(;module:
  lux
  (lux (control monad
                pipe)
       [io #- run]
       [function]
       (concurrency ["A" atom])
       (data [text "T/" Eq<Text>]
             text/format
             [ident]
             (coll [list "L/" Fold<List> Monoid<List> Monad<List>]
                   ["D" dict]
                   ["S" set])
             [number]
             [product])
       [macro #+ Monad<Lux>]
       (macro [code])
       [type]
       (type ["TC" check]))
  (luxc ["&" base]
        (lang ["la" analysis])
        ["&;" module]
        ["&;" env]
        (analyser ["&;" common]
                  ["&;" inference])))

## [Analysers]
(def: (analyse-typed-product analyse members)
  (-> &;Analyser (List Code) (Lux la;Analysis))
  (do Monad<Lux>
    [expected macro;expected-type]
    (loop [expected expected
           members members]
      (case [expected members]
        [(#;Product leftT rightT) (#;Cons leftC rightC)]
        (do @
          [leftA (&;with-expected-type leftT
                   (analyse leftC))
           rightA (recur rightT rightC)]
          (wrap (#la;Product leftA rightA)))

        [tailT (#;Cons tailC #;Nil)]
        (&;with-expected-type tailT
          (analyse tailC))

        [tailT tailC]
        (do @
          [g!tail (macro;gensym "tail")]
          (&;with-expected-type tailT
            (analyse (` ((~' _lux_case) [(~@ tailC)]
                         (~ g!tail)
                         (~ g!tail))))))
        ))))

(def: #export (normalize-record pairs)
  (-> (List [Code Code]) (Lux (List [Ident Code])))
  (mapM Monad<Lux>
        (function [[key val]]
          (case key
            [_ (#;Tag key)]
            (do Monad<Lux>
              [key (macro;normalize key)]
              (wrap [key val]))

            _
            (&;fail (format "Cannot use non-tag tokens in key positions in records: " (%code key)))))
        pairs))

(def: #export (order-record pairs)
  (-> (List [Ident Code]) (Lux [(List Code) Type]))
  (case pairs
    (#;Cons [head-k head-v] _)
    (do Monad<Lux>
      [head-k (macro;normalize head-k)
       [_ tag-set recordT] (macro;resolve-tag head-k)
       #let [size-record (list;size pairs)
             size-ts (list;size tag-set)]
       _ (if (n.= size-ts size-record)
           (wrap [])
           (&;fail (format "Record size does not match tag-set size." "\n"
                           "Expected: " (|> size-ts nat-to-int %i) "\n"
                           "  Actual: " (|> size-record nat-to-int %i) "\n"
                           "For type: " (%type recordT))))
       #let [tuple-range (list;n.range +0 (n.dec size-ts))
             tag->idx (D;from-list ident;Hash<Ident> (list;zip2 tag-set tuple-range))]
       idx->val (foldM @
                       (function [[key val] idx->val]
                         (do @
                           [key (macro;normalize key)]
                           (case (D;get key tag->idx)
                             #;None
                             (&;fail (format "Tag " (%code (code;tag key))
                                             " does not belong to tag-set for type " (%type recordT)))

                             (#;Some idx)
                             (if (D;contains? idx idx->val)
                               (&;fail (format "Cannot repeat tag inside record: " (%code (code;tag key))))
                               (wrap (D;put idx val idx->val))))))
                       (: (D;Dict Nat Code)
                          (D;new number;Hash<Nat>))
                       pairs)
       #let [ordered-tuple (L/map (function [idx]
                                    (assume (D;get idx idx->val)))
                                  tuple-range)]]
      (wrap [ordered-tuple recordT]))

    _
    (:: Monad<Lux> wrap [(list) Unit])))

(def: (tuple members)
  (-> (List la;Analysis) la;Analysis)
  (case members
    #;Nil
    #la;Unit

    (#;Cons singleton #;Nil)
    singleton

    (#;Cons left right)
    (#la;Product left (tuple right))))

(def: #export (analyse-product analyse membersC)
  (-> &;Analyser (List Code) (Lux la;Analysis))
  (do Monad<Lux>
    [expected macro;expected-type]
    (&;with-stacked-errors
      (function [_] (format "Invalid type for tuple: " (%type expected)))
      (case expected
        (#;Product _)
        (analyse-typed-product analyse membersC)

        (#;Named name unnamedT)
        (&;with-expected-type unnamedT
          (analyse-product analyse membersC))

        (#;Var id)
        (do @
          [bound? (&;within-type-env
                   (TC;bound? id))]
          (if bound?
            (do @
              [expected' (&;within-type-env
                          (TC;read-var id))]
              (&;with-expected-type expected'
                (analyse-product analyse membersC)))
            (do @
              [membersTA (mapM @ (|>. analyse &common;with-unknown-type)
                               membersC)
               _ (&;within-type-env
                  (TC;check expected
                            (type;tuple (L/map product;left membersTA))))]
              (wrap (tuple (L/map product;right membersTA))))))

        (#;UnivQ _)
        (do @
          [[var-id var] (&;within-type-env
                         TC;existential)]
          (&;with-expected-type (assume (type;apply-type expected var))
            (analyse-product analyse membersC)))

        (#;ExQ _)
        (&common;with-var
          (function [[var-id var]]
            (&;with-expected-type (assume (type;apply-type expected var))
              (analyse-product analyse membersC))))
        
        _
        (&;fail "")
        ))))

(def: (record-function-type type)
  (-> Type (Lux Type))
  (case type
    (#;Named name unnamedT)
    (do Monad<Lux>
      [unnamedT+ (record-function-type unnamedT)]
      (wrap (#;Named name unnamedT+)))

    (^template [<tag>]
      (<tag> env bodyT)
      (do Monad<Lux>
        [bodyT+ (record-function-type bodyT)]
        (wrap (<tag> env bodyT+))))
    ([#;UnivQ]
     [#;ExQ])

    (#;Product _)
    (:: Monad<Lux> wrap (type;function (type;flatten-tuple type) type))

    _
    (&;fail (format "Not a record type: " (%type type)))))

(def: (out-of-bounds-error type size tag)
  (All [a] (-> Type Nat Nat (Lux a)))
  (&;fail (format "Trying to create variant with tag beyond type's limitations." "\n"
                  " Tag: " (%i (nat-to-int tag)) "\n"
                  "Size: " (%i (nat-to-int size)) "\n"
                  "Type: " (%type type))))

(def: (variant-function-type tag expected-size type)
  (-> Nat Nat Type (Lux Type))
  (case type
    (#;Named name unnamedT)
    (do Monad<Lux>
      [unnamedT+ (variant-function-type tag expected-size unnamedT)]
      (wrap (#;Named name unnamedT+)))

    (^template [<tag>]
      (<tag> env bodyT)
      (do Monad<Lux>
        [bodyT+ (variant-function-type tag expected-size bodyT)]
        (wrap (<tag> env bodyT+))))
    ([#;UnivQ]
     [#;ExQ])

    (#;Sum _)
    (let [cases (type;flatten-variant type)
          actual-size (list;size cases)
          boundary (n.dec expected-size)]
      (cond (or (n.= expected-size actual-size)
                (and (n.> expected-size actual-size)
                     (n.< boundary tag)))
            (case (list;nth tag cases)
              (#;Some caseT)
              (:: Monad<Lux> wrap (type;function (list caseT) type))

              #;None
              (out-of-bounds-error type expected-size tag))
            
            (n.< expected-size actual-size)
            (&;fail (format "Variant type is smaller than expected." "\n"
                            "Expected: " (%i (nat-to-int expected-size)) "\n"
                            "  Actual: " (%i (nat-to-int actual-size))))

            (n.= boundary tag)
            (let [caseT (type;variant (list;drop boundary cases))]
              (:: Monad<Lux> wrap (type;function (list caseT) type)))
            
            ## else
            (out-of-bounds-error type expected-size tag)))

    _
    (&;fail (format "Not a variant type: " (%type type)))))

(def: #export (analyse-record analyse members)
  (-> &;Analyser (List [Code Code]) (Lux la;Analysis))
  (do Monad<Lux>
    [members (normalize-record members)
     [members recordT] (order-record members)
     expectedT macro;expected-type
     functionT (record-function-type recordT)
     [inferredT membersA] (&inference;apply-function analyse functionT members)
     _ (&;within-type-env
        (TC;check expectedT inferredT))]
    (wrap (tuple membersA))))

(do-template [<name> <side>]
  [(def: (<name> inner)
     (-> la;Analysis la;Analysis)
     (#la;Sum (<side> inner)))]

  [sum-left  #;Left]
  [sum-right #;Right])

(def: (variant tag size temp value)
  (-> Nat Nat Nat la;Analysis la;Analysis)
  (if (n.= (n.dec size) tag)
    (if (n.= +1 tag)
      (sum-right value)
      (L/fold (function;const sum-left)
              (sum-right value)
              (list;n.range +0 (n.- +2 tag))))
    (L/fold (function;const sum-left)
            (case value
              (#la;Sum _)
              (#la;Case value (list [(#la;BindP temp)
                                     (#la;Relative (#;Local temp))]))

              _
              value)
            (list;n.range +0 tag))))

(def: #export (analyse-tagged-sum analyse tag value)
  (-> &;Analyser Ident Code (Lux la;Analysis))
  (do Monad<Lux>
    [tag (macro;normalize tag)
     [idx group variantT] (macro;resolve-tag tag)
     #let [case-size (list;size group)]
     functionT (variant-function-type idx case-size variantT)
     [inferredT valueA+] (&inference;apply-function analyse functionT (list value))
     expectedT macro;expected-type
     _ (&;within-type-env
        (TC;check expectedT inferredT))
     temp &env;next-local]
    (wrap (variant idx case-size temp (|> valueA+ list;head assume)))))

(def: #export (analyse-sum analyse tag valueC)
  (-> &;Analyser Nat Code (Lux la;Analysis))
  (do Monad<Lux>
    [expected macro;expected-type]
    (&;with-stacked-errors
      (function [_] (format "Invalid type for variant: " (%type expected)))
      (case expected
        (#;Sum _)
        (let [flat (type;flatten-variant expected)
              type-size (list;size flat)]
          (case (list;nth tag flat)
            (#;Some variant-type)
            (do @
              [valueA (&;with-expected-type variant-type
                        (analyse valueC))
               temp &env;next-local]
              (wrap (variant tag type-size temp valueA)))

            #;None
            (out-of-bounds-error expected type-size tag)))

        (#;Named name unnamedT)
        (&;with-expected-type unnamedT
          (analyse-sum analyse tag valueC))

        (#;Var id)
        (do @
          [bound? (&;within-type-env
                   (TC;bound? id))]
          (if bound?
            (do @
              [expected' (&;within-type-env
                          (TC;read-var id))]
              (&;with-expected-type expected'
                (analyse-sum analyse tag valueC)))
            (&;fail (format "Invalid type for variant: " (%type expected)))))

        (#;UnivQ _)
        (do @
          [[var-id var] (&;within-type-env
                         TC;existential)]
          (&;with-expected-type (assume (type;apply-type expected var))
            (analyse-sum analyse tag valueC)))

        (#;ExQ _)
        (&common;with-var
          (function [[var-id var]]
            (&;with-expected-type (assume (type;apply-type expected var))
              (analyse-sum analyse tag valueC))))
        
        _
        (if (n.= +0 tag)
          (analyse valueC)
          (&;fail ""))))))