open import Level renaming (suc to succ ; zero to Zero )
module AgdaInterface where

data Maybe {n : Level } (a : Set n) : Set n where
  Nothing : Maybe a
  Just    : a @$\rightarrow$@ Maybe a

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
    pop2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
    get  : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
    get2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
    clear : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ 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 )
  pop2Stack :  (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
  pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
  getStack :  (Stack a si @$\rightarrow$@ Maybe a  @$\rightarrow$@ t) @$\rightarrow$@ t
  getStack next = get (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
  get2Stack :  (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
  get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
  clearStack : (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
  clearStack next = clear (stackMethods ) (stack ) (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))

open Stack