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1 module ModelChecking where
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2
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3 open import Level renaming (zero to Z ; suc to succ)
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4
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5 open import Data.Nat hiding (compare)
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6 open import Data.Nat.Properties as NatProp
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7 open import Data.Maybe
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8 -- open import Data.Maybe.Properties
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9 open import Data.Empty
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10 open import Data.List
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11 open import Data.Product
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12 open import Function as F hiding (const)
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13 open import Relation.Binary
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14 open import Relation.Binary.PropositionalEquality
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15 open import Relation.Nullary
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16 open import logic
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17 open import Data.Unit hiding (_≟_ ; _≤?_ ; _≤_)
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18 open import Relation.Binary.Definitions
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19
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20
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21
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22 record AtomicNat : Set where
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23 field
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24 value : ℕ
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25
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26 set : {n : Level } {t : Set n} → AtomicNat → (value : ℕ) → ( AtomicNat → t ) → t
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27 set a v next = next record { value = v }
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28
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29 record Phils : Set where
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30 field
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31 pid : ℕ
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32 left right : AtomicNat
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33
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34 putdown_rfork : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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35 putdown_rfork p next = set (Phils.right p) 0 ( λ f → next record p { right = f } )
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36
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37 putdown_lfork : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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38 putdown_lfork p next = set (Phils.left p) 0 ( λ f → next record p { left = f } )
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39
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40 thinking : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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41 thinking p next = next p
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42
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43 pickup_rfork : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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44 pickup_rfork p next = set (Phils.right p) (Phils.pid p) ( λ f → next record p { right = f } )
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45
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46 pickup_lfork : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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47 pickup_lfork p next = set (Phils.left p) (Phils.pid p) ( λ f → next record p { left = f } )
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48
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49 --eating : {n : Level} {t : Set n} → Phils → ( Phils → t ) → t
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50 --eating p next = next p
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51
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52 data Code : Set where
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53 C_putdown_rfork : Code
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54 C_putdown_lfork : Code
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55 C_thinking : Code
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56 C_pickup_rfork : Code
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57 C_pickup_lfork : Code
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58 C_eating : Code
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59
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60 record Process : Set where
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61 field
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62 phil : Phils
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63 next_code : Code
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64
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65 putdown_rfork_stub : {n : Level} {t : Set n} → Process → ( Process → t) → t
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66 putdown_rfork_stub p next = putdown_rfork ( Process.phil p ) ( λ ph → next record p { phil = ph ; next_code = C_putdown_lfork } )
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67
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68 putdown_lfork_stub : {n : Level} {t : Set n} → Process → ( Process → t) → t
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69 putdown_lfork_stub p next = putdown_lfork ( Process.phil p ) ( λ ph → next record p { phil = ph ; next_code = C_putdown_lfork } )
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70
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71 code_table : {n : Level} {t : Set n} → Code → Process → ( Process → t) → t
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72 -- code_table C_set = {!!}
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73 code_table C_putdown_rfork = putdown_rfork_stub
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74 code_table C_putdown_lfork = putdown_lfork_stub
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75 code_table C_thinking = {!!}
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76 code_table C_pickup_rfork = {!!}
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77 code_table C_pickup_lfork = {!!}
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78 code_table C_eating = {!!}
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79
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80 open Process
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81
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82 step : {n : Level} {t : Set n} → List Process → (List Process → t) → t
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83 step {n} {t} [] next0 = next0 []
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84 step {n} {t} (p ∷ ps) next0 = code_table (next_code p) p ( λ np → next0 (ps ++ ( np ∷ [] ) ))
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85
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86 test : List Process
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87 test = step ( record { phil = record { pid = 1 ; left = record { value = 1 } ; right = record { value = 1 } } ; next_code = C_putdown_rfork } ∷ [] ) ( λ ps → ps )
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88
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89 test1 : List Process
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90 test1 = step ( record { phil = record { pid = 1 ; left = record { value = 1 } ; right = record { value = 1 } } ; next_code = C_putdown_rfork } ∷ [] )
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91 $ λ ps → step ps $ λ ps → ps
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92
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93 record Phi : Set where
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94 field
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95 pid : ℕ
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96 right-hand : Bool
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97 left-hand : Bool
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98 next-code : Code
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99 open Phi
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100
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101 record Env : Set where
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102 field
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103 table : List ℕ
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104 ph : List Phi
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105 open Env
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106
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107 init-table : {n : Level} {t : Set n} → ℕ → (exit : Env → t) → t
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108 init-table n exit = init-table-loop n 0 (record {table = [] ; ph = []}) exit where
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109 init-table-loop : {n : Level} {t : Set n} → (redu inc : ℕ) → Env → (exit : Env → t) → t
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110 init-table-loop zero ind env exit = exit env
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111 init-table-loop (suc redu) ind env exit = init-table-loop redu (suc ind) record env{
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112 table = 0 ∷ (table env)
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113 ; ph = record {pid = redu ; left-hand = false ; right-hand = false ; next-code = C_thinking } ∷ (ph env) } exit
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114
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115 -- eatingも探索範囲に含める
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116 brute-force-search : {n : Level} {t : Set n} → Env → (exit : List Env → t) → t
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117 brute-force-search env exit = make-state-list 1 [] (ph env) env (env ∷ []) exit where
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118 make-state-list : {n : Level} {t : Set n} → ℕ → List Bool → List Phi → Env → (List Env) → (exit : List Env → t) → t
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119 make-state-list redu state (x ∷ pl) env envl exit with next-code x
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120 ... | C_thinking = make-state-list (redu + redu) (state ++ (false ∷ [])) pl env envl exit
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121 ... | C_eating = make-state-list (redu + redu) (state ++ (false ∷ [])) pl env envl exit
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122 ... | _ = make-state-list redu state pl env envl exit
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123 make-state-list redu state [] env envl exit = bit-force-search redu [] state env envl exit where
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124 bit-force-search : {n : Level} {t : Set n} → ℕ → (f b : List Bool )→ Env → (List Env) → (exit : List Env → t) → t
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125 bit-force-search zero f l env envl exit = exit envl
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126 bit-force-search (suc redu) f [] env envl exit = exit envl
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127 bit-force-search (suc redu) f (true ∷ bs) env envl exit = bit-force-search (suc redu) (f ++ (false ∷ [])) bs env envl exit -- 今回の対象をfalseにしてfに追加,bを次の対象にする
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128 bit-force-search (suc redu) f (false ∷ bs) env envl exit = set-state redu (f ++ (true ∷ bs)) (f ++ (true ∷ bs)) [] (ph env) env envl exit where -- 今回の対象をtrueにし,fとbを結合してそのListを代入する.かつそれをbに入れfをinitしてloopさせる
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129 set-state : {n : Level} {t : Set n} → ℕ → (origin state : List Bool ) → (f b : List Phi) → Env → (List Env) → (exit : List Env → t) → t -- 入れ替える必要のあるやつはphaseがThinkingのやつのみ
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130 set-state redu origin [] f b env envl exit = bit-force-search redu [] origin env (record env{ph = (f ++ b)} ∷ envl) exit -- Stateが先に尽きる
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131 set-state redu origin state@(s ∷ ss) f b env envl exit with b
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132 ... | [] = bit-force-search redu [] origin env (record env{ph = f} ∷ envl) exit
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133 ... | p ∷ ps with next-code p
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134 ... | C_putdown_rfork = set-state redu origin state (f ++ (p ∷ [])) ps env envl exit -- 変更対象ではないので奥を対象にする
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135 ... | C_putdown_lfork = set-state redu origin state (f ++ (p ∷ [])) ps env envl exit -- 変更対象ではないので奥を対象にする
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136 ... | C_pickup_rfork = set-state redu origin state (f ++ (p ∷ [])) ps env envl exit -- 変更対象ではないので奥を対象にする
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137 ... | C_pickup_lfork = set-state redu origin state (f ++ (p ∷ [])) ps env envl exit -- 変更対象ではないので奥を対象にする
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138 set-state redu origin (true ∷ ss) f b env envl exit | p ∷ ps | C_eating = set-state redu origin ss (f ++ (record p{next-code = C_putdown_lfork} ∷ [])) ps env envl exit -- 変更対象なので変更して奥に進む
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139 set-state redu origin (false ∷ ss) f b env envl exit | p ∷ ps | C_eating = set-state redu origin ss (f ++ (p ∷ [])) ps env envl exit -- 変更対象なので変更して奥に進む
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140 set-state redu origin (true ∷ ss) f b env envl exit | p ∷ ps | C_thinking = set-state redu origin ss (f ++ (record p{next-code = C_pickup_rfork} ∷ [])) ps env envl exit -- 変更対象なので変更して奥に進む
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141 set-state redu origin (false ∷ ss) f b env envl exit | p ∷ ps | C_thinking = set-state redu origin ss (f ++ (p ∷ [])) ps env envl exit -- 変更対象なので変更して奥に進む
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142
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143
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144
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145 test-search : List Env
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146 test-search = init-table 3 (λ e0 → brute-force-search e0 (λ e1 → e1))
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147
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148 -- テーブルをたどるために若干loopが必要
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149 pickup-rfork-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
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150 pickup-rfork-c ind p env exit = pickup-rfork-p ind [] (table env) p env exit where
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151 pickup-rfork-p : {n : Level} {t : Set n} → ℕ → (f b : List ℕ) → Phi → Env → (Env → t) → t
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152 pickup-rfork-p zero f [] p env exit = exit env
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153 pickup-rfork-p zero f (zero ∷ ts) p env exit = exit record env{ph = ((ph env) ++ (record p{right-hand = true ; next-code = C_pickup_lfork} ∷ [])); table = (f ++ ((pid p) ∷ ts))} -- 取得可能なので変更する envの後ろにappendする感じ
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154 pickup-rfork-p zero f ((suc x) ∷ ts) p env exit = exit record env{ph = ((ph env) ++ p ∷ [])} -- 取得不可能なので変更せず終了する
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155 pickup-rfork-p (suc ind) f [] p env exit = exit env
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156 pickup-rfork-p (suc ind) f (x ∷ ts) p env exit = pickup-rfork-p ind (f ++ (x ∷ [])) ts p env exit
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157
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158 pickup-lfork-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
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159 pickup-lfork-c ind p env exit = pickup-lfork-p (suc ind) [] (table env) p env exit where
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160 pickup-lfork-p : {n : Level} {t : Set n} → ℕ → (f b : List ℕ) → Phi → Env → (Env → t) → t
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161 pickup-lfork-p zero f [] p env exit with table env
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162 ... | [] = exit env
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163 ... | 0 ∷ ts = exit record env{ph = ((ph env) ++ (record p{left-hand = true ; next-code = C_eating} ∷ [])); table = ((pid p) ∷ ts)} -- 取得可能なので変更する envの後ろにappendする感じ
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164 ... | (suc x) ∷ ts = exit record env{ph = ((ph env) ++ p ∷ [])} -- 取得不可能なので変更せず終了する
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165 pickup-lfork-p zero f (0 ∷ ts) p env exit = exit record env{ph = ((ph env) ++ (record p{left-hand = true ; next-code = C_eating} ∷ [])); table = (f ++ ((pid p) ∷ ts))} -- 取得可能なので変更する envの後ろにappendする感じ
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166 pickup-lfork-p zero f ((suc x) ∷ ts) p env exit = exit record env{ph = ((ph env) ++ p ∷ [])} -- 取得不可能なので変更せず終了する
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167 pickup-lfork-p (suc ind) f [] p env exit = exit env
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168 pickup-lfork-p (suc ind) f (x ∷ ts) p env exit = pickup-lfork-p ind (f ++ (x ∷ [])) ts p env exit
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169
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170
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171 putdown-lfork-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
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172 putdown-lfork-c ind p env exit = putdown-lfork-p (suc ind) [] (table env) p env exit where
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173 putdown-lfork-p : {n : Level} {t : Set n} → ℕ → (f b : List ℕ) → Phi → Env → (Env → t) → t
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174 putdown-lfork-p zero f [] p env exit with table env
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175 ... | [] = exit env
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176 ... | x ∷ ts = exit record env{ph = ((ph env) ++ (record p{left-hand = false ; next-code = C_putdown_rfork} ∷ [])); table = (0 ∷ ts)} -- 取得可能なので変更する envの後ろにappendする感じ
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177 putdown-lfork-p zero f (x ∷ ts) p env exit = exit record env{ph = ((ph env) ++ (record p{left-hand = false ; next-code = C_putdown_rfork} ∷ [])); table = (f ++ (0 ∷ ts))} -- 取得可能なので変更する envの後ろにappendする感じ
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178 putdown-lfork-p (suc ind) f [] p env exit = exit env
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179 putdown-lfork-p (suc ind) f (x ∷ ts) p env exit = putdown-lfork-p ind (f ++ (x ∷ [])) ts p env exit
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180
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181
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182
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183 putdown-rfork-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
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184 putdown-rfork-c ind p env exit = putdown-rfork-p ind [] (table env) p env exit where
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185 putdown-rfork-p : {n : Level} {t : Set n} → ℕ → (f b : List ℕ) → Phi → Env → (Env → t) → t
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186 putdown-rfork-p zero f [] p env exit = exit env
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187 putdown-rfork-p zero f (x ∷ ts) p env exit = exit record env{ph = ((ph env) ++ (record p{right-hand = false ; next-code = C_thinking} ∷ [])); table = (f ++ (0 ∷ ts))} -- 取得可能なので変更する envの後ろにappendする感じ
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188 putdown-rfork-p (suc ind) f [] p env exit = exit env
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189 putdown-rfork-p (suc ind) f (x ∷ ts) p env exit = putdown-rfork-p ind (f ++ (x ∷ [])) ts p env exit
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190
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191
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192 thinking-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
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193 thinking-c ind p env exit = exit record env{ph = ((ph env) ++ p ∷ [])} -- 取得不要なので変更せず終了する
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194
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195 code_table-test : {n : Level} {t : Set n} → Code → ℕ → Phi → Env → (Env → t) → t
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196 code_table-test C_putdown_rfork = putdown-rfork-c
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197 code_table-test C_putdown_lfork = putdown-lfork-c
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198 code_table-test C_thinking = thinking-c
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199 code_table-test C_pickup_rfork = pickup-rfork-c
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200 code_table-test C_pickup_lfork = pickup-lfork-c
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201 code_table-test C_eating = thinking-c
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202
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203 step-c : {n : Level} {t : Set n} → Env → (exit : Env → t) → t
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204 step-c env exit = step-p (length (table env)) 0 record env{ph = []} (ph env) exit where
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205 step-p : {n : Level} {t : Set n} → (redu index : ℕ) → Env → (List Phi) → (exit : Env → t) → t
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206 step-p zero ind env pl exit = exit env
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207 step-p (suc redu) ind env [] exit = exit env
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208 step-p (suc redu) ind env (p ∷ ps) exit = code_table-test (next-code p) ind p env (λ e → step-p redu (suc ind) e ps exit )
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209
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210 step-c-debug : {n : Level} {t : Set n} → Env → (exit : List Env → t) → t
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211 step-c-debug env exit = step-p (length (table env)) 0 (record env{ph = [] } ∷ env ∷ []) (ph env) exit where
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212 step-p : {n : Level} {t : Set n} → (redu index : ℕ) → List Env → (List Phi) → (exit : List Env → t) → t
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213 step-p zero ind envl pl exit = exit envl
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214 step-p (suc redu) ind [] pl exit = exit []
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215 step-p (suc redu) ind (e ∷ envl) [] exit = exit []
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216 step-p (suc redu) ind (e ∷ envl) (p ∷ ps) exit = code_table-test (next-code p) ind p e (λ e0 → step-p redu (suc ind) (e0 ∷ envl) ps exit )
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217
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218 exec-n : {n : Level} {t : Set n} → ℕ → Env → (exit : List Env → t) → t
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219 exec-n n env exit = exec-n-p n (env ∷ []) exit where
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220 exec-n-p : {n : Level} {t : Set n} → ℕ → List Env → (exit : List Env → t) → t
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221 exec-n-p zero envl exit = exit envl
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222 exec-n-p (suc n) [] exit = exit []
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223 exec-n-p (suc n) envl@(x ∷ es) exit = step-c x (λ e → exec-n-p n (e ∷ envl) exit)
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224
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225 init-brute-force : {n : Level} {t : Set n} → List Env → (exit : List (List Env) → t) → t
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226 init-brute-force envl exit = init-brute-force-p envl [] exit where
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227 init-brute-force-p : {n : Level} {t : Set n} → List Env → List (List Env) → (exit : List (List Env) → t) → t
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228 init-brute-force-p [] envll exit = exit envll
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229 init-brute-force-p (x ∷ envl) envll exit = init-brute-force-p envl ((x ∷ []) ∷ envll) exit
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230
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231 search-brute-force-envll : {n : Level} {t : Set n} → List (List Env) → (exit : List (List Env) → t) → t
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232 search-brute-force-envll envll exit = search-brute-force-envll-p [] envll exit where
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233 search-brute-force-envll-p : {n : Level} {t : Set n} → (f b : List (List Env)) → (exit : List (List Env) → t) → t
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234 search-brute-force-envll-p f [] exit = exit f
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235 search-brute-force-envll-p f ([] ∷ bs) exit = search-brute-force-envll-p f bs exit
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236 search-brute-force-envll-p f (b@(x ∷ xs) ∷ bs) exit = brute-force-search x (λ e0 → make-brute-force-envl [] e0 b (λ e1 → search-brute-force-envll-p (f ++ e1) bs exit) ) where
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237 make-brute-force-envl : {n : Level} {t : Set n} → List (List Env) → (state p_step : List Env) → (exit : List (List Env) → t) → t
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238 make-brute-force-envl res [] xs exit = exit res
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239 make-brute-force-envl res (x ∷ state) xs exit = make-brute-force-envl (res ++ (x ∷ xs) ∷ []) state xs exit
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240
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241 step-brute-force : {n : Level} {t : Set n} → List (List Env) → (exit : List (List Env) → t) → t
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242 step-brute-force envll exit = step-brute-force-p [] envll exit where
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243 step-brute-force-p : {n : Level} {t : Set n} → (f b : List (List Env)) → (exit : List (List Env) → t) → t
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244 step-brute-force-p f [] exit = exit f
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245 step-brute-force-p f ([] ∷ bs) exit = step-brute-force-p f bs exit
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246 step-brute-force-p f ((x ∷ xs) ∷ bs) exit = step-c x (λ e0 → step-brute-force-p (f ++ ((e0 ∷ x ∷ xs) ∷ [])) bs exit)
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247
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248 exec-brute-force : {n : Level} {t : Set n} → ℕ → List (List Env) → (exit : List (List Env) → t) → t
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249 exec-brute-force n envll exit = exec-brute-force-p n envll exit where
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250 exec-brute-force-p : {n : Level} {t : Set n} → ℕ → List (List Env) → (exit : List (List Env) → t) → t
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251 exec-brute-force-p zero envll exit = exit envll
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252 exec-brute-force-p (suc n) envll exit = search-brute-force-envll envll (λ e1 → step-brute-force e1 (λ e2 → exec-brute-force-p n e2 exit))
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253
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254 model-check-deadlock : {n : Level} {t : Set n} → List (List Env) → (exit : List (List Env) → t) → t
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255 model-check-deadlock envll exit = test11 [] envll exit where
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256 test11 : {n : Level} {t : Set n} → (f b : List (List Env)) → (exit : List (List Env) → t) → t
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257 test11 f [] exit = exit f
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258 test11 f ([] ∷ bs) exit = test11 f bs exit
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259 test11 f (s@(x ∷ []) ∷ bs) exit = test11 (f ++ (s ∷ [])) bs exit
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260 test11 f (s@(x ∷ x1 ∷ []) ∷ bs) exit = test11 (f ++ (s ∷ [])) bs exit
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261 test11 f ((x ∷ x1 ∷ x2 ∷ xs) ∷ bs) exit = {!!}
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262
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263
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264
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265 data _===_ {n} {A : Set n} : List A -> List A -> Set n where
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266 reflection : {x : List A} -> x === x
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267 reflection1 : {x : List A} -> (x === x)
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268
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269 testhoge : Code → Code → ℕ
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270 testhoge C_putdown_rfork C_putdown_rfork = {!!}
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271 testhoge C_putdown_lfork C_putdown_lfork = {!!}
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272 testhoge C_pickup_rfork C_pickup_rfork = {!!}
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273 testhoge C_pickup_lfork C_pickup_lfork = {!!}
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274 testhoge _ _ = {!!}
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275
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276
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277 test-step-c : (List Env)
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278 test-step-c = brute-force-search record {
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279 table = 0 ∷ 0 ∷ 0 ∷ []
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280 ; ph = record
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281 { pid = 1
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282 ; left-hand = false
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283 ; right-hand = false
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284 ; next-code = C_pickup_rfork
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285 } ∷ record
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286 { pid = 2
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287 ; left-hand = false
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288 ; right-hand = false
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289 ; next-code = C_pickup_rfork
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290 } ∷ record
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291 { pid = 3
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292 ; left-hand = false
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293 ; right-hand = false
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294 ; next-code = C_pickup_rfork
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295 } ∷ []
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296 } (λ e2 → e2)
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297
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298 test-step-c2 : List (List Env)
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299 test-step-c2 = init-brute-force (record {
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300 table = 0 ∷ 0 ∷ 0 ∷ []
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301 ; ph = record
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302 { pid = 1
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303 ; left-hand = false
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304 ; right-hand = false
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305 ; next-code = C_thinking
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306 } ∷ record
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307 { pid = 2
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308 ; left-hand = false
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309 ; right-hand = false
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310 ; next-code = C_pickup_rfork
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311 } ∷ record
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312 { pid = 3
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313 ; left-hand = false
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314 ; right-hand = false
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315 ; next-code = C_pickup_rfork
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316 } ∷ []
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317 } ∷ []) (λ e0 → exec-brute-force 2 e0 (λ e2 → e2))
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318
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319 -- 以下メモ
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320
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321 -- eathingの状態はいらない Done
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322 -- tableはℕのList Done
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323 -- いきなりsearchしないで実行結果を持つ感じに
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324 -- stubを使うとCodeの引数がスマートになるのでやる
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325
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326 -- 実行結果をListでもっているので,stepをじっこうしても変化がなかった場合をdeadlockとして検出したい
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327 -- 東恩納先輩とおなじように,waitに入れて評価する
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328
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329 -- 余裕があったらassertにLTLの話をいれる
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330
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331 -- loop execution
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332
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333 -- concurrnt execution
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334
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335 -- state db ( binary tree of processes )
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336
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337 -- depth first ececution
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338
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339 -- verify temporal logic poroerries
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340
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341
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342
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