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

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 )