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(.module:
  [lux #*
   ["." meta]
   [abstract
    ["." monad (#+ Monad do)
     [indexed (#+ IxMonad)]]]
   [control
    ["." exception (#+ exception:)]
    ["." io (#+ IO)]
    [concurrency
     ["." promise (#+ Promise)]]
    ["<>" parser
     ["<.>" code (#+ Parser)]]]
   [data
    ["." identity (#+ Identity)]
    ["." maybe]
    ["." product]
    [text
     ["%" format (#+ format)]]
    [collection
     ["." set]
     ["." row (#+ Row)]
     ["." list ("#\." functor fold)]]]
   ["." macro
    [syntax (#+ syntax:)]]
   [math
    [number
     ["n" nat]]]
   [type
    abstract]])

(type: #export (Procedure monad input output value)
  (-> input (monad [output value])))

(type: #export (Linear monad value)
  (All [keys]
    (Procedure monad keys keys value)))

(type: #export (Affine monad permissions value)
  (All [keys]
    (Procedure monad keys [permissions keys] value)))

(type: #export (Relevant monad permissions value)
  (All [keys]
    (Procedure monad [permissions keys] keys value)))

(structure: (indexed Monad<m>)
  (All [m] (-> (Monad m) (IxMonad (Procedure m))))
  
  (def: (wrap value)
    (function (_ keys)
      (\ Monad<m> wrap [keys value])))

  (def: (bind f input)
    (function (_ keysI)
      (do Monad<m>
        [[keysT value] (input keysI)]
        ((f value) keysT)))))

(template [<name> <m> <monad> <execute> <lift>]
  [(def: #export <name>
     (IxMonad (Procedure <m>))
     (..indexed <monad>))

   (def: #export (<execute> procedure)
     (All [v] (-> (Linear <m> v) (<m> v)))
     (do <monad>
       [[_ output] (procedure [])]
       (wrap output)))

   (def: #export (<lift> procedure)
     (All [v] (-> (<m> v) (Linear <m> v)))
     (function (_ keys)
       (do <monad>
         [output procedure]
         (wrap [keys output]))))]

  [pure  Identity identity.monad run_pure  lift_pure]
  [sync  IO       io.monad       run_sync  lift_sync]
  [async Promise  promise.monad  run_async lift_async]
  )

(abstract: #export Ordered Any)

(abstract: #export Commutative Any)

(abstract: #export (Key mode key)
  Any

  (template [<name> <mode>]
    [(def: <name>
       (Ex [k] (-> Any (Key <mode> k)))
       (|>> :abstraction))]

    [ordered_key     Ordered]
    [commutative_key Commutative]
    ))

(abstract: #export (Res key value)
  value

  {#.doc "A value locked by a key."}

  (template [<name> <m> <monad> <mode> <key>]
    [(def: #export (<name> value)
       (All [v] (Ex [k] (-> v (Affine <m> (Key <mode> k) (Res k v)))))
       (function (_ keys)
         (\ <monad> wrap [[(<key> []) keys] (:abstraction value)])))]

    [ordered_pure      Identity identity.monad Ordered     ordered_key]
    [ordered_sync      IO       io.monad       Ordered     ordered_key]
    [ordered_async     Promise  promise.monad  Ordered     ordered_key]
    [commutative_sync  IO       io.monad       Commutative commutative_key]
    [commutative_pure  Identity identity.monad Commutative commutative_key]
    [commutative_async Promise  promise.monad  Commutative commutative_key]
    )

  (template [<name> <m> <monad>]
    [(def: #export (<name> resource)
       (All [v k m]
         (-> (Res k v) (Relevant <m> (Key m k) v)))
       (function (_ [key keys])
         (\ <monad> wrap [keys (:representation resource)])))]

    [read_pure  Identity identity.monad]
    [read_sync  IO       io.monad]
    [read_async Promise  promise.monad]
    ))

(exception: #export (index_cannot_be_repeated {index Nat})
  (exception.report
   ["Index" (%.nat index)]))

(exception: #export amount_cannot_be_zero)

(def: indices
  (Parser (List Nat))
  (<code>.tuple (loop [seen (set.new n.hash)]
                  (do {! <>.monad}
                    [done? <code>.end?]
                    (if done?
                      (wrap (list))
                      (do !
                        [head <code>.nat
                         _ (<>.assert (exception.construct ..index_cannot_be_repeated head)
                                      (not (set.member? seen head)))
                         tail (recur (set.add head seen))]
                        (wrap (list& head tail))))))))

(def: (no_op Monad<m>)
  (All [m] (-> (Monad m) (Linear m Any)))
  (function (_ context)
    (\ Monad<m> wrap [context []])))

(template [<name> <m> <monad>]
  [(syntax: #export (<name> {swaps ..indices})
     (macro.with_gensyms [g!_ g!context]
       (case swaps
         #.Nil
         (wrap (list (` ((~! no_op) <monad>))))

         (#.Cons head tail)
         (do {! meta.monad}
           [#let [max_idx (list\fold n.max head tail)]
            g!inputs (<| (monad.seq !) (list.repeat (inc max_idx)) (macro.gensym "input"))
            #let [g!outputs (|> (monad.fold maybe.monad
                                            (function (_ from to)
                                              (do maybe.monad
                                                [input (list.nth from g!inputs)]
                                                (wrap (row.add input to))))
                                            (: (Row Code) row.empty)
                                            swaps)
                                maybe.assume
                                row.to_list)
                  g!inputsT+ (list\map (|>> (~) (..Key ..Commutative) (`)) g!inputs)
                  g!outputsT+ (list\map (|>> (~) (..Key ..Commutative) (`)) g!outputs)]]
           (wrap (list (` (: (All [(~+ g!inputs) (~ g!context)]
                               (Procedure (~! <m>)
                                          [(~+ g!inputsT+) (~ g!context)]
                                          [(~+ g!outputsT+) (~ g!context)]
                                          .Any))
                             (function ((~ g!_) [(~+ g!inputs) (~ g!context)])
                               (\ (~! <monad>) (~' wrap) [[(~+ g!outputs) (~ g!context)] []]))))))))))]

  [exchange_pure  Identity identity.monad]
  [exchange_sync  IO       io.monad]
  [exchange_async Promise  promise.monad]
  )

(def: amount
  (Parser Nat)
  (do <>.monad
    [raw <code>.nat
     _ (<>.assert (exception.construct ..amount_cannot_be_zero [])
                  (n.> 0 raw))]
    (wrap raw)))

(template [<name> <m> <monad> <from> <to>]
  [(syntax: #export (<name> {amount ..amount})
     (macro.with_gensyms [g!_ g!context]
       (do {! meta.monad}
         [g!keys (<| (monad.seq !) (list.repeat amount) (macro.gensym "keys"))]
         (wrap (list (` (: (All [(~+ g!keys) (~ g!context)]
                             (Procedure (~! <m>)
                                        [<from> (~ g!context)]
                                        [<to> (~ g!context)]
                                        .Any))
                           (function ((~ g!_) [<from> (~ g!context)])
                             (\ (~! <monad>) (~' wrap) [[<to> (~ g!context)] []])))))))))]

  [group_pure     Identity identity.monad (~+ g!keys)   [(~+ g!keys)]]
  [group_sync     IO       io.monad       (~+ g!keys)   [(~+ g!keys)]]
  [group_async    Promise  promise.monad  (~+ g!keys)   [(~+ g!keys)]]
  [un_group_pure  Identity identity.monad [(~+ g!keys)] (~+ g!keys)]
  [un_group_sync  IO       io.monad       [(~+ g!keys)] (~+ g!keys)]
  [un_group_async Promise  promise.monad  [(~+ g!keys)] (~+ g!keys)]
  )