(;module:
  lux
  (lux (control monad
                [eq]
                ["p" parser])
       (data [text "Text/" Eq<Text>]
             text/format
             [number]
             (coll [list "List/" Monad<List> Fold<List>]
                   [dict])
             [bool]
             [product])
       [macro #+ Monad<Lux>]
       (macro [code]
              ["s" syntax #+ syntax: Syntax])
       [type]
       (type ["tc" check #+ Check Monad<Check>])
       ))

(def: (find-type-var id env)
  (-> Nat Type-Context (Lux Type))
  (case (list;find (|>. product;left (n.= id))
                   (get@ #;var-bindings env))
    (#;Some [_ (#;Some type)])
    (case type
      (#;Var id')
      (find-type-var id' env)

      _
      (:: Monad<Lux> wrap type))

    (#;Some [_ #;None])
    (macro;fail (format "Unbound type-var " (%n id)))

    #;None
    (macro;fail (format "Unknown type-var " (%n id)))
    ))

(def: (resolve-type var-name)
  (-> Ident (Lux Type))
  (do Monad<Lux>
    [raw-type (macro;find-type var-name)
     compiler macro;get-compiler]
    (case raw-type
      (#;Var id)
      (find-type-var id (get@ #;type-context compiler))

      _
      (wrap raw-type))))

(def: (find-member-type idx sig-type)
  (-> Nat Type (Check Type))
  (case sig-type
    (#;Named _ sig-type')
    (find-member-type idx sig-type')

    (#;Apply arg func)
    (case (type;apply (list arg) func)
      #;None
      (tc;fail (format "Cannot apply type " (%type func) " to type " (%type arg)))

      (#;Some sig-type')
      (find-member-type idx sig-type'))

    (#;Product left right)
    (if (n.= +0 idx)
      (:: Monad<Check> wrap left)
      (find-member-type (n.dec idx) right))

    _
    (if (n.= +0 idx)
      (:: Monad<Check> wrap sig-type)
      (tc;fail (format "Cannot find member type " (%n idx) " for " (%type sig-type))))))

(def: (find-member-name member)
  (-> Ident (Lux Ident))
  (case member
    ["" simple-name]
    (macro;either (do Monad<Lux>
                    [member (macro;normalize member)
                     _ (macro;resolve-tag member)]
                    (wrap member))
                  (do Monad<Lux>
                    [this-module-name macro;current-module-name
                     imp-mods (macro;imported-modules this-module-name)
                     tag-lists (mapM @ macro;tag-lists imp-mods)
                     #let [tag-lists (|> tag-lists List/join (List/map product;left) List/join)
                           candidates (list;filter (. (Text/= simple-name) product;right)
                                                   tag-lists)]]
                    (case candidates
                      #;Nil
                      (macro;fail (format "Unknown tag: " (%ident member)))
                      
                      (#;Cons winner #;Nil)
                      (wrap winner)
                      
                      _
                      (macro;fail (format "Too many candidate tags: " (%list %ident candidates))))))

    _
    (:: Monad<Lux> wrap member)))

(def: (resolve-member member)
  (-> Ident (Lux [Nat Type]))
  (do Monad<Lux>
    [member (find-member-name member)
     [idx tag-list sig-type] (macro;resolve-tag member)]
    (wrap [idx sig-type])))

(def: (prepare-defs this-module-name defs)
  (-> Text (List [Text Def]) (List [Ident Type]))
  (|> defs
      (list;filter (function [[name [def-type def-anns def-value]]]
                     (macro;struct? def-anns)))
      (List/map (function [[name [def-type def-anns def-value]]]
                  [[this-module-name name] def-type]))))

(def: local-env
  (Lux (List [Ident Type]))
  (do Monad<Lux>
    [local-batches macro;locals
     #let [total-locals (List/fold (function [[name type] table]
                                     (dict;put~ name type table))
                                   (: (dict;Dict Text Type)
                                      (dict;new text;Hash<Text>))
                                   (List/join local-batches))]]
    (wrap (|> total-locals
              dict;entries
              (List/map (function [[name type]] [["" name] type]))))))

(def: local-structs
  (Lux (List [Ident Type]))
  (do Monad<Lux>
    [this-module-name macro;current-module-name
     defs (macro;defs this-module-name)]
    (wrap (prepare-defs this-module-name defs))))

(def: import-structs
  (Lux (List [Ident Type]))
  (do Monad<Lux>
    [this-module-name macro;current-module-name
     imp-mods (macro;imported-modules this-module-name)
     export-batches (mapM @ (function [imp-mod]
                              (do @
                                [exports (macro;exports imp-mod)]
                                (wrap (prepare-defs imp-mod exports))))
                          imp-mods)]
    (wrap (List/join export-batches))))

(def: (apply-function-type func arg)
  (-> Type Type (Check Type))
  (case func
    (#;Named _ func')
    (apply-function-type func' arg)

    (#;UnivQ _)
    (do Monad<Check>
      [[id var] tc;create-var]
      (apply-function-type (default (undefined)
                             (type;apply (list var) func))
                           arg))

    (#;Function input output)
    (do Monad<Check>
      [_ (tc;check input arg)]
      (wrap output))

    _
    (tc;fail (format "Invalid function type: " (%type func)))))

(def: (concrete-type type)
  (-> Type (Check [(List Nat) Type]))
  (case type
    (#;UnivQ _)
    (do Monad<Check>
      [[id var] tc;create-var
       [ids final-output] (concrete-type (default (undefined)
                                           (type;apply (list var) type)))]
      (wrap [(#;Cons id ids)
             final-output]))
    
    _
    (:: Monad<Check> wrap [(list) type])))

(def: (check-apply member-type input-types output-type)
  (-> Type (List Type) Type (Check []))
  (do Monad<Check>
    [member-type' (foldM Monad<Check>
                         (function [input member]
                           (apply-function-type member input))
                         member-type
                         input-types)]
    (tc;check output-type member-type')))

(type: #rec Instance
  {#constructor Ident
   #dependencies (List Instance)})

(def: (test-provision provision context dep alts)
  (-> (-> Compiler Type-Context Type (Check Instance))
      Type-Context Type (List [Ident Type])
      (Lux (List Instance)))
  (do Monad<Lux>
    [compiler macro;get-compiler]
    (case (|> alts
              (List/map (function [[alt-name alt-type]]
                          (case (tc;run context
                                        (do Monad<Check>
                                          [[tvars alt-type] (concrete-type alt-type)
                                           #let [[deps alt-type] (type;flatten-function alt-type)]
                                           _ (tc;check dep alt-type)
                                           context' tc;get-context
                                           =deps (mapM @ (provision compiler context') deps)]
                                          (wrap =deps)))
                            (#;Left error)
                            (list)

                            (#;Right =deps)
                            (list [alt-name =deps]))))
              List/join)
      #;Nil
      (macro;fail (format "No candidates for provisioning: " (%type dep)))

      found
      (wrap found))))

(def: (provision compiler context dep)
  (-> Compiler Type-Context Type (Check Instance))
  (case (macro;run compiler
                   ($_ macro;either
                       (do Monad<Lux> [alts local-env] (test-provision provision context dep alts))
                       (do Monad<Lux> [alts local-structs] (test-provision provision context dep alts))
                       (do Monad<Lux> [alts import-structs] (test-provision provision context dep alts))))
    (#;Left error)
    (tc;fail error)

    (#;Right candidates)
    (case candidates
      #;Nil
      (tc;fail (format "No candidates for provisioning: " (%type dep)))

      (#;Cons winner #;Nil)
      (:: Monad<Check> wrap winner)

      _
      (tc;fail (format "Too many candidates for provisioning: " (%type dep) " --- " (%list (. %ident product;left) candidates))))
    ))

(def: (test-alternatives sig-type member-idx input-types output-type alts)
  (-> Type Nat (List Type) Type (List [Ident Type]) (Lux (List Instance)))
  (do Monad<Lux>
    [compiler macro;get-compiler
     context macro;type-context]
    (case (|> alts
              (List/map (function [[alt-name alt-type]]
                          (case (tc;run context
                                        (do Monad<Check>
                                          [[tvars alt-type] (concrete-type alt-type)
                                           #let [[deps alt-type] (type;flatten-function alt-type)]
                                           _ (tc;check alt-type sig-type)
                                           member-type (find-member-type member-idx alt-type)
                                           _ (check-apply member-type input-types output-type)
                                           context' tc;get-context
                                           =deps (mapM @ (provision compiler context') deps)]
                                          (wrap =deps)))
                            (#;Left error)
                            (list)

                            (#;Right =deps)
                            (list [alt-name =deps]))))
              List/join)
      #;Nil
      (macro;fail (format "No alternatives for " (%type (type;function input-types output-type))))

      found
      (wrap found))))

(def: (find-alternatives sig-type member-idx input-types output-type)
  (-> Type Nat (List Type) Type (Lux (List Instance)))
  (let [test (test-alternatives sig-type member-idx input-types output-type)]
    ($_ macro;either
        (do Monad<Lux> [alts local-env] (test alts))
        (do Monad<Lux> [alts local-structs] (test alts))
        (do Monad<Lux> [alts import-structs] (test alts)))))

(def: (var? input)
  (-> Code Bool)
  (case input
    [_ (#;Symbol _)]
    true

    _
    false))

(def: (join-pair [l r])
  (All [a] (-> [a a] (List a)))
  (list l r))

(def: (instance$ [constructor dependencies])
  (-> Instance Code)
  (case dependencies
    #;Nil
    (code;symbol constructor)

    _
    (` ((~ (code;symbol constructor)) (~@ (List/map instance$ dependencies))))))

(syntax: #export (::: [member s;symbol]
                      [args (p;alt (p;seq (p;some s;symbol) s;end!)
                                   (p;seq (p;some s;any) s;end!))])
  {#;doc (doc "Automatic structure selection (for type-class style polymorphism)."
              "This feature layers type-class style polymorphism on top of Lux's signatures and structures."
              "When calling a polymorphic function, or using a polymorphic constant,"
              "this macro will check the types of the arguments, and the expected type for the whole expression"
              "and it will search in the local scope, the module's scope and the imports' scope"
              "in order to find suitable structures to satisfy those requirements."
              "If a single alternative is found, that one will be used automatically."
              "If no alternative is found, or if more than one alternative is found (ambiguity)"
              "a compile-time error will be raised, to alert the user."
              "Examples:"
              "Nat equality"
              (:: number;Eq<Nat> = x y)
              (::: = x y)
              "Can optionally add the prefix of the module where the signature was defined."
              (::: eq;= x y)
              "(List Nat) equality"
              (::: =
                   (list;n.range +1 +10)
                   (list;n.range +1 +10))
              "(Functor List) map"
              (::: map n.inc (list;n.range +0 +9))
              "Caveat emptor: You need to make sure to import the module of any structure you want to use."
              "Otherwise, this macro will not find it.")}
  (case args
    (#;Left [args _])
    (do @
      [[member-idx sig-type] (resolve-member member)
       input-types (mapM @ resolve-type args)
       output-type macro;expected-type
       chosen-ones (find-alternatives sig-type member-idx input-types output-type)]
      (case chosen-ones
        #;Nil
        (macro;fail (format "No structure option could be found for member: " (%ident member)))

        (#;Cons chosen #;Nil)
        (wrap (list (` (:: (~ (instance$ chosen))
                           (~ (code;local-symbol (product;right member)))
                           (~@ (List/map code;symbol args))))))

        _
        (macro;fail (format "Too many options available: "
                            (|> chosen-ones
                                (List/map (. %ident product;left))
                                (text;join-with ", "))
                            " --- for type: " (%type sig-type)))))

    (#;Right [args _])
    (do @
      [labels (seqM @ (list;repeat (list;size args)
                                   (macro;gensym "")))
       #let [retry (` (let [(~@ (|> (list;zip2 labels args) (List/map join-pair) List/join))]
                        (;;::: (~ (code;symbol member)) (~@ labels))))]]
      (wrap (list retry)))
    ))