record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
  field
    putImpl : treeImpl @$\rightarrow$@ a @$\rightarrow$@ (treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
    getImpl  : treeImpl @$\rightarrow$@ (treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
open TreeMethods

record Tree  {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
  field
    tree : treeImpl
    treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
  putTree : a @$\rightarrow$@ (Tree treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
  putTree d next = putImpl (treeMethods ) tree d (\t1 @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ))
  getTree : (Tree treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
  getTree next = getImpl (treeMethods ) tree (\t1 d @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ) d )
open Tree

record RedBlackTree {n m : Level } {t : Set m} (a k : Set n) : Set (m Level.@$\sqcup$@ n) where
  field
    root : Maybe (Node a k)
    nodeStack : SingleLinkedStack  (Node a k)
    compare : k @$\rightarrow$@ k @$\rightarrow$@ CompareResult {n}
open RedBlackTree