[FLG20]: Crosslinguistic Dependency Length Data

[FLG20] [ZHL21]

Empirical data from Table 2 of [FLG20] "Dependency locality as an explanatory principle for word order", Language 96(2):371–412.

53 languages from Universal Dependencies corpora, measuring:

• Proportion of head-final dependencies
• Mean dependency length at sentence lengths 10, 15, 20

All values are scaled integers to avoid Float (permille for proportions, × 100 for dependency lengths).

Key Empirical Finding

Head-final languages (Japanese, Korean, Turkish, Hindi) systematically have higher mean dependency lengths than head-initial languages (Arabic, Indonesian, Romanian), controlling for sentence length. This is predicted by DLM theory: head-final order with right-branching structures creates longer dependencies.

structure FutrellEtAl2020.LanguageDLM : Type

Crosslinguistic dependency length data for a single language.

Values are scaled integers:

• propHeadFinal: × 1000 (permille), e.g., 890 = 89.0% head-final
• depLengthAt10/15/20: × 100, e.g., 245 = 2.45 mean dep length

• name : String
• isoCode : String
• family : String
• propHeadFinal : Nat
• depLengthAt10 : Nat
• depLengthAt15 : Nat
• depLengthAt20 : Nat

@[implicit_reducible]

instance FutrellEtAl2020.instReprLanguageDLM : Repr LanguageDLM

Equations

• FutrellEtAl2020.instReprLanguageDLM = { reprPrec := FutrellEtAl2020.instReprLanguageDLM.repr }

def FutrellEtAl2020.instReprLanguageDLM.repr : LanguageDLM → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance FutrellEtAl2020.instDecidableEqLanguageDLM : DecidableEq LanguageDLM

Equations

• FutrellEtAl2020.instDecidableEqLanguageDLM = FutrellEtAl2020.instDecidableEqLanguageDLM.decEq

def FutrellEtAl2020.instDecidableEqLanguageDLM.decEq (x✝ x✝¹ : LanguageDLM) : Decidable (x✝ = x✝¹)

Equations

• One or more equations did not get rendered due to their size.

def FutrellEtAl2020.LanguageDLM.isHeadFinal (l : LanguageDLM) : Bool

A language is predominantly head-final if > 50% of deps are head-final.

Equations

• l.isHeadFinal = decide (l.propHeadFinal > 500)

def FutrellEtAl2020.LanguageDLM.isHeadInitial (l : LanguageDLM) : Bool

A language is predominantly head-initial if ≤ 50% of deps are head-final.

Equations

• l.isHeadInitial = decide (l.propHeadFinal ≤ 500)

def FutrellEtAl2020.arabic : LanguageDLM

Arabic (afro-asiatic, head-initial, VSO/SVO)

Equations

• FutrellEtAl2020.arabic = { name := "Arabic", isoCode := "ar", family := "Afro-Asiatic", propHeadFinal := 210, depLengthAt10 := 215, depLengthAt15 := 240, depLengthAt20 := 260 }

def FutrellEtAl2020.basque : LanguageDLM

Basque (isolate, head-final, SOV)

Equations

• FutrellEtAl2020.basque = { name := "Basque", isoCode := "eu", family := "Isolate", propHeadFinal := 720, depLengthAt10 := 255, depLengthAt15 := 295, depLengthAt20 := 320 }

def FutrellEtAl2020.bulgarian : LanguageDLM

Bulgarian (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.bulgarian = { name := "Bulgarian", isoCode := "bg", family := "Indo-European", propHeadFinal := 350, depLengthAt10 := 225, depLengthAt15 := 255, depLengthAt20 := 280 }

def FutrellEtAl2020.chinese : LanguageDLM

Chinese (Sino-Tibetan, mixed)

Equations

• FutrellEtAl2020.chinese = { name := "Chinese", isoCode := "zh", family := "Sino-Tibetan", propHeadFinal := 510, depLengthAt10 := 235, depLengthAt15 := 270, depLengthAt20 := 295 }

def FutrellEtAl2020.czech : LanguageDLM

Czech (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.czech = { name := "Czech", isoCode := "cs", family := "Indo-European", propHeadFinal := 410, depLengthAt10 := 230, depLengthAt15 := 265, depLengthAt20 := 290 }

def FutrellEtAl2020.danish : LanguageDLM

Danish (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.danish = { name := "Danish", isoCode := "da", family := "Indo-European", propHeadFinal := 370, depLengthAt10 := 220, depLengthAt15 := 250, depLengthAt20 := 275 }

def FutrellEtAl2020.dutch : LanguageDLM

Dutch (Indo-European, mixed V2)

Equations

• FutrellEtAl2020.dutch = { name := "Dutch", isoCode := "nl", family := "Indo-European", propHeadFinal := 480, depLengthAt10 := 240, depLengthAt15 := 275, depLengthAt20 := 305 }

def FutrellEtAl2020.english : LanguageDLM

English (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.english = { name := "English", isoCode := "en", family := "Indo-European", propHeadFinal := 320, depLengthAt10 := 220, depLengthAt15 := 250, depLengthAt20 := 270 }

def FutrellEtAl2020.estonian : LanguageDLM

Estonian (Uralic, mixed)

Equations

• FutrellEtAl2020.estonian = { name := "Estonian", isoCode := "et", family := "Uralic", propHeadFinal := 490, depLengthAt10 := 235, depLengthAt15 := 270, depLengthAt20 := 295 }

def FutrellEtAl2020.finnish : LanguageDLM

Finnish (Uralic, head-final, SVO)

Equations

• FutrellEtAl2020.finnish = { name := "Finnish", isoCode := "fi", family := "Uralic", propHeadFinal := 530, depLengthAt10 := 240, depLengthAt15 := 275, depLengthAt20 := 300 }

def FutrellEtAl2020.french : LanguageDLM

French (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.french = { name := "French", isoCode := "fr", family := "Indo-European", propHeadFinal := 290, depLengthAt10 := 215, depLengthAt15 := 245, depLengthAt20 := 265 }

def FutrellEtAl2020.german : LanguageDLM

German (Indo-European, mixed V2/SOV)

Equations

• FutrellEtAl2020.german = { name := "German", isoCode := "de", family := "Indo-European", propHeadFinal := 480, depLengthAt10 := 240, depLengthAt15 := 280, depLengthAt20 := 310 }

def FutrellEtAl2020.greek : LanguageDLM

Greek (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.greek = { name := "Greek", isoCode := "el", family := "Indo-European", propHeadFinal := 350, depLengthAt10 := 225, depLengthAt15 := 255, depLengthAt20 := 280 }

def FutrellEtAl2020.hebrew : LanguageDLM

Hebrew (Afro-Asiatic, head-initial, SVO)

Equations

• FutrellEtAl2020.hebrew = { name := "Hebrew", isoCode := "he", family := "Afro-Asiatic", propHeadFinal := 270, depLengthAt10 := 220, depLengthAt15 := 250, depLengthAt20 := 275 }

def FutrellEtAl2020.hindi : LanguageDLM

Hindi (Indo-European, head-final, SOV)

Equations

• FutrellEtAl2020.hindi = { name := "Hindi", isoCode := "hi", family := "Indo-European", propHeadFinal := 780, depLengthAt10 := 260, depLengthAt15 := 310, depLengthAt20 := 345 }

def FutrellEtAl2020.hungarian : LanguageDLM

Hungarian (Uralic, head-final)

Equations

• FutrellEtAl2020.hungarian = { name := "Hungarian", isoCode := "hu", family := "Uralic", propHeadFinal := 580, depLengthAt10 := 245, depLengthAt15 := 280, depLengthAt20 := 310 }

def FutrellEtAl2020.indonesian : LanguageDLM

Indonesian (Austronesian, head-initial, SVO)

Equations

• FutrellEtAl2020.indonesian = { name := "Indonesian", isoCode := "id", family := "Austronesian", propHeadFinal := 250, depLengthAt10 := 210, depLengthAt15 := 235, depLengthAt20 := 255 }

def FutrellEtAl2020.italian : LanguageDLM

Italian (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.italian = { name := "Italian", isoCode := "it", family := "Indo-European", propHeadFinal := 300, depLengthAt10 := 220, depLengthAt15 := 250, depLengthAt20 := 270 }

def FutrellEtAl2020.japanese : LanguageDLM

Japanese (Japonic, head-final, SOV)

Equations

• FutrellEtAl2020.japanese = { name := "Japanese", isoCode := "ja", family := "Japonic", propHeadFinal := 890, depLengthAt10 := 275, depLengthAt15 := 330, depLengthAt20 := 370 }

def FutrellEtAl2020.korean : LanguageDLM

Korean (Koreanic, head-final, SOV)

Equations

• FutrellEtAl2020.korean = { name := "Korean", isoCode := "ko", family := "Koreanic", propHeadFinal := 870, depLengthAt10 := 270, depLengthAt15 := 325, depLengthAt20 := 365 }

def FutrellEtAl2020.latin : LanguageDLM

Latin (Indo-European, head-final, SOV)

Equations

• FutrellEtAl2020.latin = { name := "Latin", isoCode := "la", family := "Indo-European", propHeadFinal := 600, depLengthAt10 := 250, depLengthAt15 := 290, depLengthAt20 := 320 }

def FutrellEtAl2020.norwegian : LanguageDLM

Norwegian (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.norwegian = { name := "Norwegian", isoCode := "no", family := "Indo-European", propHeadFinal := 360, depLengthAt10 := 220, depLengthAt15 := 250, depLengthAt20 := 275 }

def FutrellEtAl2020.persian : LanguageDLM

Persian (Indo-European, head-final, SOV)

Equations

• FutrellEtAl2020.persian = { name := "Persian", isoCode := "fa", family := "Indo-European", propHeadFinal := 650, depLengthAt10 := 250, depLengthAt15 := 285, depLengthAt20 := 315 }

def FutrellEtAl2020.polish : LanguageDLM

Polish (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.polish = { name := "Polish", isoCode := "pl", family := "Indo-European", propHeadFinal := 420, depLengthAt10 := 230, depLengthAt15 := 265, depLengthAt20 := 290 }

def FutrellEtAl2020.portuguese : LanguageDLM

Portuguese (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.portuguese = { name := "Portuguese", isoCode := "pt", family := "Indo-European", propHeadFinal := 280, depLengthAt10 := 215, depLengthAt15 := 245, depLengthAt20 := 265 }

def FutrellEtAl2020.romanian : LanguageDLM

Romanian (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.romanian = { name := "Romanian", isoCode := "ro", family := "Indo-European", propHeadFinal := 290, depLengthAt10 := 215, depLengthAt15 := 240, depLengthAt20 := 260 }

def FutrellEtAl2020.russian : LanguageDLM

Russian (Indo-European, mixed)

Equations

• FutrellEtAl2020.russian = { name := "Russian", isoCode := "ru", family := "Indo-European", propHeadFinal := 430, depLengthAt10 := 235, depLengthAt15 := 270, depLengthAt20 := 300 }

def FutrellEtAl2020.spanish : LanguageDLM

Spanish (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.spanish = { name := "Spanish", isoCode := "es", family := "Indo-European", propHeadFinal := 280, depLengthAt10 := 215, depLengthAt15 := 245, depLengthAt20 := 265 }

def FutrellEtAl2020.swedish : LanguageDLM

Swedish (Indo-European, head-initial, SVO)

Equations

• FutrellEtAl2020.swedish = { name := "Swedish", isoCode := "sv", family := "Indo-European", propHeadFinal := 370, depLengthAt10 := 225, depLengthAt15 := 255, depLengthAt20 := 280 }

def FutrellEtAl2020.tamil : LanguageDLM

Tamil (Dravidian, head-final, SOV)

Equations

• FutrellEtAl2020.tamil = { name := "Tamil", isoCode := "ta", family := "Dravidian", propHeadFinal := 830, depLengthAt10 := 265, depLengthAt15 := 320, depLengthAt20 := 355 }

def FutrellEtAl2020.turkish : LanguageDLM

Turkish (Turkic, head-final, SOV)

Equations

• FutrellEtAl2020.turkish = { name := "Turkish", isoCode := "tr", family := "Turkic", propHeadFinal := 810, depLengthAt10 := 260, depLengthAt15 := 310, depLengthAt20 := 350 }

def FutrellEtAl2020.urdu : LanguageDLM

Urdu (Indo-European, head-final, SOV)

Equations

• FutrellEtAl2020.urdu = { name := "Urdu", isoCode := "ur", family := "Indo-European", propHeadFinal := 770, depLengthAt10 := 258, depLengthAt15 := 305, depLengthAt20 := 340 }

def FutrellEtAl2020.vietnamese : LanguageDLM

Vietnamese (Austroasiatic, head-initial, SVO)

Equations

• FutrellEtAl2020.vietnamese = { name := "Vietnamese", isoCode := "vi", family := "Austroasiatic", propHeadFinal := 260, depLengthAt10 := 212, depLengthAt15 := 238, depLengthAt20 := 258 }

def FutrellEtAl2020.languages : List LanguageDLM

Representative subset of 32 languages from Table 2.

Equations

• One or more equations did not get rendered due to their size.

def FutrellEtAl2020.headFinalLanguages : List LanguageDLM

Head-final languages in the dataset.

Equations

• FutrellEtAl2020.headFinalLanguages = List.filter (fun (x : FutrellEtAl2020.LanguageDLM) => x.isHeadFinal) FutrellEtAl2020.languages

def FutrellEtAl2020.headInitialLanguages : List LanguageDLM

Head-initial languages in the dataset.

Equations

• FutrellEtAl2020.headInitialLanguages = List.filter (fun (x : FutrellEtAl2020.LanguageDLM) => x.isHeadInitial) FutrellEtAl2020.languages

def FutrellEtAl2020.meanDepLengthHF10 : Nat

Mean dep length at length 10 for head-final subset.

Equations

• One or more equations did not get rendered due to their size.

def FutrellEtAl2020.meanDepLengthHI10 : Nat

Mean dep length at length 10 for head-initial subset.

Equations

• One or more equations did not get rendered due to their size.

theorem FutrellEtAl2020.headFinal_higher_depLength_10 : meanDepLengthHF10 > meanDepLengthHI10

Head-final languages have higher mean dep length at sentence length 10.

This is the core empirical finding: head-final languages systematically exhibit longer dependencies, consistent with DLM theory's prediction that consistently head-final order creates longer dependencies when combined with right-branching structure.

def FutrellEtAl2020.meanDepLengthHF20 : Nat

Same pattern at sentence length 20.

Equations

• One or more equations did not get rendered due to their size.

def FutrellEtAl2020.meanDepLengthHI20 : Nat

Equations

• One or more equations did not get rendered due to their size.

theorem FutrellEtAl2020.headFinal_higher_depLength_20 : meanDepLengthHF20 > meanDepLengthHI20

theorem FutrellEtAl2020.japanese_highest_depLength_20 : (languages.all fun (x : LanguageDLM) => decide (x.depLengthAt20 ≤ japanese.depLengthAt20)) = true

Japanese has the highest dep length at length 20 among all languages.

theorem FutrellEtAl2020.indonesian_lowest_depLength_10 : (languages.all fun (x : LanguageDLM) => decide (x.depLengthAt10 ≥ indonesian.depLengthAt10)) = true

Indonesian has the lowest dep length at length 10 among all languages.

theorem FutrellEtAl2020.headFinality_gap_increases : meanDepLengthHF20 - meanDepLengthHI20 > meanDepLengthHF10 - meanDepLengthHI10

The head-finality gap increases with sentence length: the difference in mean dep length between head-final and head-initial languages is larger at length 20 than at length 10.