(.module:
  [lux (#- function)
   ["_" test (#+ Test)]
   [abstract
    [monad (#+ do)]
    ["." enum]]
   [control
    [pipe (#+ case>)]
    ["." maybe]]
   [data
    [number
     ["n" nat]]
    [collection
     ["." list ("#\." functor)]]]
   [math
    ["r" random (#+ Random) ("#\." monad)]]
   [tool
    [compiler
     [analysis (#+ Arity)]
     ["." reference (#+ Register)]
     ["." synthesis (#+ Synthesis)]]]]
  ["." // #_
   ["#." case]
   [//
    [common (#+ Runner)]]])

(def: max_arity
  Arity
  10)

(def: arity
  (Random Arity)
  (|> r.nat (r\map (|>> (n.% max_arity) (n.max 1)))))

(def: (local arity)
  (-> Arity (Random Register))
  (|> r.nat (r\map (|>> (n.% arity) inc))))

(def: function
  (Random [Arity Register Synthesis])
  (do r.monad
    [arity ..arity
     local (..local arity)]
    (in [arity local
         (synthesis.function/abstraction
          {#synthesis.environment (list)
           #synthesis.arity arity
           #synthesis.body (synthesis.variable/local local)})])))

(def: .public (spec run)
  (-> Runner Test)
  (do {! r.monad}
    [[arity local functionS] ..function
     partial_arity (|> r.nat (\ ! map (|>> (n.% arity) (n.max 1))))
     inputs (r.list arity r.safe_frac)
     .let [expectation (maybe.assume (list.item (dec local) inputs))
           inputsS (list\map (|>> synthesis.f64) inputs)]]
    ($_ _.and
        (_.test "Can read arguments."
                (|> (synthesis.function/apply {#synthesis.function functionS
                                               #synthesis.arguments inputsS})
                    (run "with_local")
                    (//case.verify expectation)))
        (_.test "Can partially apply functions."
                (or (n.= 1 arity)
                    (let [preS (list.first partial_arity inputsS)
                          postS (list.after partial_arity inputsS)
                          partialS (synthesis.function/apply {#synthesis.function functionS
                                                              #synthesis.arguments preS})]
                      (|> (synthesis.function/apply {#synthesis.function partialS
                                                     #synthesis.arguments postS})
                          (run "partial_application")
                          (//case.verify expectation)))))
        (_.test "Can read environment."
                (or (n.= 1 arity)
                    (let [environment (|> partial_arity
                                          (enum.range n.enum 1)
                                          (list\map (|>> #reference.Local)))
                          variableS (if (n.<= partial_arity local)
                                      (synthesis.variable/foreign (dec local))
                                      (synthesis.variable/local (|> local (n.- partial_arity))))
                          inner_arity (n.- partial_arity arity)
                          innerS (synthesis.function/abstraction
                                  {#synthesis.environment environment
                                   #synthesis.arity inner_arity
                                   #synthesis.body variableS})
                          outerS (synthesis.function/abstraction
                                  {#synthesis.environment (list)
                                   #synthesis.arity partial_arity
                                   #synthesis.body innerS})]
                      (|> (synthesis.function/apply {#synthesis.function outerS
                                                     #synthesis.arguments inputsS})
                          (run "with_foreign")
                          (//case.verify expectation)))))
        )))