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1 module stack where
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2
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3 open import Relation.Binary.PropositionalEquality
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4
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5 data Bool : Set where
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6 True : Bool
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7 False : Bool
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8
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9 data Maybe (a : Set) : Set where
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10 Nothing : Maybe a
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11 Just : a -> Maybe a
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12
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13 record Stack {a t : Set} (stackImpl : Set) : Set where
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14 field
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15 stack : stackImpl
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16 push : stackImpl -> a -> (stackImpl -> t) -> t
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17 pop : stackImpl -> (stackImpl -> Maybe a -> t) -> t
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18
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19 data Element (a : Set) : Set where
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20 cons : a -> Maybe (Element a) -> Element a
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21
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22 datum : {a : Set} -> Element a -> a
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23 datum (cons a _) = a
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24
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25 next : {a : Set} -> Element a -> Maybe (Element a)
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26 next (cons _ n) = n
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27
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28
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29 {-
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30 -- cannot define recrusive record definition. so use linked list with maybe.
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31 record Element {l : Level} (a : Set l) : Set (suc l) where
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32 field
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33 datum : a -- `data` is reserved by Agda.
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34 next : Maybe (Element a)
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35 -}
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36
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37
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38
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39 record SingleLinkedStack (a : Set) : Set where
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40 field
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41 top : Maybe (Element a)
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42 open SingleLinkedStack
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43
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44 pushSingleLinkedStack : {Data t : Set} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
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45 pushSingleLinkedStack stack datum next = next stack1
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46 where
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47 element = cons datum (top stack)
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48 stack1 = record {top = Just element}
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49
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50
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51 popSingleLinkedStack : {a t : Set} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
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52 popSingleLinkedStack stack cs with (top stack)
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53 ... | Nothing = cs stack Nothing
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54 ... | Just d = cs stack1 (Just data1)
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55 where
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56 data1 = datum d
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57 stack1 = record { top = (next d) }
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58
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59
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60 emptySingleLinkedStack : {a : Set} -> SingleLinkedStack a
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61 emptySingleLinkedStack = record {top = Nothing}
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62
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63 createSingleLinkedStack : {a b : Set} -> Stack {a} {b} (SingleLinkedStack a)
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64 createSingleLinkedStack = record { stack = emptySingleLinkedStack
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65 ; push = pushSingleLinkedStack
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66 ; pop = popSingleLinkedStack
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67 }
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68
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69
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70
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71 test01 : {a : Set} -> SingleLinkedStack a -> Maybe a -> Bool
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72 test01 stack _ with (top stack)
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73 ... | (Just _) = True
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74 ... | Nothing = False
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75
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76
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77 test02 : {a : Set} -> SingleLinkedStack a -> Bool
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78 test02 stack = (popSingleLinkedStack stack) test01
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79
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80 test03 : {a : Set} -> a -> Bool
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81 test03 v = pushSingleLinkedStack emptySingleLinkedStack v test02
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82
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83
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84 lemma : {A : Set} {a : A} -> test03 a ≡ False
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85 lemma = refl
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