module bt where

open import Data.Nat
open import Level renaming (zero to Z ; suc to succ)
open import Data.List

open import Data.Nat.Properties as NatProp -- <-cmp
open import Relation.Binary

open import Function as F hiding (const)

data bt {n : Level} (A : Set n) : Set n where
  leaf : bt A
  node : (key-t : ℕ) → (value : A) →
    (ltree : bt A ) → (rtree : bt A ) → bt A

record Env {n : Level} (A : Set n) : Set n where
  field
    varn : ℕ
    varv : A
    vart : bt A
    varl : List (bt A)
open Env

bt-depth1 : {n : Level} {A : Set n} → (env : Env A ) → ℕ
bt-depth1 env  with vart env
... | tree = bt-depth-c tree where
    bt-depth-c : {n : Level} {A : Set n} → (tree : bt A ) → ℕ
    bt-depth-c leaf = zero
    bt-depth-c (node key value lt rt) = suc (Data.Nat._⊔_ (bt-depth-c lt ) ( bt-depth-c rt))

test-env : {n : Level} {A : Set n} →  Env ℕ
test-env = record {varn = 0; varv = 4 ; vart = (node 3 2 leaf (node 1 1 leaf (node 3 5 leaf leaf))); varl = []}

test-depth1 :  ℕ
test-depth1 = bt-depth1 record {varn = 0; varv = 4;  vart = (node 3 0 leaf (node 1 1 leaf (node 3 5 leaf leaf))); varl = []}

find1 : {n m : Level} {A : Set n} {t : Set m} → (env : Env A )
           → (next : (env : Env A ) → t )
           → (exit : (env : Env A ) → t ) → t
find1 env next exit = find1-c (varn env) (vart env) env next exit where
    find1-c : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (tree : bt A) → (env : Env A )
           → (next : (env : Env A ) → t )
           → (exit : (env : Env A ) → t ) → t
    find1-c key leaf env next exit = exit env
    find1-c key n@(node key-t value ltree rtree) env next exit with <-cmp key key-t
    ... | tri< a ¬b ¬c = find1-c key ltree record env {vart = ltree ; varl = (n ∷ (varl env))} next exit
    ... | tri≈ ¬a b ¬c = exit record env {vart = n}
    ... | tri> ¬a ¬b c = find1-c key rtree record env {vart = rtree ; varl = (n ∷ (varl env))} next exit

find-loop-1 : {n m : Level} {A : Set n} {t : Set m} → (env : Env A )
    → (exit : (env : Env A ) → t) → t
find-loop-1 env exit = find1 env exit exit

fin-cg : {n m : Level} {A : Set n} {t : Set m} → t → (env : Env A ) → Env A
fin-cg t = (λ env → env )

test-cg = find-loop-1 record {varn = 5; varv = 4; vart = (node 2 2 (node 1 1 leaf leaf) (node 4 4 leaf (node 5 5 leaf leaf))); varl = []} (λ env → env )

replaceNode1 : {n m : Level} {A : Set n} {t : Set m} → (env : Env A )
    → (next : Env A → t) → t
replaceNode1 env next with vart env
... | leaf = next record env {vart = (node (varn env) (varv env) leaf leaf) }
... | node key-t value ltree rtree = next record env {vart = (node (varn env) (varv env) ltree rtree) }

replace1 : {n m : Level} {A : Set n} {t : Set m} → (env : Env A )
    → (next : Env A → t )
    → (exit : Env A → t) → t
replace1 env next exit = replace1-c (varl env) env next exit where
    replace1-c : {n m : Level} {A : Set n} {t : Set m} → List (bt A) → (env : Env A )
        → (next : Env A → t )
        → (exit : Env A → t) → t
    replace1-c st env next exit with st
    ... | [] = exit env
    ... | leaf ∷ st1 = replace1-c st1 env next exit
    ... | n@(node key-t value ltree rtree) ∷ st1 with <-cmp (varn env) (key-t)
    ... | tri< a ¬b ¬c = replace1-c st1 record env{vart = (node key-t value (vart env) rtree); varl = st1} next exit
    ... | tri≈ ¬a b ¬c = replace1-c st1 record env{vart = (node key-t (varv env) ltree rtree); varl = st1} next exit
    ... | tri> ¬a ¬b c = replace1-c st1 record env{vart = (node key-t value ltree (vart env)); varl = st1} next exit

replace-loop1 : {n m : Level} {A : Set n} {t : Set m} → (env : Env A )
    → (exit : (env : Env A ) → t) → t
replace-loop1 env exit = replace1 env exit exit

insertTree1 : {n m : Level} {A : Set n} {t : Set m} → (tree : bt A) → (key : ℕ) → (value : A) → (next : Env A  → t ) → t
insertTree1 tree key value exit = find-loop-1 record{varn = key; varv = value; vart = tree ; varl = []}
  $ λ env → replaceNode1 env
    $ λ env → replace-loop1 env exit

replaceTree1 : {n m : Level} {A : Set n} {t : Set m} → (tree : bt A) → (key : ℕ) → (value : A) → (next : Env A  → t ) → t
replaceTree1 tree key value exit = find-loop-1 record{varn = key; varv = value; vart = tree ; varl = []}
  $ λ env → replaceNode1 env exit

test-insert = insertTree1 (node 2 2 (node 1 1 leaf leaf) (node 4 4 leaf (node 5 5 leaf leaf))) 0 5 (λ env → env )

test-insert1 = replaceTree1 (node 2 2 (node 1 1 leaf leaf) (node 4 4 leaf (node 5 5 leaf leaf))) 0 5 (λ env → env )