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(.module:
  [lux #*
   [abstract
    [equivalence (#+ Equivalence)]
    [hash (#+ Hash)]
    [order (#+ Order)]
    [enum (#+ Enum)]
    [codec (#+ Codec)]]
   [control
    ["." try (#+ Try)]
    ["." exception (#+ exception:)]]
   [data
    ["." text]]
   [math
    [number
     ["n" nat]]]])

(type: #export Month
  #January
  #February
  #March
  #April
  #May
  #June
  #July
  #August
  #September
  #October
  #November
  #December)

(structure: #export equivalence
  (Equivalence Month)
  
  (def: (= reference sample)
    (case [reference sample]
      (^template [<tag>]
        [[<tag> <tag>]
         true])
      ([#January]
       [#February]
       [#March]
       [#April]
       [#May]
       [#June]
       [#July]
       [#August]
       [#September]
       [#October]
       [#November]
       [#December])

      _
      false)))

(with_expansions [<pairs> (as_is [01 #January]
                                 [02 #February]
                                 [03 #March]
                                 [04 #April]
                                 [05 #May]
                                 [06 #June]
                                 [07 #July]
                                 [08 #August]
                                 [09 #September]
                                 [10 #October]
                                 [11 #November]
                                 [12 #December])]
  (def: #export (number month)
    (-> Month Nat)
    (case month
      (^template [<number> <month>]
        [<month> <number>])
      (<pairs>)))

  (exception: #export (invalid_month {number Nat})
    (exception.report
     ["Number" (\ n.decimal encode number)]
     ["Valid range" ($_ "lux text concat"
                        (\ n.decimal encode (..number #January))
                        " ~ "
                        (\ n.decimal encode (..number #December)))]))

  (def: #export (by_number number)
    (-> Nat (Try Month))
    (case number
      (^template [<number> <month>]
        [<number> (#try.Success <month>)])
      (<pairs>)
      _ (exception.throw ..invalid_month [number])))
  )

(structure: #export hash
  (Hash Month)

  (def: &equivalence ..equivalence)
  (def: hash ..number))

(structure: #export order
  (Order Month)
  
  (def: &equivalence ..equivalence)
  
  (def: (< reference sample)
    (n.< (..number reference) (..number sample))))

(structure: #export enum
  (Enum Month)
  
  (def: &order ..order)
  
  (def: (succ month)
    (case month
      #January   #February
      #February  #March
      #March     #April
      #April     #May
      #May       #June
      #June      #July
      #July      #August
      #August    #September
      #September #October
      #October   #November
      #November  #December
      #December  #January))
  
  (def: (pred month)
    (case month
      #February  #January
      #March     #February
      #April     #March
      #May       #April
      #June      #May
      #July      #June
      #August    #July
      #September #August
      #October   #September
      #November  #October
      #December  #November
      #January   #December)))

(def: #export (days month)
  (-> Month Nat)
  (case month
    (^template [<days> <month>]
      [<month> <days>])
    ([31 #January]
     [28 #February]
     [31 #March]
     
     [30 #April]
     [31 #May]
     [30 #June]
     
     [31 #July]
     [31 #August]
     [30 #September]
     
     [31 #October]
     [30 #November]
     [31 #December])))

(def: #export (leap_year_days month)
  (-> Month Nat)
  (case month
    #February (inc (..days month))
    _ (..days month)))

(def: #export year
  (List Month)
  (list #January
        #February
        #March
        #April
        #May
        #June
        #July
        #August
        #September
        #October
        #November
        #December))

(exception: #export (not_a_month_of_the_year {value Text})
  (exception.report
   ["Value" (text.format value)]))

(structure: #export codec
  (Codec Text Month)
  
  (def: (encode value)
    (case value
      #January "January"
      #February "February"
      #March "March"
      #April "April"
      #May "May"
      #June "June"
      #July "July"
      #August "August"
      #September "September"
      #October "October"
      #November "November"
      #December "December"))
  (def: (decode value)
    (case value
      "January" (#try.Success #January)
      "February" (#try.Success #February)
      "March" (#try.Success #March)
      "April" (#try.Success #April)
      "May" (#try.Success #May)
      "June" (#try.Success #June)
      "July" (#try.Success #July)
      "August" (#try.Success #August)
      "September" (#try.Success #September)
      "October" (#try.Success #October)
      "November" (#try.Success #November)
      "December" (#try.Success #December)
      _ (exception.throw ..not_a_month_of_the_year [value]))))