record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.!$\sqcup$! n) where
  field
    push : stackImpl !$\rightarrow$! a !$\rightarrow$! (stackImpl !$\rightarrow$! t) !$\rightarrow$! t
    pop  : stackImpl !$\rightarrow$! (stackImpl !$\rightarrow$! Maybe a !$\rightarrow$! t) !$\rightarrow$! t
open StackMethods

record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.!$\sqcup$! n) where
  field
    stack : si
    stackMethods : StackMethods {n} {m} a {t} si
  pushStack :  a !$\rightarrow$! (Stack a si !$\rightarrow$! t) !$\rightarrow$! t
  pushStack d next = push (stackMethods ) (stack ) d (\s1 !$\rightarrow$! next (record {stack = s1 ; stackMethods = stackMethods } ))
  popStack : (Stack a si !$\rightarrow$! Maybe a  !$\rightarrow$! t) !$\rightarrow$! t
  popStack next = pop (stackMethods ) (stack ) (\s1 d1 !$\rightarrow$! next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
open Stack