(;module:
  lux
  (lux [function]
       (data (coll [list "L/" Fold<List>]))))

(type: #export #rec Pattern
  (#BoolP Bool)
  (#NatP Nat)
  (#IntP Int)
  (#DegP Deg)
  (#RealP Real)
  (#TextP Text)
  (#TupleP (List Pattern))
  (#VariantP Nat Nat Pattern)
  (#BindP Nat))

(type: #export #rec Analysis
  #Unit
  (#Bool Bool)
  (#Nat Nat)
  (#Int Int)
  (#Deg Deg)
  (#Real Real)
  (#Text Text)
  (#Sum (Either Analysis Analysis))
  (#Product Analysis Analysis)
  (#Case Analysis (List [Pattern Analysis]))
  (#Function Scope Analysis)
  (#Apply Analysis Analysis)
  (#Procedure Text (List Analysis))
  (#Variable Ref)
  (#Definition Ident))

## Variants get analysed as binary sum types for the sake of semantic
## simplicity.
## This is because you can encode a variant of any size using just
## binary sums by nesting them.

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

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

(def: #export (sum tag size temp value)
  (-> Nat Nat Nat Analysis 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
              (#Sum _)
              (#Case value (list [(#BindP temp)
                                  (#Variable (#;Local temp))]))

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

## Tuples get analysed into binary products for the sake of semantic
## simplicity, since products/pairs can encode tuples of any length
## through nesting.

(def: #export (product members)
  (-> (List Analysis) Analysis)
  (case members
    #;Nil
    #Unit

    (#;Cons singleton #;Nil)
    singleton

    (#;Cons left right)
    (#Product left (product right))))

## Function application gets analysed into single-argument
## applications, since every other kind of application can be encoded
## into a finite series of single-argument applications.

(def: #export (apply args func)
  (-> (List Analysis) Analysis Analysis)
  (L/fold (function [arg func] (#Apply arg func))
          func
          args))