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(.module:
  [lux (#- loop)
   [control
    [monad (#+ do)]
    ["p" parser]]
   [data
    [maybe ("maybe/" Monad<Maybe>)]
    [collection [list ("list/" Functor<List>)]]]
   [macro
    [code]
    [syntax]]]
  [// (#+ Path Abstraction Synthesis)
   [///
    [reference (#+ Register Variable)]
    [compiler
     [analysis (#+ Environment)]]]])

(type: #export (Transform a)
  (-> a (Maybe a)))

(def: (some? maybe)
  (All [a] (-> (Maybe a) Bool))
  (case maybe
    (#.Some _) true
    #.None     false))

(template: #export (self)
  (#//.Reference (reference.local +0)))

(template: (recursive-apply args)
  (#//.Apply (self) args))

(def: proper Bool true)
(def: improper Bool false)

(def: (proper? exprS)
  (-> Synthesis Bool)
  (case exprS
    (^ (self))
    improper

    (#//.Structure structure)
    (case structure
      (#//.Variant variantS)
      (proper? (get@ #analysis.value variantS))
      
      (#//.Tuple membersS+)
      (list.every? proper? membersS+))

    (#//.Control controlS)
    (case controlS
      (#//.Branch branchS)
      (case branchS
        (#//.Case inputS pathS)
        (and (proper? inputS)
             (.loop [pathS pathS]
               (case pathS
                 (^or (#//.Alt leftS rightS) (#//.Seq leftS rightS))
                 (and (recur leftS) (recur rightS))

                 (#//.Then bodyS)
                 (proper? bodyS)
                 
                 _
                 proper)))

        (#//.Let inputS register bodyS)
        (and (proper? inputS)
             (proper? bodyS))

        (#//.If inputS thenS elseS)
        (and (proper? inputS)
             (proper? thenS)
             (proper? elseS)))

      (#//.Loop loopS)
      (case loopS
        (#//.Scope scopeS)
        (and (list.every? proper? (get@ #//.inits scopeS))
             (proper? (get@ #//.iteration scopeS)))

        (#//.Recur argsS)
        (list.every? proper? argsS))

      (#//.Function functionS)
      (case functionS
        (#//.Abstraction environment arity bodyS)
        (list.every? reference.self? environment)

        (#//.Apply funcS argsS)
        (and (proper? funcS)
             (list.every? proper? argsS))))

    (#//.Extension [name argsS])
    (list.every? proper? argsS)

    _
    proper))

(def: (path-recursion synthesis-recursion)
  (-> (Transform Synthesis) (Transform Path))
  (function (recur pathS)
    (case pathS
      (#//.Alt leftS rightS)
      (let [leftS' (recur leftS)
            rightS' (recur rightS)]
        (if (or (some? leftS')
                (some? rightS'))
          (#.Some (#//.Alt (maybe.default leftS leftS')
                           (maybe.default rightS rightS')))
          #.None))
      
      (#//.Seq leftS rightS)
      (maybe/map (|>> (#//.Seq leftS)) (recur rightS))

      (#//.Then bodyS)
      (maybe/map (|>> #//.Then) (synthesis-recursion bodyS))
      
      _
      #.None)))

(def: #export (recursion arity)
  (-> Nat (Transform Synthesis))
  (function (recur exprS)
    (case exprS
      (#//.Control controlS)
      (case controlS
        (#//.Branch branchS)
        (case branchS
          (#//.Case inputS pathS)
          (|> pathS
              (path-recursion recur)
              (maybe/map (|>> (#//.Case inputS) #//.Branch #//.Control)))

          (#//.Let inputS register bodyS)
          (maybe/map (|>> (#//.Let inputS register) #//.Branch #//.Control)
                     (recur bodyS))

          (#//.If inputS thenS elseS)
          (let [thenS' (recur thenS)
                elseS' (recur elseS)]
            (if (or (some? thenS')
                    (some? elseS'))
              (#.Some (|> (#//.If inputS
                                  (maybe.default thenS thenS')
                                  (maybe.default elseS elseS'))
                          #//.Branch #//.Control))
              #.None)))

        (^ (#//.Function (recursive-apply argsS)))
        (if (n/= arity (list.size argsS))
          (#.Some (|> argsS #//.Recur #//.Loop #//.Control))
          #.None)

        _
        #.None)

      _
      #.None)))

(def: (resolve environment)
  (-> Environment (Transform Variable))
  (function (_ variable)
    (case variable
      (#reference.Foreign register)
      (list.nth register environment)

      _
      (#.Some variable))))

(def: (adjust-path adjust-synthesis offset)
  (-> (Transform Synthesis) Register (Transform Path))
  (function (recur pathS)
    (case pathS
      (#//.Bind register)
      (#.Some (#//.Bind (n/+ offset register)))

      (^template [<tag>]
        (<tag> leftS rightS)
        (do maybe.Monad<Maybe>
          [leftS' (recur leftS)
           rightS' (recur rightS)]
          (wrap (<tag> leftS' rightS'))))
      ([#//.Alt] [#//.Seq])
      
      (#//.Then bodyS)
      (|> bodyS adjust-synthesis (maybe/map (|>> #//.Then)))

      _
      (#.Some pathS))))

(def: (adjust scope-environment offset)
  (-> Environment Register (Transform Synthesis))
  (function (recur exprS)
    (case exprS
      (#//.Structure structureS)
      (case structureS
        (#//.Variant variantS)
        (do maybe.Monad<Maybe>
          [valueS' (|> variantS (get@ #analysis.value) recur)]
          (wrap (|> variantS
                    (set@ #analysis.value valueS')
                    #//.Variant
                    #//.Structure)))
        
        (#//.Tuple membersS+)
        (|> membersS+
            (monad.map maybe.Monad<Maybe> recur)
            (maybe/map (|>> #//.Tuple #//.Structure))))

      (#//.Reference reference)
      (case reference
        (^ (reference.constant constant))
        (#.Some exprS)

        (^ (reference.local register))
        (#.Some (#//.Reference (reference.local (n/+ offset register))))

        (^ (reference.foreign register))
        (|> scope-environment
            (list.nth register)
            (maybe/map (|>> #reference.Variable #//.Reference))))

      (^ (//.branch/case [inputS pathS]))
      (do maybe.Monad<Maybe>
        [inputS' (recur inputS)
         pathS' (adjust-path recur offset pathS)]
        (wrap (|> pathS' [inputS'] //.branch/case)))

      (^ (//.branch/let [inputS register bodyS]))
      (do maybe.Monad<Maybe>
        [inputS' (recur inputS)
         bodyS' (recur bodyS)]
        (wrap (//.branch/let [inputS' register bodyS'])))

      (^ (//.branch/if [inputS thenS elseS]))
      (do maybe.Monad<Maybe>
        [inputS' (recur inputS)
         thenS' (recur thenS)
         elseS' (recur elseS)]
        (wrap (//.branch/if [inputS' thenS' elseS'])))

      (^ (//.loop/scope scopeS))
      (do maybe.Monad<Maybe>
        [inits' (|> scopeS
                    (get@ #//.inits)
                    (monad.map maybe.Monad<Maybe> recur))
         iteration' (recur (get@ #//.iteration scopeS))]
        (wrap (//.loop/scope {#//.start (|> scopeS (get@ #//.start) (n/+ offset))
                              #//.inits inits'
                              #//.iteration iteration'})))

      (^ (//.loop/recur argsS))
      (|> argsS
          (monad.map maybe.Monad<Maybe> recur)
          (maybe/map (|>> //.loop/recur)))
      

      (^ (//.function/abstraction [environment arity bodyS]))
      (do maybe.Monad<Maybe>
        [environment' (monad.map maybe.Monad<Maybe>
                                 (resolve scope-environment)
                                 environment)]
        (wrap (//.function/abstraction [environment' arity bodyS])))
      
      (^ (//.function/apply [function arguments]))
      (do maybe.Monad<Maybe>
        [function' (recur function)
         arguments' (monad.map maybe.Monad<Maybe> recur arguments)]
        (wrap (//.function/apply [function' arguments'])))

      (#//.Extension [name argsS])
      (|> argsS
          (monad.map maybe.Monad<Maybe> recur)
          (maybe/map (|>> [name] #//.Extension)))

      _
      (#.Some exprS))))

(def: #export (loop environment num-locals inits functionS)
  (-> Environment Nat (List Synthesis) Abstraction (Maybe Synthesis))
  (let [bodyS (get@ #//.body functionS)]
    (if (and (n/= (list.size inits)
                  (get@ #//.arity functionS))
             (proper? bodyS))
      (|> bodyS
          (adjust environment num-locals)
          (maybe/map (|>> [(inc num-locals) inits] //.loop/scope)))
      #.None)))