223 lines
9.3 KiB
Agda
223 lines
9.3 KiB
Agda
module Data.SortedMap
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import Prelude
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data T23 : Nat -> U -> U -> U where
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Leaf : ∀ k v. k -> v -> T23 Z k v
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Node2 : ∀ h k v. T23 h k v -> k -> T23 h k v -> T23 (S h) k v
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Node3 : ∀ h k v. T23 h k v -> k -> T23 h k v -> k -> T23 h k v -> T23 (S h) k v
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lookupT23 : ∀ h k v. (k → k → Ordering) -> k -> T23 h k v -> Maybe (k × v)
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lookupT23 compare key (Leaf k v)= case compare k key of
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EQ => Just (k,v)
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_ => Nothing
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lookupT23 compare key (Node2 t1 k1 t2) =
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case compare key k1 of
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GT => lookupT23 compare key t2
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_ => lookupT23 compare key t1
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lookupT23 compare key (Node3 t1 k1 t2 k2 t3) =
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case compare key k1 of
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GT => case compare key k2 of
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GT => lookupT23 compare key t3
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_ => lookupT23 compare key t2
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_ => lookupT23 compare key t1
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insertT23 : ∀ h k v. (k → k → Ordering) -> k -> v -> T23 h k v -> Either (T23 h k v) (T23 h k v × k × T23 h k v)
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insertT23 compare key value (Leaf k v) = case compare key k of
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EQ => Left (Leaf key value)
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LT => Right (Leaf key value, key, Leaf k v)
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GT => Right (Leaf k v, k, Leaf key value)
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insertT23 compare key value (Node2 t1 k1 t2) =
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case compare key k1 of
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GT => case insertT23 compare key value t2 of
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Left t2' => Left (Node2 t1 k1 t2')
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Right (a,b,c) => Left (Node3 t1 k1 a b c)
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_ => case insertT23 compare key value t1 of
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Left t1' => Left (Node2 t1' k1 t2)
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Right (a,b,c) => Left (Node3 a b c k1 t2)
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insertT23 compare key value (Node3 t1 k1 t2 k2 t3) =
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case compare key k1 of
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GT => case compare key k2 of
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GT => case insertT23 compare key value t3 of
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Left t3' => Left (Node3 t1 k1 t2 k2 t3')
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Right (a,b,c) => Right (Node2 t1 k1 t2, k2, Node2 a b c)
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_ => case insertT23 compare key value t2 of
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Left t2' => Left (Node3 t1 k1 t2' k2 t3)
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Right (a,b,c) => Right (Node2 t1 k1 a, b, Node2 c k2 t3)
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_ =>
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case insertT23 compare key value t1 of
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Left t1' => Left (Node3 t1' k1 t2 k2 t3)
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Right (a,b,c) => Right (Node2 a b c, k1, Node2 t2 k2 t3)
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-- This is cribbed from Idris. Deleting nodes takes a bit of code.
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Hole : Nat → U → U → U
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Hole Z k v = Unit
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Hole (S n) k v = T23 n k v
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Node4 : ∀ k v h. T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → T23 (S (S h)) k v
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Node4 t1 k1 t2 k2 t3 k3 t4 = Node2 (Node2 t1 k1 t2) k2 (Node2 t3 k3 t4)
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Node5 : ∀ k v h. T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → T23 (S (S h)) k v
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Node5 a b c d e f g h i = Node2 (Node2 a b c) d (Node3 e f g h i)
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Node6 : ∀ k v h. T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → T23 (S (S h)) k v
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Node6 a b c d e f g h i j k = Node2 (Node3 a b c d e) f (Node3 g h i j k)
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Node7 : ∀ k v h. T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → k → T23 h k v → T23 (S (S h)) k v
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Node7 a b c d e f g h i j k l m = Node3 (Node3 a b c d e) f (Node2 g h i) j (Node2 k l m)
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merge1 : ∀ k v h. T23 h k v → k → T23 (S h) k v → k → T23 (S h) k v → T23 (S (S h)) k v
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merge1 a b (Node2 c d e) f (Node2 g h i) = Node5 a b c d e f g h i
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merge1 a b (Node2 c d e) f (Node3 g h i j k) = Node6 a b c d e f g h i j k
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merge1 a b (Node3 c d e f g) h (Node2 i j k) = Node6 a b c d e f g h i j k
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merge1 a b (Node3 c d e f g) h (Node3 i j k l m) = Node7 a b c d e f g h i j k l m
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merge2 : ∀ k v h. T23 (S h) k v → k → T23 h k v → k → T23 (S h) k v → T23 (S (S h)) k v
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merge2 (Node2 a b c) d e f (Node2 g h i) = Node5 a b c d e f g h i
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merge2 (Node2 a b c) d e f (Node3 g h i j k) = Node6 a b c d e f g h i j k
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merge2 (Node3 a b c d e) f g h (Node2 i j k) = Node6 a b c d e f g h i j k
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merge2 (Node3 a b c d e) f g h (Node3 i j k l m) = Node7 a b c d e f g h i j k l m
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merge3 : ∀ k v h. T23 (S h) k v → k → T23 (S h) k v → k → T23 h k v → T23 (S (S h)) k v
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merge3 (Node2 a b c) d (Node2 e f g) h i = Node5 a b c d e f g h i
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merge3 (Node2 a b c) d (Node3 e f g h i) j k = Node6 a b c d e f g h i j k
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merge3 (Node3 a b c d e) f (Node2 g h i) j k = Node6 a b c d e f g h i j k
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merge3 (Node3 a b c d e) f (Node3 g h i j k) l m = Node7 a b c d e f g h i j k l m
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-- height is erased in the data everywhere but the top, but needed for case
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-- I wonder if we could use a 1 + 1 + 1 type instead of Either Tree Hole and condense this
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deleteT23 : ∀ k v. (k → k → Ordering) → (h : Nat) -> k -> T23 h k v -> Either (T23 h k v) (Hole h k v)
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deleteT23 compare Z key (Leaf k v) = case compare k key of
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EQ => Right MkUnit
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_ => Left (Leaf k v)
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deleteT23 compare (S Z) key (Node2 t1 k1 t2) =
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case compare key k1 of
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GT => case deleteT23 compare Z key t2 of
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Left t2 => Left (Node2 t1 k1 t2)
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Right MkUnit => Right t1
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_ => case deleteT23 compare Z key t1 of
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Left t1 => Left (Node2 t1 k1 t2)
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Right _ => Right t2
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deleteT23 compare (S Z) key (Node3 t1 k1 t2 k2 t3) =
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case compare key k1 of
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GT => case compare key k2 of
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GT => case deleteT23 compare _ key t3 of
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Left t3 => Left (Node3 t1 k1 t2 k2 t3)
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Right _ => Left (Node2 t1 k1 t2)
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_ => case deleteT23 compare _ key t2 of
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Left t2 => Left (Node3 t1 k1 t2 k2 t3)
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Right _ => Left (Node2 t1 k1 t3)
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_ => case deleteT23 compare _ key t1 of
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Left t1 => Left (Node3 t1 k1 t2 k2 t3)
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Right MkUnit => Left (Node2 t2 k2 t3)
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deleteT23 compare (S (S h)) key (Node2 t1 k1 t2) =
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case compare key k1 of
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GT => case deleteT23 compare _ key t2 of
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Left t2 => Left (Node2 t1 k1 t2)
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Right t2 => case t1 of
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Node2 a b c => Right (Node3 a b c k1 t2)
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Node3 a b c d e => Left (Node4 a b c d e k1 t2)
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_ => case deleteT23 compare (S h) key t1 of
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Left t1 => Left (Node2 t1 k1 t2)
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Right t1 => case t2 of
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Node2 t2' k2' t3' => Right (Node3 t1 k1 t2' k2' t3')
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Node3 t2 k2 t3 k3 t4 => Left $ Node4 t1 k1 t2 k2 t3 k3 t4
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deleteT23 compare (S (S h)) key (Node3 t1 k1 t2 k2 t3) =
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case compare key k1 of
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GT => case compare key k2 of
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GT => case deleteT23 compare _ key t3 of
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Left t3 => Left (Node3 t1 k1 t2 k2 t3)
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Right t3 => Left (merge3 t1 k1 t2 k2 t3)
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_ => case deleteT23 compare _ key t2 of
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Left t2 => Left (Node3 t1 k1 t2 k2 t3)
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Right t2 => Left (merge2 t1 k1 t2 k2 t3)
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_ => case deleteT23 compare _ key t1 of
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Left t1 => Left (Node3 t1 k1 t2 k2 t3)
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Right t1 => Left (merge1 t1 k1 t2 k2 t3)
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treeLeft : ∀ h k v. T23 h k v → (k × v)
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treeLeft (Leaf k v) = (k, v)
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treeLeft (Node2 t1 _ _) = treeLeft t1
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treeLeft (Node3 t1 _ _ _ _) = treeLeft t1
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treeRight : ∀ h k v. T23 h k v → (k × v)
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treeRight (Leaf k v) = (k, v)
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treeRight (Node2 _ _ t2) = treeRight t2
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treeRight (Node3 _ _ _ _ t3) = treeRight t3
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data SortedMap : U -> U -> U where
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EmptyMap : ∀ k v. (k → k → Ordering) → SortedMap k v
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-- h not erased so we know what happens in delete
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MapOf : ∀ k v. {h : Nat} → (k → k → Ordering) → T23 h k v → SortedMap k v
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deleteMap : ∀ k v. k → SortedMap k v → SortedMap k v
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deleteMap key m@(EmptyMap _) = m
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-- REVIEW if I split h separately in a nested case, it doesn't sort out Hole
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deleteMap key (MapOf {k} {v} {Z} compare tree) = case deleteT23 compare Z key tree of
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Left t => MapOf compare t
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Right t => EmptyMap compare
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deleteMap key (MapOf {k} {v} {S n} compare tree) = case deleteT23 compare (S n) key tree of
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Left t => MapOf compare t
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Right t => MapOf compare t
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leftMost : ∀ k v. SortedMap k v → Maybe (k × v)
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leftMost (MapOf compare m) = Just (treeLeft m)
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leftMost _ = Nothing
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rightMost : ∀ k v. SortedMap k v → Maybe (k × v)
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rightMost (MapOf compare m) = Just (treeRight m)
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rightMost _ = Nothing
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-- TODO issue with metas and case if written as `do` block
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pop : ∀ k v. SortedMap k v → Maybe ((k × v) × SortedMap k v)
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pop m = case leftMost m of
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Just (k,v) => Just ((k,v), deleteMap k m)
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Nothing => Nothing
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lookupMap : ∀ k v. k -> SortedMap k v -> Maybe (k × v)
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lookupMap k (MapOf compare map) = lookupT23 compare k map
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lookupMap k _ = Nothing
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lookupMap' : ∀ k v. k -> SortedMap k v -> Maybe v
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lookupMap' k (MapOf compare map) = snd <$> lookupT23 compare k map
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lookupMap' k _ = Nothing
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updateMap : ∀ k v. k -> v -> SortedMap k v -> SortedMap k v
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updateMap k v (EmptyMap compare) = MapOf compare $ Leaf k v
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updateMap k v (MapOf compare map) = case insertT23 compare k v map of
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Left map' => MapOf compare map'
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Right (a, b, c) => MapOf compare (Node2 a b c)
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toList : ∀ k v. SortedMap k v → List (k × v)
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toList {k} {v} (MapOf compare smap) = reverse $ go smap Nil
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where
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go : ∀ h. T23 h k v → List (k × v) → List (k × v)
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go (Leaf k v) acc = (k, v) :: acc
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go (Node2 t1 k1 t2) acc = go t2 (go t1 acc)
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go (Node3 t1 k1 t2 k2 t3) acc = go t3 $ go t2 $ go t1 acc
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toList _ = Nil
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emptyMap : ∀ k v. {{Ord k}} → SortedMap k v
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emptyMap = EmptyMap compare
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mapFromList : ∀ k v. {{Ord k}} → List (k × v) → SortedMap k v
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mapFromList {k} {v} stuff = foldl go emptyMap stuff
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where
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go : SortedMap k v → k × v → SortedMap k v
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go map (k, v) = updateMap k v map
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foldMap : ∀ a b. (b → b → b) → SortedMap a b → List (a × b) → SortedMap a b
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foldMap f m Nil = m
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foldMap f m ((a,b) :: xs) = case lookupMap a m of
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Nothing => foldMap f (updateMap a b m) xs
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Just (_, b') => foldMap f (updateMap a (f b' b) m) xs
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listValues : ∀ k v. SortedMap k v → List v
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listValues sm = map snd $ toList sm
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