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dict.ya
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dict.ya
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package dict
import pair
import ord
import nat
import list
import maybe
import bool
import text
where
type Dict (V: Type) {
Tip,
Bin (size: Nat) (key: Text) (val: V) (left: Dict V) (right: Dict V),
}
def Dict.empty (0 V: Type) : Dict V
= Dict.Tip V
def Dict.single (0 V: Type) (k: Text) (v: V): Dict V
= Dict.Bin V 1 k v (Dict.Tip V) (Dict.Tip V)
def Dict.null (0 V: Type) (m: Dict V) : Bool
= (case m) (λ _ => Bool) (Bool.True) (λ _ _ _ _ _ => Bool.False)
def Dict.size (0 V: Type) (m: Dict V) : Nat
= (case m) (λ _ => Nat) 0 (λ size _ _ _ _ => size)
def Dict.lookup (0 V: Type) (key: Text) (m: Dict V): Maybe V
=
letrec go (k: Text) (m: Dict V): Maybe V = (case m) (λ _ => Maybe V)
(Maybe.None V)
(λ _ kx x l r => (case (Text.compare k kx)) (λ _ => Maybe V)
(go k l)
(Maybe.Some V x)
(go k r)
);
go key m
def Dict.lookupAssoc (0 V: Type) (key: Text) (m: Dict V): Maybe (Pair Text V)
=
letrec go (k: Text) (m: Dict V): Maybe (Pair Text V) = (case m) (λ _ => Maybe (Pair Text V))
(Maybe.None (Pair Text V))
(λ _ kx x l r => (case (Text.compare k kx)) (λ _ => Maybe (Pair Text V))
(go k l)
(Maybe.Some (Pair Text V) (Pair.New Text V k x))
(go k r)
);
go key m
def Dict.member (0 V: Type) (key: Text) (m: Dict V): Bool
=
letrec go (k: Text) (m: Dict V): Bool = (case m) (λ _ => Bool)
(Bool.False)
(λ _ kx _ l r => (case (Text.compare k kx)) (λ _ => Bool)
(go k l)
(Bool.True)
(go k r)
);
go key m
def Dict.notMember (0 V: Type) (key: Text) (m: Dict V): Bool
= Bool.not (Dict.member V key m)
def Dict.find (0 V: Type) (default: V) (key: Text) (m: Dict V): V
= Maybe.default V (default) (Dict.lookup V key m)
def Dict.bin (0 V: Type) (k: Text) (v: V) (left right: Dict V): Dict V
= Dict.Bin V (Nat.S (Nat.add (Dict.size V left) (Dict.size V right))) k v left right
def Dict.rotateLeft (V: Type) (k: Text) (v: V) (left right: Dict V): Dict V =
(case right) (λ _ => Dict V)
(Dict.empty V)
(λ _ _ _ ly ry => Bool.if (Dict V) (Nat.lth (Dict.size V ly) (Nat.mul 2 (Dict.size V ry)))
((case right) (λ _ => Dict V)
(Dict.empty V)
(λ _ k2 v2 left2 right2 => Dict.bin V k2 v2 (Dict.bin V k v left left2) right2)
)
((case right) (λ _ => Dict V)
(Dict.empty V)
(λ _ k2 v2 left2 right2 => (case left2) (λ _ => Dict V)
(Dict.empty V)
(λ _ k3 v3 left3 right3 => Dict.bin V k3 v3 (Dict.bin V k v left left3) (Dict.bin V k2 v2 right3 right2))
)
)
)
def Dict.rotateRight (V: Type) (k: Text) (v: V) (left right: Dict V): Dict V =
(case left) (λ _ => Dict V)
(Dict.empty V)
(λ _ _ _ ly ry => Bool.if (Dict V) (Nat.lth (Dict.size V ry) (Nat.mul 2 (Dict.size V ly)))
((case left) (λ _ => Dict V)
(Dict.empty V)
(λ _ k2 v2 left2 right2 => Dict.bin V k2 v2 left2 (Dict.bin V k v left2 right2)))
((case left) (λ _ => Dict V)
(Dict.empty V)
(λ _ k2 v2 left2 right2 => (case right2) (λ _ => Dict V)
(Dict.empty V)
(λ _ k3 v3 left3 right3 => Dict.bin V k3 v3 (Dict.bin V k2 v2 left2 left3) (Dict.bin V k v right3 right))
)
)
)
def Dict.balance (V: Type) (k: Text) (v: V) (left right: Dict V): Dict V
= let leftSize: Nat = Dict.size V left;
let rightSize: Nat = Dict.size V right;
let xSize: Nat = Nat.S (Nat.add leftSize rightSize);
Bool.if (Dict V) (Nat.lte (Nat.add leftSize rightSize) 1)
(Dict.Bin V xSize k v left right)
(Bool.if (Dict V) (Nat.gte rightSize (Nat.mul 5 leftSize))
(Dict.rotateLeft V k v left right)
(Bool.if (Dict V) (Nat.gte leftSize (Nat.mul 5 rightSize))
(Dict.rotateRight V k v left right)
(Dict.Bin V xSize k v left right)
)
)
def Dict.deleteFindMin (V: Type) (m: Dict V): Maybe (Pair (Pair Text V) (Dict V))
= (case m) (λ _ => Maybe (Pair (Pair Text V) (Dict V)))
(Maybe.None (Pair (Pair Text V) (Dict V)))
(λ _ k v l r => (case l) (λ _ => Maybe (Pair (Pair Text V) (Dict V)))
(Maybe.Some (Pair (Pair Text V) (Dict V)) (Pair.New (Pair Text V) (Dict V) (Pair.New Text V k v) r))
(λ _ _ _ _ _ => Maybe.map (Pair (Pair Text V) (Dict V)) (Pair (Pair Text V) (Dict V))
(λ p =>
Pair.map (Pair Text V) (Dict V) (Dict V)
(λ newLeft => Dict.balance V k v newLeft r)
p
)
(Dict.deleteFindMin V l)
))
def Dict.deleteFindMax (V: Type) (m: Dict V): Maybe (Pair (Pair Text V) (Dict V))
= (case m) (λ _ => Maybe (Pair (Pair Text V) (Dict V)))
(Maybe.None (Pair (Pair Text V) (Dict V)))
(λ _ k v l r => (case r) (λ _ => Maybe (Pair (Pair Text V) (Dict V)))
(Maybe.Some (Pair (Pair Text V) (Dict V))(Pair.New (Pair Text V) (Dict V) (Pair.New Text V k v) l))
(λ _ _ _ _ _ => Maybe.map (Pair (Pair Text V) (Dict V)) (Pair (Pair Text V) (Dict V))
(λ p =>
Pair.map (Pair Text V) (Dict V) (Dict V)
(λ newRight => Dict.balance V k v l newRight)
p
)
(Dict.deleteFindMax V l)
))
def Dict.glue (V: Type) (left right: Dict V): Dict V
= (case left) (λ _ => Dict V)
(right)
(λ _ _ _ _ _ => (case right) (λ _ => Dict V)
(left)
(λ _ _ _ _ _ => (Bool.if (Dict V) (Nat.gth (Dict.size V left) (Dict.size V right))
((case (Dict.deleteFindMax V left)) (λ _ => Dict V)
(Dict.empty V)
(λ result =>
let keyValue: Pair Text V = Pair.fst (Pair Text V) (Dict V) result;
let newLeft: Dict V = Pair.snd (Pair Text V) (Dict V) result;
let maxKey: Text = Pair.fst Text V keyValue;
let maxValue: V = Pair.snd Text V keyValue;
Dict.balance V maxKey maxValue newLeft right)
)
((case (Dict.deleteFindMin V right)) (λ _ => Dict V)
(Dict.empty V)
(λ result =>
let keyValue: Pair Text V = Pair.fst (Pair Text V) (Dict V) result;
let newRight: Dict V = Pair.snd (Pair Text V) (Dict V) result;
let minKey: Text = Pair.fst Text V keyValue;
let minValue: V = Pair.snd Text V keyValue;
Dict.balance V minKey minValue left newRight)
)
)
)
)
def Dict.insert (V: Type) (k: Text) (v: V) (m: Dict V): Dict V
= (case m) (λ _ => Dict V)
(Dict.single V k v)
(λ s actK actV left right =>
(case (Text.compare k actK)) (λ _ => Dict V)
(Dict.balance V actK actV (Dict.insert V k v left) right)
(Dict.Bin V s k v left right)
(Dict.balance V actK actV left (Dict.insert V k v right))
)
def Dict.delete (V: Type) (k: Text) (m: Dict V): Dict V
= (case m) (λ _ => Dict V)
(Dict.Tip V)
(λ s actK actV left right =>
(case (Text.compare k actK)) (λ _ => Dict V)
(Dict.balance V actK actV (Dict.delete V k left) right)
(Dict.glue V left right)
(Dict.balance V actK actV left (Dict.delete V k right))
)