--- a/GearsRBTree.agda	Mon Nov 23 15:42:10 2020 +0900
+++ b/GearsRBTree.agda	Tue Nov 24 16:36:48 2020 +0900
@@ -101,6 +101,7 @@
     ; ltree = (bt-node (record { key = record { coler = red ; number = x }; ltree = l; rtree = rl }) )
     ; rtree = rr }) ) n stack
 
+
 -- skew
 skew : rbt → ℕ → List rbt → rbt
 skew bt-empty n stack = bt-empty
@@ -117,26 +118,21 @@
 
 
 --treeをmerge
-
 merge-tree node n []  = init_node_coler node
 merge-tree node n (bt-empty ∷ xs) =  bt-empty
 merge-tree target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) with <-cmp n x
 merge-tree target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri≈ ¬a b ¬c
   = skew (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r } ) ) x xs
-  -- merge-tree (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r } ) ) xs
 
 merge-tree target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri> ¬a ¬b c
   = skew (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = target } ) ) x xs
-  -- merge-tree (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = target } ) ) xs
 
 merge-tree target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri< a ¬b ¬c
   = skew (bt-node (record { key = record { coler = y; number = x }; ltree = target; rtree = r } ) ) x xs
-  -- merge-tree (bt-node (record { key = record { coler = y; number = x }; ltree = target; rtree = r } ) ) xs
 
 
 rbt-insert : rbt → ℕ → List rbt → rbt
 rbt-insert bt-empty n stack = merge-tree (bt-node (record { key = record { coler = red ; number = n }; ltree = bt-empty; rtree = bt-empty }) ) n stack
--- ( bt-node (record { key = record { coler = red ; nu mber = n }; ltree = bt-empty; rtree = bt-empty }) ) -- mergeに遷移する
 rbt-insert (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack with <-cmp x n
 rbt-insert (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack | tri≈ ¬a b ¬c
   = (bt-node (record { key = record { coler = y ; number = x }; ltree = l; rtree = r }) )

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/bt_t.agda	Tue Nov 24 16:36:48 2020 +0900
@@ -0,0 +1,162 @@
+module bt_t where
+
+
+open import Data.Nat hiding (compare)
+open import Data.Nat.Properties as NatProp -- <-cmp
+open import Relation.Binary
+open import Data.List
+
+-- → t を適用するために必要だった
+open import Level renaming ( suc to succ ; zero to Zero )
+open import Level
+
+
+data col : Set where
+  black : col
+  red : col
+
+record node (A B : Set) : Set where
+  field
+    coler : A
+    number : B
+
+record tree (A B C : Set) : Set where
+  field
+    key : A
+    ltree : B
+    rtree : C
+
+data bst : Set where
+  bt-empty : bst
+  bt-node  : (node : tree (node col ℕ) bst bst ) → bst
+
+record Env : Set (succ Zero) where
+  field
+    vart : bst
+    varn : ℕ
+    varl : List bst
+open Env
+
+data Cond : Set (succ Zero) where
+  nextcond : Env → Cond → Cond
+  exitcond : Env → Cond
+open Cond
+
+
+whileTest_next : {l : Level} {t : Set l}  → (c10 : bst) → (n : ℕ) → (list : List bst) → (next : Env → t) → (exit : Env → t) → t
+whileTest_next c10 n list next exit = next (record {vart = c10 ; varn = n ; varl = list} )
+
+--whileTest_exit : {l : Level} {t : Set l}  → (c10 : bst) → (n : ℕ) → (list : List bst) → (next : Env → t) → (exit : Env → t) → t
+--whileTest_exit c10 n list next exit = exit (record {vart = c10 ; varn = n ; varl = list} )
+
+merge-tree :  {le : Level} {t : Set le} → Env → (next : Env → t) → (exit : Env → t) → t
+
+whileTest_next1 : {l : Level} {t : Set l}  → (c10 : bst) → (n : ℕ) → (list : List bst) → Cond → Cond
+whileTest c10 next1 n list (nextcond x next) = {!!}
+whileTest c10 next1 n list (exitcond x) = {!!}
+
+
+
+-- test : {l : Level} {t : Set l} → (Code : Env → t) → t
+-- test next = next (record {vart = bt-node (record { key = record { coler = red ; number = 0 }; ltree = bt-empty; rtree = bt-empty }); varn = 3; varl = []} )
+
+merge-tree node@record { vart = vart ; varn = varn ; varl = [] } next exit = exit node
+merge-tree node@record { vart = vart ; varn = varn ; varl = (bt-empty ∷ varl₁) } next exit = exit node
+merge-tree record { vart = vart ; varn = varn ; varl = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = rtree } ∷ varl₁) } next exit with <-cmp varn number
+merge-tree record { vart = vart ; varn = varn ; varl = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = rtree } ∷ varl₁) } next exit | tri≈ ¬a b ¬c
+  = next record { vart = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = rtree }) ; varn = varn ; varl = varl₁ }
+
+merge-tree record { vart = vart ; varn = varn ; varl = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = rtree } ∷ varl₁) } next exit | tri> ¬a ¬b c
+  = next record { vart = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = vart }) ; varn = varn ; varl = varl₁ }
+
+merge-tree record { vart = vart ; varn = varn ; varl = (bt-node record { key = record { coler = coler ; number = number } ; ltree = ltree ; rtree = rtree } ∷ varl₁) } next exit | tri< a ¬b ¬c
+  = next record { vart = (bt-node record { key = record { coler = coler ; number = number } ; ltree = vart ; rtree = rtree }) ; varn = varn ; varl = varl₁ }
+
+{-
+merge-tree {le} {t} node n []  = node
+merge-tree node n (bt-empty ∷ xs) =  bt-empty
+merge-tree target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) with <-cmp n x
+merge-tree {le} {t} target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri≈ ¬a b ¬c
+  = merge-tree {le} {t} (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r } ) ) x xs
+
+merge-tree {le} {t} target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri> ¬a ¬b c
+  = merge-tree {le} {t} (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = target } ) ) x xs
+
+merge-tree {le} {t} target n ( (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) ∷ xs) | tri< a ¬b ¬c
+  = merge-tree {le} {t} (bt-node (record { key = record { coler = y; number = x }; ltree = target; rtree = r } ) ) x xs
+-}
+
+-- insert
+bt-insert : {le : Level} {t : Set le} → Env → (next : Env → t) → (exit : Env → t) → t
+-- mergeへ遷移する
+bt-insert (record { vart = bt-empty ; varn = varn ; varl = varl }) next exit
+  = exit (record { vart = (bt-node (record { key = record { coler = red ; number = varn }; ltree = bt-empty; rtree = bt-empty })) ; varn = varn ; varl = varl })
+
+-- 場合分けを行う
+bt-insert record {vart = (bt-node record { key = record { coler = y; number = x } ; ltree = ltree ; rtree = rtree }) ; varn = n ; varl = varl } next exit with <-cmp x n
+bt-insert node@(record { vart = (bt-node record { key = key ; ltree = ltree ; rtree = rtree }) ; varn = varn ; varl = varl } ) next exit | tri≈ ¬a b ¬c
+  = exit node
+
+bt-insert record {vart = (bt-node record { key = key ; ltree = ltree ; rtree = rtree }) ; varn = varn ; varl = varl } next exit | tri> ¬a ¬b c
+  = next (record {vart = ltree ; varn = varn ; varl = (bt-node record { key = key ; ltree = bt-empty ; rtree = rtree }) ∷ varl })
+
+bt-insert record {vart = (bt-node record { key = key ; ltree = ltree ; rtree = rtree }) ; varn = varn ; varl = varl } next exit | tri< a ¬b ¬c
+  = next (record {vart = rtree ; varn = varn ; varl = (bt-node record { key = key ; ltree = ltree ; rtree = bt-empty }) ∷ varl })
+
+-- normal loop without termination
+{-# TERMINATING #-}
+insert : {l : Level} {t : Set l} → Env → (exit : Env → t) → t
+insert env exit = bt-insert env (λ env → insert env exit ) exit
+
+{-# TERMINATING #-}
+merge : {l : Level} {t : Set l} → Env → (exit : Env → t) → t
+merge env exit = merge-tree env (λ env → merge env exit ) exit
+
+-- equivalent of whileLoopP but it looks like an induction on varn
+
+--whileTestP : {l : Level} {t : Set l} → (c10 : ℕ) → (c11 : ℕ) → (Code : Envc → t) → t
+--whileTestP c10 n next = next (record {varn = c10 ; vari = 0 ; c10 = c10 } )
+
+whileTestP : {l : Level} {t : Set l} → (tree : bst) → (n : ℕ) → (Code : Env → t) → t
+whileTestP tree n next = next (record {vart = tree ; varn = n ; varl = [] } )
+
+whileTestPCall :  (tree : bst) → (n : ℕ)  → Env
+whileTestPCall tree n = whileTestP {_} {_} tree n (λ env → insert env (λ env → merge env (λ env →  env)) )
+
+test1 = whileTestPCall bt-empty 1
+test2 = whileTestPCall (vart test1) 2
+
+--whileTestPCall tree n = whileTestP {_} {_} tree n (λ env → merge env (λ env2 →  env2))
+{-
+bt-insert bt-empty n stack = merge-tree {le} {t} (bt-node (record { key = record { coler = red ; number = n }; ltree = bt-empty; rtree = bt-empty }) ) n stack
+bt-insert (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack with <-cmp x n
+bt-insert (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack | tri≈ ¬a b ¬c
+  = (bt-node (record { key = record { coler = y ; number = x }; ltree = l; rtree = r }) )
+bt-insert {le} {t} (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack | tri> ¬a ¬b c
+  = bt-insert {le} {t} l n ( (bt-node (record { key = record { coler = y ; number = x }; ltree = bt-empty; rtree = r }) ) ∷ stack)
+bt-insert  {le} {t} (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) n stack | tri< a ¬b ¬c
+  = bt-insert {le} {t} r n ( (bt-node (record { key = record { coler = y ; number = x }; ltree = l; rtree = bt-empty }) ) ∷ stack )
+-}
+
+init_node_coler : bst → bst
+init_node_coler bt-empty = bt-empty
+init_node_coler (bt-node (record { key = record { coler = y; number = x }; ltree = l; rtree = r }) ) = (bt-node (record { key = record { coler = black; number = x }; ltree = l; rtree = r }) )
+
+
+--insert : bst → ℕ → bst
+--insert node x = init_node_coler (bt-insert node x)
+
+{-
+-- 以下test部分
+test-rbt1 : {le : Level} {t : Set le} → bst
+test-rbt1 {le} {t} = bt-insert {le} {t} bt-empty 0 []
+
+test-rbt2 : {le : Level} {t : Set le} → bst
+test-rbt2 {le} {t} = bt-insert {le} {t} test-rbt1 1 []
+
+--test-rbt3 = bt-insert test-rbt2 2 []
+--test-rbt4 = bt-insert test-rbt3 3 []
+--test-rbt5 = bt-insert test-rbt4 4 []
+--test-rbt6 = bt-insert test-rbt5 5 []
+-}
+