element a) @$\rightarrow$@ Element a
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56
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57
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58 datum : {n : Level } {a : Set n} @$\rightarrow$@ Element a @$\rightarrow$@ a
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59 datum (cons a _) = a
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60
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61 next : {n : Level } {a : Set n} @$\rightarrow$@ Element a @$\rightarrow$@ Maybe (Element a)
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62 next (cons _ n) = n
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63 --}
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64
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65
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66 -- cannot define recrusive record definition. so use linked list with maybe.
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67 record Element {l : Level} (a : Set l) : Set l where
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68 inductive
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69 constructor cons
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70 field
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71 datum : a -- `data` is reserved by Agda.
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72 next : Maybe (Element a)
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73
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74 open Element
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75
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76
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77 record SingleLinkedStack {n : Level } (a : Set n) : Set n where
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78 field
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79 top : Maybe (Element a)
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80 open SingleLinkedStack
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81
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82 pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} @$\rightarrow$@ SingleLinkedStack Data @$\rightarrow$@ Data @$\rightarrow$@ (Code : SingleLinkedStack Data @$\rightarrow$@ t) @$\rightarrow$@ t
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83 pushSingleLinkedStack stack datum next = next stack1
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84 where
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85 element = cons datum (top stack)
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86 stack1 = record {top = Just element}
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87
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88
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89 popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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90 popSingleLinkedStack stack cs with (top stack)
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91 ... | Nothing = cs stack Nothing
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92 ... | Just d = cs stack1 (Just data1)
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93 where
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94 data1 = datum d
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95 stack1 = record { top = (next d) }
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96
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97 pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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98 pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
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99 ... | Nothing = cs stack Nothing Nothing
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100 ... | Just d = pop2SingleLinkedStack' {n} {m} stack cs
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101 where
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102 pop2SingleLinkedStack' : {n m : Level } {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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103 pop2SingleLinkedStack' stack cs with (next d)
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104 ... | Nothing = cs stack Nothing Nothing
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105 ... | Just d1 = cs (record {top = (next d1)}) (Just (datum d)) (Just (datum d1))
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106
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107
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108 getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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109 getSingleLinkedStack stack cs with (top stack)
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110 ... | Nothing = cs stack Nothing
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111 ... | Just d = cs stack (Just data1)
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112 where
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113 data1 = datum d
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114
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115 get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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116 get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
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117 ... | Nothing = cs stack Nothing Nothing
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118 ... | Just d = get2SingleLinkedStack' {n} {m} stack cs
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119 where
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120 get2SingleLinkedStack' : {n m : Level} {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
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121 get2SingleLinkedStack' stack cs with (next d)
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122 ... | Nothing = cs stack Nothing Nothing
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123 ... | Just d1 = cs stack (Just (datum d)) (Just (datum d1))
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124
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125 clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (SingleLinkedStack a @$\rightarrow$@ t) @$\rightarrow$@ t
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126 clearSingleLinkedStack stack next = next (record {top = Nothing})
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127
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128
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129 emptySingleLinkedStack : {n : Level } {a : Set n} @$\rightarrow$@ SingleLinkedStack a
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130 emptySingleLinkedStack = record {top = Nothing}
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131
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132 -----
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133 -- Basic stack implementations are specifications of a Stack
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134 --
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135 singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ StackMethods {n} {m} a {t} (SingleLinkedStack a)
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136 singleLinkedStackSpec = record {
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137 push = pushSingleLinkedStack
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138 ; pop = popSingleLinkedStack
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139 ; pop2 = pop2SingleLinkedStack
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140 ; get = getSingleLinkedStack
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141 ; get2 = get2SingleLinkedStack
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142 ; clear = clearSingleLinkedStack
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143 }
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144
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145 createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ Stack {n} {m} a {t} (SingleLinkedStack a)
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146 createSingleLinkedStack = record {
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147 stack = emptySingleLinkedStack ;
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148 stackMethods = singleLinkedStackSpec
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149 }
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