module Chapter3.IDesc.FreeMonad.Examples.FileSystem where

open import Data.Unit
open import Data.Nat hiding (_*_)
open import Data.Fin
open import Data.Vec hiding (_>>=_)
open import Data.Product
open import Data.String

open import Relation.Binary.PropositionalEquality

open import Chapter1.Logic

open import Chapter2.IDesc
open import Chapter2.IDesc.Tagged
open import Chapter2.IDesc.Fixpoint

open import Chapter3.IDesc.FreeMonad
open import Chapter3.IDesc.FreeMonad.IMonad
open import Chapter3.IDesc.FreeMonad.Monad


data State : Set where
  Closed Open : State

infix 50 _⊢_
_⊢_ : {I : Set}(X : Set)(k : I)  Pow I
X  k = λ k'  k'  k × X

-- Or, equivalently:
--data _⊢_ {I : Set}(X : Set)(k : I) : Pow I where
--  witness : (wit : X) → (X ⊢ k) k


ΣFS : tagDesc State
ΣFS = (0 ,  _  [])) ,
       { Closed  1 
         ; Open  2 }) ,
       { Closed  -- open:
                    ( String λ _  
                    ( State λ s 
                       λ _  
                     `var s)  `1)   [] 
         ; Open  -- read:
                  ( State λ s  
                    (s  Open × String) λ _ 
                   `var s)  `1 
                  -- close:
                  ( State λ s 
                    (s  Closed × ) λ _  
                   `var s)  `1  [] })

FS : (State  Set)  State  Set
FS = _*_ ΣFS

return : ∀{X}  X  FS X
return = `v {D = ΣFS}


openFile : (fname : String)  FS  _  ) Closed
openFile fname =  suc zero , fname ,  s  return {X = λ _  }) , tt 

readFile : FS  s  s  Open × String) Open
readFile =  suc zero  ,  s  return {X = String  Open})  , tt 

closeFile : FS  s  s  Closed × ) Open
closeFile =  suc (suc zero) ,  s  return {X =   Closed}) , tt 


example : FS  s  s  Closed × String) Closed
example = openFile "test.txt" >>= λ {
          {Closed} tt  
            -- File do not exists, silently abort
            return (refl , "") ; 
          {Open} tt  
            -- File successfully opened
            readFile >>= λ {
            -- Upon reading, file stays open:
            {Closed} (() , _) ; 
            {Open} (refl , str)  
              closeFile >>= λ {
              -- Upon closing, file is closed:
              {Open} (() , _) ; 
              {Closed} (refl , tt)  
                return (refl , str) }}}
  where open RawIMonad (monad ΣFS) hiding (return)