Copyright	(c) Nicolás Rodríguez 2021
License	GPL-3
Maintainer	Nicolás Rodríguez
Stability	experimental
Portability	POSIX
Safe Haskell	Safe
Language	Haskell2010

Data.Tree.Node

Description

Definition of nodes for the type safe trees, along with a constructor and a value getter.

Synopsis

data Node :: Nat -> Type -> Type
mkNode :: Proxy k -> a -> Node k a
getValue :: Node k a -> a

Documentation

data Node :: Nat -> Type -> Type Source #

Node constructor. It receives a value of an arbitrary type (of kind Type) and returns a new Node. At the type level, it has the type a of the value and a key k of kind Nat. A key may be defined through explicit type signature, like Node 'a' :: Node 6 Char.

Instances

Instances details

(t ~ 'ForkTree l (Node n a1) r, a ~ LookupValueType x t t, o ~ CmpNat x n, Lookupable' x a ('ForkTree l (Node n a1) r) o) => Lookupable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Intern.Lookup Methods lookup :: forall (l0 :: Tree) (n0 :: Nat) a10 (r0 :: Tree). ('ForkTree l (Node n a1) r ~ 'ForkTree l0 (Node n0 a10) r0, Member x ('ForkTree l (Node n a1) r) ('ForkTree l (Node n a1) r) ~ 'True) => Proxy x -> BST ('ForkTree l (Node n a1) r) -> a Source #
(o ~ CmpNat x n, Insertable' x a ('ForkTree l (Node n a1) r) o) => Insertable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Intern.Insert Associated Types type Insert x a ('ForkTree l (Node n a1) r) :: Tree Source # Methods insert :: Node x a -> BST ('ForkTree l (Node n a1) r) -> BST (Insert x a ('ForkTree l (Node n a1) r)) Source #
(t ~ 'ForkTree l (Node n a1) r, a ~ LookupValueType x t t, o ~ CmpNat x n, Lookupable' x a ('ForkTree l (Node n a1) r) o) => Lookupable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Lookup Methods lookup :: forall (l0 :: Tree) (n0 :: Nat) a10 (r0 :: Tree). ('ForkTree l (Node n a1) r ~ 'ForkTree l0 (Node n0 a10) r0, Member x ('ForkTree l (Node n a1) r) ('ForkTree l (Node n a1) r) ~ 'True) => Proxy x -> ITree ('ForkTree l (Node n a1) r) -> a Source #
(o ~ CmpNat x n, Insertable' x a ('ForkTree l (Node n a1) r) o) => Insertable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert x a ('ForkTree l (Node n a1) r) :: Tree Source # Methods insert :: Node x a -> ITree ('ForkTree l (Node n a1) r) -> ITree (Insert x a ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, ProofIsBSTInsert' x a ('ForkTree l (Node n a1) r) o) => ProofIsBSTInsert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.InsertProofs Methods proofIsBSTInsert :: Proxy (Node x a) -> IsBSTT ('ForkTree l (Node n a1) r) -> IsBSTT (Insert x a ('ForkTree l (Node n a1) r)) Source #
(t ~ 'ForkTree l (Node n a1) r, a ~ LookupValueType x t t, Lookupable' x a t (CmpNat x n)) => Lookupable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Lookup Methods lookup :: forall (l0 :: Tree) (n0 :: Nat) a10 (r0 :: Tree). ('ForkTree l (Node n a1) r ~ 'ForkTree l0 (Node n0 a10) r0, Member x ('ForkTree l (Node n a1) r) ('ForkTree l (Node n a1) r) ~ 'True) => Proxy x -> AVL ('ForkTree l (Node n a1) r) -> a Source #
(o ~ CmpNat x n, Insertable' x a ('ForkTree l (Node n a1) r) o) => Insertable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Insert Associated Types type Insert x a ('ForkTree l (Node n a1) r) :: Tree Source # Methods insert :: Node x a -> AVL ('ForkTree l (Node n a1) r) -> AVL (Insert x a ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, Insertable' x a ('ForkTree l (Node n a1) r) o) => Insertable x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert x a ('ForkTree l (Node n a1) r) :: Tree Source # Methods insert :: Node x a -> ITree ('ForkTree l (Node n a1) r) -> ITree (Insert x a ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, ProofIsBalancedInsert' x a ('ForkTree l (Node n a1) r) o) => ProofIsBalancedInsert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.InsertProofs Methods proofIsBalancedInsert :: Proxy (Node x a) -> IsBalancedT ('ForkTree l (Node n a1) r) -> IsBalancedT (Insert x a ('ForkTree l (Node n a1) r)) Source #
ProofIsBSTInsert' x a ('ForkTree l (Node n a1) r) (CmpNat x n) => ProofIsBSTInsert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.InsertProofs Methods proofIsBSTInsert :: Proxy (Node x a) -> IsBSTT ('ForkTree l (Node n a1) r) -> IsBSTT (Insert x a ('ForkTree l (Node n a1) r)) Source #
(r ~ 'ForkTree rl (Node rn rna) rr, o ~ CmpNat x rn, Insertable' x a r o) => Insertable' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) -> Proxy 'GT -> ITree (Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT) Source #
Show a => Insertable' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) 'EmptyTree) -> Proxy 'GT -> ITree (Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT) Source #
(l ~ 'ForkTree ll (Node ln lna) lr, o ~ CmpNat x ln, Insertable' x a l o) => Insertable' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) -> Proxy 'LT -> ITree (Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT) Source #
Show a => Insertable' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree 'EmptyTree (Node n a1) r) -> Proxy 'LT -> ITree (Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT) Source #
Show a => Insertable' x a ('ForkTree l (Node n a1) r) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) r) 'EQ :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) r) -> Proxy 'EQ -> ITree (Insert' x a ('ForkTree l (Node n a1) r) 'EQ) Source #
(r ~ 'ForkTree rl (Node rn rna) rr, o ~ CmpNat x rn, Insertable' x a r o, Balanceable ('ForkTree l (Node n a1) (Insert' x a r o))) => Insertable' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) -> Proxy 'GT -> ITree (Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT)
(Show a, Balanceable ('ForkTree l (Node n a1) ('ForkTree 'EmptyTree (Node x a) 'EmptyTree))) => Insertable' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) 'EmptyTree) -> Proxy 'GT -> ITree (Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT)
(l ~ 'ForkTree ll (Node ln lna) lr, o ~ CmpNat x ln, Insertable' x a l o, Balanceable ('ForkTree (Insert' x a l o) (Node n a1) r)) => Insertable' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) -> Proxy 'LT -> ITree (Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT)
(Show a, Balanceable ('ForkTree ('ForkTree 'EmptyTree (Node x a) 'EmptyTree) (Node n a1) r)) => Insertable' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree 'EmptyTree (Node n a1) r) -> Proxy 'LT -> ITree (Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT)
Show a => Insertable' x a ('ForkTree l (Node n a1) r) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert Associated Types type Insert' x a ('ForkTree l (Node n a1) r) 'EQ :: Tree Source # Methods insert' :: Node x a -> ITree ('ForkTree l (Node n a1) r) -> Proxy 'EQ -> ITree (Insert' x a ('ForkTree l (Node n a1) r) 'EQ)
(o ~ CmpNat x n, Deletable' x ('ForkTree l (Node n a1) r) o) => Deletable x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Intern.Delete Associated Types type Delete x ('ForkTree l (Node n a1) r) :: Tree Source # Methods delete :: Proxy x -> BST ('ForkTree l (Node n a1) r) -> BST (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, Deletable' x ('ForkTree l (Node n a1) r) o) => Deletable x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete x ('ForkTree l (Node n a1) r) :: Tree Source # Methods delete :: Proxy x -> ITree ('ForkTree l (Node n a1) r) -> ITree (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, ProofIsBSTDelete' x ('ForkTree l (Node n a1) r) o) => ProofIsBSTDelete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.DeleteProofs Methods proofIsBSTDelete :: Proxy x -> IsBSTT ('ForkTree l (Node n a1) r) -> IsBSTT (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, Deletable' x ('ForkTree l (Node n a1) r) o) => Deletable x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Delete Associated Types type Delete x ('ForkTree l (Node n a1) r) :: Tree Source # Methods delete :: Proxy x -> AVL ('ForkTree l (Node n a1) r) -> AVL (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, Deletable' x ('ForkTree l (Node n a1) r) o) => Deletable x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete x ('ForkTree l (Node n a1) r) :: Tree Source # Methods delete :: Proxy x -> ITree ('ForkTree l (Node n a1) r) -> ITree (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, ProofIsBalancedDelete' x ('ForkTree l (Node n a1) r) o) => ProofIsBalancedDelete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.DeleteProofs Methods proofIsBalancedDelete :: Proxy x -> IsBalancedT ('ForkTree l (Node n a1) r) -> IsBalancedT (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x n, ProofIsBSTDelete' x ('ForkTree l (Node n a1) r) o) => ProofIsBSTDelete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.DeleteProofs Methods proofIsBSTDelete :: Proxy x -> IsBSTT ('ForkTree l (Node n a1) r) -> IsBSTT (Delete x ('ForkTree l (Node n a1) r)) Source #
(o ~ CmpNat x rn, Deletable' x ('ForkTree rl (Node rn ra) rr) o) => Deletable' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'GT -> ITree (Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT) Source #
Deletable' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree l (Node n a1) 'EmptyTree) -> Proxy 'GT -> ITree (Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT) Source #
(o ~ CmpNat x ln, Deletable' x ('ForkTree ll (Node ln la) lr) o) => Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) -> Proxy 'LT -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT) Source #
Deletable' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) r) -> Proxy 'LT -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT) Source #
(l ~ 'ForkTree ll (Node ln la) lr, Show (MaxValue l), MaxKeyDeletable l, Maxable l) => Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ) Source #
Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ) Source #
Deletable' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ) Source #
Deletable' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ) Source #
(o ~ CmpNat x rn, r ~ 'ForkTree rl (Node rn ra) rr, Deletable' x r o, Balanceable ('ForkTree l (Node n a1) (Delete' x r o))) => Deletable' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'GT -> ITree (Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT)
Deletable' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree l (Node n a1) 'EmptyTree) -> Proxy 'GT -> ITree (Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT)
(l ~ 'ForkTree ll (Node ln la) lr, o ~ CmpNat x ln, Deletable' x l o, Balanceable ('ForkTree (Delete' x l (CmpNat x ln)) (Node n a1) r)) => Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) -> Proxy 'LT -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT)
Deletable' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) r) -> Proxy 'LT -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT)
(l ~ 'ForkTree ll (Node ln la) lr, r ~ 'ForkTree rl (Node rn ra) rr, Show (MaxValue l), MaxKeyDeletable l, Maxable l, Balanceable ('ForkTree (MaxKeyDelete l) (Node (MaxKey l) (MaxValue l)) r)) => Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ)
Deletable' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ)
Deletable' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ)
Deletable' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ :: Tree Source # Methods delete' :: Proxy x -> ITree ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) -> Proxy 'EQ -> ITree (Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ)
Show a => Show (Node k a) Source #
Instance details Defined in Data.Tree.Node Methods showsPrec :: Int -> Node k a -> ShowS # show :: Node k a -> String # showList :: [Node k a] -> ShowS #
Maxable ('ForkTree rl (Node rn ra) rr) => Maxable ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type MaxKey ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) :: Nat Source # type MaxValue ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source # Methods maxValue :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr) ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> MaxValue ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Maxable ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type MaxKey ('ForkTree l (Node n a1) 'EmptyTree) :: Nat Source # type MaxValue ('ForkTree l (Node n a1) 'EmptyTree) Source # Methods maxValue :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) 'EmptyTree ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) 'EmptyTree) -> MaxValue ('ForkTree l (Node n a1) 'EmptyTree) Source #
MaxKeyDeletable ('ForkTree rl (Node rn ra) rr) => MaxKeyDeletable ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) :: Tree Source # Methods maxKeyDelete :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr) ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> ITree (MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr))) Source #
MaxKeyDeletable ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete Associated Types type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) :: Tree Source # Methods maxKeyDelete :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) 'EmptyTree ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) 'EmptyTree) -> ITree (MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree)) Source #
(IsBSTC l, IsBSTC r, LtN l n ~ 'True, GtN r n ~ 'True) => IsBSTC ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Constructors Methods isBSTT :: IsBSTT ('ForkTree l (Node n a) r) Source #
(us ~ UnbalancedState (Height l) (Height r), Balanceable' ('ForkTree l (Node n a) r) us) => Balanceable ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Balance Associated Types type Balance ('ForkTree l (Node n a) r) :: Tree Source # Methods balance :: AlmostAVL ('ForkTree l (Node n a) r) -> AVL (Balance ('ForkTree l (Node n a) r)) Source #
(IsBalancedC l, IsBalancedC r, BalancedHeights (Height l) (Height r) n ~ 'True) => IsBalancedC ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Constructors Methods isBalancedT :: IsBalancedT ('ForkTree l (Node n a) r) Source #
(us ~ UnbalancedState (Height l) (Height r), Balanceable' ('ForkTree l (Node n a) r) us) => Balanceable ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Balance ('ForkTree l (Node n a) r) :: Tree Source # Methods balance :: ITree ('ForkTree l (Node n a) r) -> ITree (Balance ('ForkTree l (Node n a) r)) Source #
(r ~ 'ForkTree rl (Node rn ra) rr, MaxKeyDeletable r, Balanceable ('ForkTree l (Node n a1) (MaxKeyDelete r))) => MaxKeyDeletable ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) :: Tree Source # Methods maxKeyDelete :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr) ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) -> ITree (MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr))) Source #
MaxKeyDeletable ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete Associated Types type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) :: Tree Source # Methods maxKeyDelete :: forall (l0 :: Tree) (n0 :: Nat) a10 (r :: Tree). 'ForkTree l (Node n a1) 'EmptyTree ~ 'ForkTree l0 (Node n0 a10) r => ITree ('ForkTree l (Node n a1) 'EmptyTree) -> ITree (MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree)) Source #
(us ~ UnbalancedState (Height l) (Height r), LtN l n ~ 'True, GtN r n ~ 'True, ProofIsBalancedBalance' ('ForkTree l (Node n a) r) us) => ProofIsBalancedBalance ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.BalanceProofs Methods proofIsBalancedBalance :: IsAlmostBalancedT ('ForkTree l (Node n a) r) -> IsBalancedT (Balance ('ForkTree l (Node n a) r)) Source #
(us ~ UnbalancedState (Height l) (Height r), ProofIsBSTBalance' ('ForkTree l (Node n a) r) us) => ProofIsBSTBalance ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.BalanceProofs Methods proofIsBSTBalance :: IsBSTT ('ForkTree l (Node n a) r) -> IsBSTT (Balance ('ForkTree l (Node n a) r)) Source #
(us ~ UnbalancedState (Height l) (Height r), ProofGtNBalance' ('ForkTree l (Node n1 a) r) n us) => ProofGtNBalance ('ForkTree l (Node n1 a) r) n Source #
Instance details Defined in Data.Tree.AVL.Intern.Balance Methods proofGtNBalance :: AlmostAVL ('ForkTree l (Node n1 a) r) -> Proxy n -> GtN (Balance ('ForkTree l (Node n1 a) r)) n :~: 'True Source #
(us ~ UnbalancedState (Height l) (Height r), ProofLtNBalance' ('ForkTree l (Node n1 a) r) n us) => ProofLtNBalance ('ForkTree l (Node n1 a) r) n Source #
Instance details Defined in Data.Tree.AVL.Intern.Balance Methods proofLtNBalance :: AlmostAVL ('ForkTree l (Node n1 a) r) -> Proxy n -> LtN (Balance ('ForkTree l (Node n1 a) r)) n :~: 'True Source #
(bs ~ BalancedState (Height rl) (Height rr), Rotateable ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced bs) => Balanceable' ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Balance' ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced :: Tree Source # Methods balance' :: ITree ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'RightUnbalanced -> ITree (Balance' ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced) Source #
Balanceable' ('ForkTree l (Node n a) r) 'NotUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Balance' ('ForkTree l (Node n a) r) 'NotUnbalanced :: Tree Source # Methods balance' :: ITree ('ForkTree l (Node n a) r) -> Proxy 'NotUnbalanced -> ITree (Balance' ('ForkTree l (Node n a) r) 'NotUnbalanced) Source #
(bs ~ BalancedState (Height ll) (Height lr), Rotateable ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced bs) => Balanceable' ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Balance' ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced :: Tree Source # Methods balance' :: ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) -> Proxy 'LeftUnbalanced -> ITree (Balance' ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced) Source #
(us ~ UnbalancedState (Height l) (Height r), ProofGtNBalance' ('ForkTree l (Node n1 a) r) n us) => ProofGtNBalance ('ForkTree l (Node n1 a) r) n Source #
Instance details Defined in Data.Tree.AVL.Extern.BalanceProofs Methods proofGtNBalance :: IsBSTT ('ForkTree l (Node n1 a) r) -> Proxy n -> GtN (Balance ('ForkTree l (Node n1 a) r)) n :~: 'True Source #
(us ~ UnbalancedState (Height l) (Height r), ProofLtNBalance' ('ForkTree l (Node n1 a) r) n us) => ProofLtNBalance ('ForkTree l (Node n1 a) r) n Source #
Instance details Defined in Data.Tree.AVL.Extern.BalanceProofs Methods proofLtNBalance :: IsBSTT ('ForkTree l (Node n1 a) r) -> Proxy n -> LtN (Balance ('ForkTree l (Node n1 a) r)) n :~: 'True Source #
Rotateable ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) 'RightUnbalanced 'LeftHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) 'RightUnbalanced 'LeftHeavy :: Tree Source # Methods rotate :: ITree ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) -> Proxy 'RightUnbalanced -> Proxy 'LeftHeavy -> ITree (Rotate ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) 'RightUnbalanced 'LeftHeavy) Source #
Rotateable ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'Balanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'Balanced :: Tree Source # Methods rotate :: ITree ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'RightUnbalanced -> Proxy 'Balanced -> ITree (Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'Balanced) Source #
Rotateable ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'RightHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'RightHeavy :: Tree Source # Methods rotate :: ITree ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) -> Proxy 'RightUnbalanced -> Proxy 'RightHeavy -> ITree (Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'RightHeavy) Source #
Rotateable ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) 'LeftUnbalanced 'RightHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) 'LeftUnbalanced 'RightHeavy :: Tree Source # Methods rotate :: ITree ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) -> Proxy 'LeftUnbalanced -> Proxy 'RightHeavy -> ITree (Rotate ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) 'LeftUnbalanced 'RightHeavy) Source #
Rotateable ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'Balanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'Balanced :: Tree Source # Methods rotate :: ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) -> Proxy 'LeftUnbalanced -> Proxy 'Balanced -> ITree (Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'Balanced) Source #
Rotateable ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'LeftHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance Associated Types type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'LeftHeavy :: Tree Source # Methods rotate :: ITree ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) -> Proxy 'LeftUnbalanced -> Proxy 'LeftHeavy -> ITree (Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'LeftHeavy) Source #
type Insert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Intern.Insert type Insert x a ('ForkTree l (Node n a1) r)
type Insert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert x a ('ForkTree l (Node n a1) r) = Insert' x a ('ForkTree l (Node n a1) r) (CmpNat x n)
type Insert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Insert type Insert x a ('ForkTree l (Node n a1) r)
type Insert x a ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert x a ('ForkTree l (Node n a1) r) = Insert' x a ('ForkTree l (Node n a1) r) (CmpNat x n)
type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT = 'ForkTree l (Node n a1) (Insert' x a ('ForkTree rl (Node rn rna) rr) (CmpNat x rn))
type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT = 'ForkTree l (Node n a1) ('ForkTree 'EmptyTree (Node x a) 'EmptyTree)
type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT = 'ForkTree (Insert' x a ('ForkTree ll (Node ln lna) lr) (CmpNat x ln)) (Node n a1) r
type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT = 'ForkTree ('ForkTree 'EmptyTree (Node x a) 'EmptyTree) (Node n a1) r
type Insert' x a ('ForkTree l (Node n a1) r) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) r) 'EQ = 'ForkTree l (Node n a) r
type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) ('ForkTree rl (Node rn rna) rr)) 'GT = Balance ('ForkTree l (Node n a1) (Insert' x a ('ForkTree rl (Node rn rna) rr) (CmpNat x rn)))
type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) 'EmptyTree) 'GT = Balance ('ForkTree l (Node n a1) ('ForkTree 'EmptyTree (Node x a) 'EmptyTree))
type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert' x a ('ForkTree ('ForkTree ll (Node ln lna) lr) (Node n a1) r) 'LT = Balance ('ForkTree (Insert' x a ('ForkTree ll (Node ln lna) lr) (CmpNat x ln)) (Node n a1) r)
type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert' x a ('ForkTree 'EmptyTree (Node n a1) r) 'LT = Balance ('ForkTree ('ForkTree 'EmptyTree (Node x a) 'EmptyTree) (Node n a1) r)
type Insert' x a ('ForkTree l (Node n a1) r) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Insert type Insert' x a ('ForkTree l (Node n a1) r) 'EQ = 'ForkTree l (Node n a) r
type Delete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Intern.Delete type Delete x ('ForkTree l (Node n a1) r)
type Delete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete x ('ForkTree l (Node n a1) r) = Delete' x ('ForkTree l (Node n a1) r) (CmpNat x n)
type Delete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Delete type Delete x ('ForkTree l (Node n a1) r)
type Delete x ('ForkTree l (Node n a1) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete x ('ForkTree l (Node n a1) r) = Delete' x ('ForkTree l (Node n a1) r) (CmpNat x n)
type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT = 'ForkTree l (Node n a1) (Delete' x ('ForkTree rl (Node rn ra) rr) (CmpNat x rn))
type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT = 'ForkTree l (Node n a1) 'EmptyTree
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT = 'ForkTree (Delete' x ('ForkTree ll (Node ln la) lr) (CmpNat x ln)) (Node n a1) r
type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT = 'ForkTree 'EmptyTree (Node n a1) r
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ = 'ForkTree (MaxKeyDelete ('ForkTree ll (Node ln la) lr)) (Node (MaxKey ('ForkTree ll (Node ln la) lr)) (MaxValue ('ForkTree ll (Node ln la) lr))) ('ForkTree rl (Node rn ra) rr)
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ = 'ForkTree ll (Node ln la) lr
type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ = 'ForkTree rl (Node rn ra) rr
type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ = 'EmptyTree
type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'GT = Balance ('ForkTree l (Node n a1) (Delete' x ('ForkTree rl (Node rn ra) rr) (CmpNat x rn)))
type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree l (Node n a1) 'EmptyTree) 'GT = 'ForkTree l (Node n a1) 'EmptyTree
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) r) 'LT = Balance ('ForkTree (Delete' x ('ForkTree ll (Node ln la) lr) (CmpNat x ln)) (Node n a1) r)
type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) r) 'LT = 'ForkTree 'EmptyTree (Node n a1) r
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ = Balance ('ForkTree (MaxKeyDelete ('ForkTree ll (Node ln la) lr)) (Node (MaxKey ('ForkTree ll (Node ln la) lr)) (MaxValue ('ForkTree ll (Node ln la) lr))) ('ForkTree rl (Node rn ra) rr))
type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a1) 'EmptyTree) 'EQ = 'ForkTree ll (Node ln la) lr
type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) ('ForkTree rl (Node rn ra) rr)) 'EQ = 'ForkTree rl (Node rn ra) rr
type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type Delete' x ('ForkTree 'EmptyTree (Node n a1) 'EmptyTree) 'EQ = 'EmptyTree
type MaxKey ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxKey ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) = MaxKey ('ForkTree rl (Node rn ra) rr)
type MaxKey ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxKey ('ForkTree l (Node n a1) 'EmptyTree) = n
type MaxValue ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxValue ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) = MaxValue ('ForkTree rl (Node rn ra) rr)
type MaxValue ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxValue ('ForkTree l (Node n a1) 'EmptyTree) = a1
type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) = 'ForkTree l (Node n a1) (MaxKeyDelete ('ForkTree rl (Node rn ra) rr))
type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.BST.Extern.Delete type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) = l
type Balance ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Intern.Balance type Balance ('ForkTree l (Node n a) r)
type Balance ('ForkTree l (Node n a) r) Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Balance ('ForkTree l (Node n a) r) = Balance' ('ForkTree l (Node n a) r) (UnbalancedState (Height l) (Height r))
type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type MaxKeyDelete ('ForkTree l (Node n a1) ('ForkTree rl (Node rn ra) rr)) = Balance ('ForkTree l (Node n a1) (MaxKeyDelete ('ForkTree rl (Node rn ra) rr)))
type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) Source #
Instance details Defined in Data.Tree.AVL.Extern.Delete type MaxKeyDelete ('ForkTree l (Node n a1) 'EmptyTree) = l
type Balance' ('ForkTree l (Node n a) r) 'NotUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Balance' ('ForkTree l (Node n a) r) 'NotUnbalanced = 'ForkTree l (Node n a) r
type Balance' ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Balance' ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced = Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced (BalancedState (Height rl) (Height rr))
type Balance' ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Balance' ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced = Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced (BalancedState (Height ll) (Height lr))
type Rotate ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) 'RightUnbalanced 'LeftHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree l (Node n a) ('ForkTree ('ForkTree rll (Node rln rla) rlr) (Node rn ra) rr)) 'RightUnbalanced 'LeftHeavy = 'ForkTree ('ForkTree l (Node n a) rll) (Node rln rla) ('ForkTree rlr (Node rn ra) rr)
type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'Balanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'Balanced = 'ForkTree ('ForkTree l (Node n a) rl) (Node rn ra) rr
type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'RightHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree l (Node n a) ('ForkTree rl (Node rn ra) rr)) 'RightUnbalanced 'RightHeavy = 'ForkTree ('ForkTree l (Node n a) rl) (Node rn ra) rr
type Rotate ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) 'LeftUnbalanced 'RightHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree ('ForkTree ll (Node ln la) ('ForkTree lrl (Node lrn lra) lrr)) (Node n a) r) 'LeftUnbalanced 'RightHeavy = 'ForkTree ('ForkTree ll (Node ln la) lrl) (Node lrn lra) ('ForkTree lrr (Node n a) r)
type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'Balanced Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'Balanced = 'ForkTree ll (Node ln la) ('ForkTree lr (Node n a) r)
type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'LeftHeavy Source #
Instance details Defined in Data.Tree.AVL.Extern.Balance type Rotate ('ForkTree ('ForkTree ll (Node ln la) lr) (Node n a) r) 'LeftUnbalanced 'LeftHeavy = 'ForkTree ll (Node ln la) ('ForkTree lr (Node n a) r)

mkNode :: Proxy k -> a -> Node k a Source #

Node constructor. Besides the value to be stored, it receives the key through a Proxy. It may be used like node = mkNode (Proxy::Proxy 6) 'a'.

getValue :: Node k a -> a Source #

Value getter from a Node.