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(.module:
  [lux #*
   [abstract
    ["." interval (#+ Interval)]
    [monoid (#+ Monoid)]]
   [data
    [number (#+ hex)
     ["." nat ("#;." interval)]]
    [collection
     ["." list]
     [tree
      ["." finger (#+ Tree)]]]]
   [type
    abstract]]
  [// (#+ Char)])

(abstract: #export Segment
  {}
  (Interval Char)

  (def: empty (:abstraction (interval.between nat.enum nat;top nat;bottom)))

  (structure: monoid (Monoid Segment)
    (def: identity ..empty)
    (def: (compose left right)
      (let [left (:representation left)
            right (:representation right)]
        (:abstraction
         (interval.between nat.enum
                           (n/min (:: left bottom)
                                  (:: right bottom))
                           (n/max (:: left top)
                                  (:: right top)))))))

  (def: #export (segment start end)
    (-> Char Char Segment)
    (:abstraction (interval.between nat.enum (n/min start end) (n/max start end))))

  (template [<name> <slot>]
    [(def: #export <name>
       (-> Segment Char)
       (|>> :representation (get@ <slot>)))]

    [start #interval.bottom]
    [end   #interval.top]
    )

  (def: #export (size segment)
    (-> Segment Nat)
    (let [start (get@ #interval.bottom (:representation segment))
          end (get@ #interval.top (:representation segment))]
      (|> end (n/- start) inc)))

  (def: #export (within? segment char)
    (All [a] (-> Segment Char Bit))
    (interval.within? (:representation segment) char))
  )

(template [<name> <start> <end>]
  [(def: #export <name> Segment (..segment (hex <start>) (hex <end>)))]

  ## Normal segments
  [basic-latin                             "0000"  "007F"]
  [latin-1-supplement                      "00A0"  "00FF"]
  [latin-extended-a                        "0100"  "017F"]
  [latin-extended-b                        "0180"  "024F"]
  [ipa-extensions                          "0250"  "02AF"]
  [spacing-modifier-letters                "02B0"  "02FF"]
  [combining-diacritical-marks             "0300"  "036F"]
  [greek-and-coptic                        "0370"  "03FF"]
  [cyrillic                                "0400"  "04FF"]
  [cyrillic-supplementary                  "0500"  "052F"]
  [armenian                                "0530"  "058F"]
  [hebrew                                  "0590"  "05FF"]
  [arabic                                  "0600"  "06FF"]
  [syriac                                  "0700"  "074F"]
  [thaana                                  "0780"  "07BF"]
  [devanagari                              "0900"  "097F"]
  [bengali                                 "0980"  "09FF"]
  [gurmukhi                                "0A00"  "0A7F"]
  [gujarati                                "0A80"  "0AFF"]
  [oriya                                   "0B00"  "0B7F"]
  [tamil                                   "0B80"  "0BFF"]
  [telugu                                  "0C00"  "0C7F"]
  [kannada                                 "0C80"  "0CFF"]
  [malayalam                               "0D00"  "0D7F"]
  [sinhala                                 "0D80"  "0DFF"]
  [thai                                    "0E00"  "0E7F"]
  [lao                                     "0E80"  "0EFF"]
  [tibetan                                 "0F00"  "0FFF"]
  [myanmar                                 "1000"  "109F"]
  [georgian                                "10A0"  "10FF"]
  [hangul-jamo                             "1100"  "11FF"]
  [ethiopic                                "1200"  "137F"]
  [cherokee                                "13A0"  "13FF"]
  [unified-canadian-aboriginal-syllabics   "1400"  "167F"]
  [ogham                                   "1680"  "169F"]
  [runic                                   "16A0"  "16FF"]
  [tagalog                                 "1700"  "171F"]
  [hanunoo                                 "1720"  "173F"]
  [buhid                                   "1740"  "175F"]
  [tagbanwa                                "1760"  "177F"]
  [khmer                                   "1780"  "17FF"]
  [mongolian                               "1800"  "18AF"]
  [limbu                                   "1900"  "194F"]
  [tai-le                                  "1950"  "197F"]
  [khmer-symbols                           "19E0"  "19FF"]
  [phonetic-extensions                     "1D00"  "1D7F"]
  [latin-extended-additional               "1E00"  "1EFF"]
  [greek-extended                          "1F00"  "1FFF"]
  [general-punctuation                     "2000"  "206F"]
  [superscripts-and-subscripts             "2070"  "209F"]
  [currency-symbols                        "20A0"  "20CF"]
  [combining-diacritical-marks-for-symbols "20D0"  "20FF"]
  [letterlike-symbols                      "2100"  "214F"]
  [number-forms                            "2150"  "218F"]
  [arrows                                  "2190"  "21FF"]
  [mathematical-operators                  "2200"  "22FF"]
  [miscellaneous-technical                 "2300"  "23FF"]
  [control-pictures                        "2400"  "243F"]
  [optical-character-recognition           "2440"  "245F"]
  [enclosed-alphanumerics                  "2460"  "24FF"]
  [box-drawing                             "2500"  "257F"]
  [block-elements                          "2580"  "259F"]
  [geometric-shapes                        "25A0"  "25FF"]
  [miscellaneous-symbols                   "2600"  "26FF"]
  [dingbats                                "2700"  "27BF"]
  [miscellaneous-mathematical-symbols-a    "27C0"  "27EF"]
  [supplemental-arrows-a                   "27F0"  "27FF"]
  [braille-patterns                        "2800"  "28FF"]
  [supplemental-arrows-b                   "2900"  "297F"]
  [miscellaneous-mathematical-symbols-b    "2980"  "29FF"]
  [supplemental-mathematical-operators     "2A00"  "2AFF"]
  [miscellaneous-symbols-and-arrows        "2B00"  "2BFF"]
  [cjk-radicals-supplement                 "2E80"  "2EFF"]
  [kangxi-radicals                         "2F00"  "2FDF"]
  [ideographic-description-characters      "2FF0"  "2FFF"]
  [cjk-symbols-and-punctuation             "3000"  "303F"]
  [hiragana                                "3040"  "309F"]
  [katakana                                "30A0"  "30FF"]
  [bopomofo                                "3100"  "312F"]
  [hangul-compatibility-jamo               "3130"  "318F"]
  [kanbun                                  "3190"  "319F"]
  [bopomofo-extended                       "31A0"  "31BF"]
  [katakana-phonetic-extensions            "31F0"  "31FF"]
  [enclosed-cjk-letters-and-months         "3200"  "32FF"]
  [cjk-compatibility                       "3300"  "33FF"]
  [cjk-unified-ideographs-extension-a      "3400"  "4DBF"]
  [yijing-hexagram-symbols                 "4DC0"  "4DFF"]
  [cjk-unified-ideographs                  "4E00"  "9FFF"]
  [yi-syllables                            "A000"  "A48F"]
  [yi-radicals                             "A490"  "A4CF"]
  [hangul-syllables                        "AC00"  "D7AF"]
  [high-surrogates                         "D800"  "DB7F"]
  [high-private-use-surrogates             "DB80"  "DBFF"]
  [low-surrogates                          "DC00"  "DFFF"]
  [private-use-area                        "E000"  "F8FF"]
  [cjk-compatibility-ideographs            "F900"  "FAFF"]
  [alphabetic-presentation-forms           "FB00"  "FB4F"]
  [arabic-presentation-forms-a             "FB50"  "FDFF"]
  [variation-selectors                     "FE00"  "FE0F"]
  [combining-half-marks                    "FE20"  "FE2F"]
  [cjk-compatibility-forms                 "FE30"  "FE4F"]
  [small-form-variants                     "FE50"  "FE6F"]
  [arabic-presentation-forms-b             "FE70"  "FEFF"]
  [halfwidth-and-fullwidth-forms           "FF00"  "FFEF"]
  [specials                                "FFF0"  "FFFF"]
  [linear-b-syllabary                      "10000" "1007F"]
  [linear-b-ideograms                      "10080" "100FF"]
  [aegean-numbers                          "10100" "1013F"]
  [old-italic                              "10300" "1032F"]
  [gothic                                  "10330" "1034F"]
  [ugaritic                                "10380" "1039F"]
  [deseret                                 "10400" "1044F"]
  [shavian                                 "10450" "1047F"]
  [osmanya                                 "10480" "104AF"]
  [cypriot-syllabary                       "10800" "1083F"]
  [byzantine-musical-symbols               "1D000" "1D0FF"]
  [musical-symbols                         "1D100" "1D1FF"]
  [tai-xuan-jing-symbols                   "1D300" "1D35F"]
  [mathematical-alphanumeric-symbols       "1D400" "1D7FF"]
  [cjk-unified-ideographs-extension-b      "20000" "2A6DF"]
  [cjk-compatibility-ideographs-supplement "2F800" "2FA1F"]
  [tags                                    "E0000" "E007F"]

  ## Specialized segments
  [basic-latin/upper-alpha                 "0041"  "005A"]
  [basic-latin/lower-alpha                 "0061"  "007A"]
  )

(type: #export Set (Tree Segment []))

(def: (singleton segment)
  (-> Segment Set)
  {#finger.monoid ..monoid
   #finger.node (#finger.Leaf segment [])})

(def: #export (set segments)
  (-> (List Segment) Set)
  (case segments
    (^ (list))
    (..singleton (:: ..monoid identity))
    
    (^ (list singleton))
    (..singleton singleton)
    
    (^ (list left right))
    (..singleton (:: ..monoid compose left right))
    
    _
    (let [[sides extra] (n//% 2 (list.size segments))
          [left+ right+] (list.split (n/+ sides extra) segments)]
      (finger.branch (set left+)
                     (set right+)))))

(def: half/0
  (List Segment)
  (list basic-latin
        latin-1-supplement
        latin-extended-a
        latin-extended-b
        ipa-extensions
        spacing-modifier-letters
        combining-diacritical-marks
        greek-and-coptic
        cyrillic
        cyrillic-supplementary
        armenian
        hebrew
        arabic
        syriac
        thaana
        devanagari
        bengali
        gurmukhi
        gujarati
        oriya
        tamil
        telugu
        kannada
        malayalam
        sinhala
        thai
        lao
        tibetan
        myanmar
        georgian
        hangul-jamo
        ethiopic
        cherokee
        unified-canadian-aboriginal-syllabics
        ogham
        runic
        tagalog
        hanunoo
        buhid
        tagbanwa
        khmer
        mongolian
        limbu
        tai-le
        khmer-symbols
        phonetic-extensions
        latin-extended-additional
        greek-extended
        general-punctuation
        superscripts-and-subscripts
        currency-symbols
        combining-diacritical-marks-for-symbols
        letterlike-symbols
        number-forms
        arrows
        mathematical-operators
        miscellaneous-technical
        control-pictures
        optical-character-recognition
        enclosed-alphanumerics
        box-drawing
        ))

(def: half/1
  (List Segment)
  (list block-elements
        geometric-shapes
        miscellaneous-symbols
        dingbats
        miscellaneous-mathematical-symbols-a
        supplemental-arrows-a
        braille-patterns
        supplemental-arrows-b
        miscellaneous-mathematical-symbols-b
        supplemental-mathematical-operators
        miscellaneous-symbols-and-arrows
        cjk-radicals-supplement
        kangxi-radicals
        ideographic-description-characters
        cjk-symbols-and-punctuation
        hiragana
        katakana
        bopomofo
        hangul-compatibility-jamo
        kanbun
        bopomofo-extended
        katakana-phonetic-extensions
        enclosed-cjk-letters-and-months
        cjk-compatibility
        cjk-unified-ideographs-extension-a
        yijing-hexagram-symbols
        cjk-unified-ideographs
        yi-syllables
        yi-radicals
        hangul-syllables
        high-surrogates
        high-private-use-surrogates
        low-surrogates
        private-use-area
        cjk-compatibility-ideographs
        alphabetic-presentation-forms
        arabic-presentation-forms-a
        variation-selectors
        combining-half-marks
        cjk-compatibility-forms
        small-form-variants
        arabic-presentation-forms-b
        halfwidth-and-fullwidth-forms
        specials
        linear-b-syllabary
        linear-b-ideograms
        aegean-numbers
        old-italic
        gothic
        ugaritic
        deseret
        shavian
        osmanya
        cypriot-syllabary
        byzantine-musical-symbols
        musical-symbols
        tai-xuan-jing-symbols
        mathematical-alphanumeric-symbols
        cjk-unified-ideographs-extension-b
        cjk-compatibility-ideographs-supplement
        tags
        ))

(def: #export full
  Set
  (finger.branch (set half/0) (set half/1)))

(template [<name> <segments>]
  [(def: #export <name> Set (set <segments>))]

  [ascii             (list basic-latin)]
  [ascii/alpha       (list basic-latin/upper-alpha basic-latin/lower-alpha)]
  [ascii/upper-alpha (list basic-latin/upper-alpha)]
  [ascii/lower-alpha (list basic-latin/lower-alpha)]
  )