Standard Average European: A Linguistic Area

@cite{haspelmath-2001}

Formalization of @cite{haspelmath-2001}'s argument that the core European languages — the Romance, Germanic, Balkan, and Balto-Slavic families plus the westernmost Finno-Ugric languages — form a Sprachbund (linguistic area) called Standard Average European (SAE), defined by a dozen shared structural features that are absent in the geographically and genealogically adjacent languages.

This study instantiates the framework-neutral schema in Theories.Diachronic.Areal: SAE is a LinguisticArea SAELanguage SAEFeature whose feature set is the twelve major Europeanisms of §2 of the paper, whose reference frame is the four samples §1 demands (area, cofamilial, adjacent, world), and whose areality is verified feature-by-feature against @cite{haspelmath-2001}'s Maps 107.1–107.12.

The cluster-map gradience of §4 (most notably the Charlemagne nucleus formed by French and German) is recovered automatically from the discrete feature data via LinguisticArea.clusterScore and nucleus.

Architectural notes

• Languages and features are local inductives: the paper surveys a specific sample and committing to its boundaries is appropriate here. A SAELanguage.toWALS bridge maps each language to its WALS code where one exists.
• The paper's Maps 107.1–107.12 are the primary source for every isogloss. Each paper-based isogloss (e.g. articleLgs, vplusNILgs) is the explicit set Haspelmath plots on the corresponding map. For the six features with a directly comparable WALS chapter (37A, 38A, 47A, 101A, 107A, 115A, 121A), a sibling wals*Lgs set is derived from Data.WALS.F*.allData via walsClassifies. The two are intentionally not unioned: where they disagree, that disagreement is a fact about Haspelmath's classification vs. WALS's encoding and should remain visible to readers and to bridge theorems.
• Isoglosses are Finset SAELanguage (the schema's Isogloss is a transparent abbreviation for Finset L). All filter predicates are decidable, so the four areality criteria reduce to decide against the computable rational Isogloss.density.

inductive Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage : Type

Languages surveyed by @cite{haspelmath-2001}, partitioned by their role in the four reference samples (area / cofamilial / adjacent / world).

The list follows the paper's coverage but is necessarily a subset — the maps include Sami, Mordvin, Komi, Udmurt, Mari, Tatar, Kalmyk, Lezgian, etc. We retain enough of each subgroup to make the four samples non-empty and to preserve the paper's headline findings (French/German nucleus, Celtic/Basque/Turkic margin).

• French : SAELanguage
• Italian : SAELanguage
• Spanish : SAELanguage
• Portuguese : SAELanguage
• Romanian : SAELanguage
• Catalan : SAELanguage
• German : SAELanguage
• Dutch : SAELanguage
• English : SAELanguage
• Swedish : SAELanguage
• Norwegian : SAELanguage
• Danish : SAELanguage
• Icelandic : SAELanguage
• Russian : SAELanguage
• Polish : SAELanguage
• Czech : SAELanguage
• Bulgarian : SAELanguage
• SerboCroatian : SAELanguage
• Ukrainian : SAELanguage
• Greek : SAELanguage
• Albanian : SAELanguage
• Macedonian : SAELanguage
• Latvian : SAELanguage
• Lithuanian : SAELanguage
• Hungarian : SAELanguage
• Finnish : SAELanguage
• Estonian : SAELanguage
• Welsh : SAELanguage
• Irish : SAELanguage
• Breton : SAELanguage
• Basque : SAELanguage
• Turkish : SAELanguage
• Maltese : SAELanguage
• Persian : SAELanguage
• HindiUrdu : SAELanguage
• Armenian : SAELanguage
• Lezgian : SAELanguage
• Georgian : SAELanguage
• Mongolian : SAELanguage
• Indonesian : SAELanguage
• Yoruba : SAELanguage
• Japanese : SAELanguage
• Mandarin : SAELanguage
• Swahili : SAELanguage
• Quechua : SAELanguage

@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instDecidableEqSAELanguage : DecidableEq SAELanguage

Equations

• Phenomena.ArealTypology.Studies.Haspelmath2001.instDecidableEqSAELanguage x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAELanguage.repr : SAELanguage → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAELanguage : Repr SAELanguage

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• Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAELanguage = { reprPrec := Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAELanguage.repr }

@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instFintypeSAELanguage : Fintype SAELanguage

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def Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.toWALS : SAELanguage → Option String

WALS code for each SAELanguage where one exists. WALS codes are 3-letter identifiers used by the World Atlas of Language Structures (the v2020.4 codes in Data.WALS.Features.*). Returns none for languages outside the WALS sample (currently: every SAELanguage constructor maps to a code, but the return type is Option String to accommodate future additions to SAELanguage that may not be in WALS).

Equations

• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.French.toWALS = some "fre"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Italian.toWALS = some "ita"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Spanish.toWALS = some "spa"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Portuguese.toWALS = some "por"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Romanian.toWALS = some "rom"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Catalan.toWALS = some "ctl"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.German.toWALS = some "ger"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Dutch.toWALS = some "dut"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.English.toWALS = some "eng"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Swedish.toWALS = some "swe"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Norwegian.toWALS = some "nor"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Danish.toWALS = some "dsh"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Icelandic.toWALS = some "ice"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Russian.toWALS = some "rus"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Polish.toWALS = some "pol"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Czech.toWALS = some "cze"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Bulgarian.toWALS = some "bul"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.SerboCroatian.toWALS = some "scr"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Ukrainian.toWALS = some "ukr"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Greek.toWALS = some "grk"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Albanian.toWALS = some "alb"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Macedonian.toWALS = some "mcd"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Latvian.toWALS = some "lat"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Lithuanian.toWALS = some "lit"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Hungarian.toWALS = some "hun"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Finnish.toWALS = some "fin"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Estonian.toWALS = some "est"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Welsh.toWALS = some "wel"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Irish.toWALS = some "iri"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Breton.toWALS = some "bre"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Basque.toWALS = some "bsq"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Turkish.toWALS = some "tur"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Maltese.toWALS = some "mlt"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Persian.toWALS = some "prs"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.HindiUrdu.toWALS = some "hin"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Armenian.toWALS = some "arm"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Lezgian.toWALS = some "lez"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Georgian.toWALS = some "geo"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Mongolian.toWALS = some "kha"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Indonesian.toWALS = some "ind"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Yoruba.toWALS = some "yor"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Japanese.toWALS = some "jpn"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Mandarin.toWALS = some "mnd"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Swahili.toWALS = some "swa"
• Phenomena.ArealTypology.Studies.Haspelmath2001.SAELanguage.Quechua.toWALS = some "qcu"

def Phenomena.ArealTypology.Studies.Haspelmath2001.walsClassifies {V : Type} [BEq V] (data : List (Data.WALS.Datapoint V)) (pred : V → Bool) (l : SAELanguage) : Prop

Generic WALS classifier: language l has a value in WALS chapter data that satisfies the boolean predicate pred. Returns False when l lacks a WALS code or the chapter has no entry for it.

This is the bridging primitive for all WALS-grounded isoglosses below. Used as walsClassifies Data.WALS.F121A.allData (· == .particle) to ask "does WALS 121A classify this language as having a particle comparative?". The result is propositional with a derivable Decidable instance, so it slots directly into Finset.filter.

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@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.walsClassifies.instDecidable {V : Type} [BEq V] (data : List (Data.WALS.Datapoint V)) (pred : V → Bool) (l : SAELanguage) : Decidable (walsClassifies data pred l)

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inductive Phenomena.ArealTypology.Studies.Haspelmath2001.SAEFeature : Type

The twelve "Europeanisms" identified in §2 of @cite{haspelmath-2001}. Each is the subject of one of Maps 107.1–107.12.

• definiteIndefiniteArticles : SAEFeature

  §2.1, Map 107.1: Both definite and indefinite articles present.

• relativeClausesWithRelPro : SAEFeature

  §2.2, Map 107.2: Postnominal relative clauses introduced by an inflecting relative pronoun (e.g. der/die/das, qui/que).

• havePerfect : SAEFeature

  §2.3, Map 107.3: Transitive perfect formed by 'have' + past participle.

• nominativeExperiencers : SAEFeature

  §2.4, Map 107.4: Predominant generalization of experiencer-as-nominative (English-style I like it) over inverting (it pleases me).

• participialPassive : SAEFeature

  §2.5, Map 107.5: Canonical participial passive with copula + participle.

• anticausativeProminence : SAEFeature

  §2.6, Map 107.6: Anticausative-prominent inchoative–causative pairs.

• dativeExternalPossessor : SAEFeature

  §2.7, Map 107.7: Dative external possessors (e.g. German Die Mutter wäscht dem Kind die Haare).

• negativePronounsNoVerbalNeg : SAEFeature

  §2.8, Map 107.8: Negative pronouns without obligatory verbal negation (V + NI type, e.g. French personne ne vient, German niemand kommt).

• particleComparative : SAEFeature

  §2.9, Map 107.9: Particle comparatives (English than, Latin quam).

• relativeBasedEquative : SAEFeature

  §2.10, Map 107.10: Equative constructions based on relative-clause structure (Catalan tan Z com X).

• strictAgreement : SAEFeature

  §2.11, Map 107.11: Strict subject agreement — subject affixes that cannot stand alone with referential force (German ich arbeite, not arbeite).

• intensifierReflexiveDifferentiation : SAEFeature

  §2.12, Map 107.12: Differentiated intensifier vs. reflexive forms (German selbst vs. sich, Russian sam vs. sebja).

@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instDecidableEqSAEFeature : DecidableEq SAEFeature

Equations

• Phenomena.ArealTypology.Studies.Haspelmath2001.instDecidableEqSAEFeature x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAEFeature.repr : SAEFeature → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAEFeature : Repr SAEFeature

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• Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAEFeature = { reprPrec := Phenomena.ArealTypology.Studies.Haspelmath2001.instReprSAEFeature.repr }

@[implicit_reducible]

instance Phenomena.ArealTypology.Studies.Haspelmath2001.instFintypeSAEFeature : Fintype SAEFeature

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsHasDefiniteArticle : Finset SAELanguage

WALS-derived: languages classified by F37A (Definite Articles) as having a definite article (any of the three positive values).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsHasIndefiniteArticle : Finset SAELanguage

WALS-derived: languages classified by F38A (Indefinite Articles) as having any indefinite article distinct from "no indefinite article" or "indefinite-only of an unrelated kind".

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsArticleLgs : Finset SAELanguage

WALS-derived intersection: languages with both a definite and an indefinite article in the WALS data, matching @cite{haspelmath-2001} §2.1.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.articleLgs : Finset SAELanguage

Languages with both definite and indefinite articles (Map 107.1).

The paper's reading: Romance, Germanic (except Icelandic), Greek, Albanian, Macedonian, Bulgarian (the edin particle is treated as a budding indefinite article), and Hungarian. Icelandic is excluded — it has a suffixed definite article but no indefinite article.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.relProLgs : Finset SAELanguage

Languages with relative-pronoun relative clauses (Map 107.2).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.havePerfectLgs : Finset SAELanguage

Languages with the 'have'-perfect (Map 107.3).

@cite{haspelmath-2001} §2.3 restricts this isogloss to the Romance and Germanic families plus a Balkan/peripheral fringe — Albanian, Greek, Macedonian (an innovation: ima + verbal adjective), and (parts of) Czech. Bulgarian and Serbo-Croatian retain the inherited Slavic 'be'+l-participle perfect rather than the 'have' construction.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.nomExpLgs : Finset SAELanguage

Languages with predominant nominative-experiencer coding (Map 107.4).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsPassiveLgs : Finset SAELanguage

WALS-derived parallel: languages classified by F107A (Passive Constructions) as having a passive present. F107A counts any passive (periphrastic, morphological, etc.), so this is a strict superset of Haspelmath's copula+participle criterion.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.particPassiveLgs : Finset SAELanguage

Languages with a canonical participial passive (Map 107.5).

The Romance and Germanic copula+participle pattern, extended through Slavic and Baltic and into Greek, Albanian, Macedonian, and Irish.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.anticausativeLgs : Finset SAELanguage

Anticausative-prominent languages (Map 107.6: ≥ 70% anticausative).

@cite{haspelmath-2001} §2.6 / Map 107.6 marks only the languages whose inchoative–causative pairs are anticausative-prominent on the Haspelmath 1993 figures. Romance is partially excluded (only French/Romanian register as prominent; Italian/Spanish/Portuguese fall on the causative-prominent side). The full SAE marking is German, French, Russian, Greek, Romanian, Lithuanian, English.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.dativeExtPossLgs : Finset SAELanguage

Languages with dative external possessors (Map 107.7).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsVplusNILgs : Finset SAELanguage

WALS-derived parallel: languages classified by F115A (Negative Indefinite Pronouns and Predicate Negation) as not requiring predicate negation alongside the negative pronoun. Strict subset of Haspelmath's criterion: F115A.noPredicateNegation captures only the rigid V+NI type (predominantly Germanic), whereas Haspelmath's §2.8 also includes Romance languages where the predicate negative is optional or weakening.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.vplusNILgs : Finset SAELanguage

Languages with V + NI negation (no obligatory verbal negation; Map 107.8).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsParticleCompLgs : Finset SAELanguage

WALS-derived parallel: languages classified by F121A (Comparative Constructions) as having a particle comparative.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.particleCompLgs : Finset SAELanguage

Languages with particle comparatives (Map 107.9).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.relEquativeLgs : Finset SAELanguage

Languages with relative-based equatives (Map 107.10).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsStrictAgrLgs : Finset SAELanguage

WALS-derived parallel: languages classified by F101A (Expression of Pronominal Subjects) as requiring obligatory subject pronouns.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.strictAgrLgs : Finset SAELanguage

Languages with strict subject agreement (Map 107.11).

A language has strict agreement when subject pronouns are obligatory even in the presence of subject agreement on the verb (i.e., subject-agreement affixes lack referential force on their own). Russian and the pro-drop Romance languages (Italian, Spanish, Portuguese, Romanian) fail this criterion. Welsh has rich agreement but allows pro-drop, so it is also excluded.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.walsIntRefDiffLgs : Finset SAELanguage

WALS-derived parallel: languages classified by F47A (Intensifiers and Reflexive Pronouns) as having differentiated forms.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.intRefDiffLgs : Finset SAELanguage

Languages with differentiated intensifier vs. reflexive forms (Map 107.12).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.isoglossFinset : SAEFeature → Finset SAELanguage

Dispatch from feature to its isogloss (as a Finset).

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def Phenomena.ArealTypology.Studies.Haspelmath2001.isoglossFor (f : SAEFeature) : Theories.Diachronic.Areal.Isogloss SAELanguage

Dispatch to the schema's Isogloss = Finset SAELanguage type.

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• Phenomena.ArealTypology.Studies.Haspelmath2001.isoglossFor f = Phenomena.ArealTypology.Studies.Haspelmath2001.isoglossFinset f

def Phenomena.ArealTypology.Studies.Haspelmath2001.europeanReference : Theories.Diachronic.Areal.ArealReference SAELanguage

The four reference samples for evaluating areality, per @cite{haspelmath-2001} §1.

• area: the core European languages (Romance, Germanic, Balkan, Balto-Slavic, marginal Finno-Ugric) that the paper proposes as SAE.
• cofamilial: other Indo-European branches (eastern IE: Iranian, Indic, Armenian) that lie outside the area; presence of a feature in these would point to PIE inheritance rather than areal contact.
• adjacent: geographically adjacent non-SAE languages (Celtic west, Turkic
  • Nakh-Daghestanian east, Semitic south); presence here would suggest a wider regional drift rather than a strictly European phenomenon.
• world: a small worldwide sample for the (iv) "not common worldwide" criterion.

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def Phenomena.ArealTypology.Studies.Haspelmath2001.sae : Theories.Diachronic.Areal.LinguisticArea SAELanguage SAEFeature

Standard Average European as a LinguisticArea: the 12 diagnostic features of @cite{haspelmath-2001} §2 over the European/cofamilial/ adjacent/world reference frame.

LinguisticArea does not require every diagnostic feature to satisfy the strict IsAreal predicate at any particular threshold — and indeed, several SAE features (anticausative prominence, V+NI negation, strict agreement) do not pass strict majority on Haspelmath's own data. This matches the paper: @cite{haspelmath-2001}'s actual argument runs through the cluster maps of §4, not through per-feature majority thresholds.

Per-feature IsArealAt claims for the strongly-attested subset are proved separately below; clusterScore and nucleus are computed across all 12.

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theorem Phenomena.ArealTypology.Studies.Haspelmath2001.articles_isAreal : Theories.Diachronic.Areal.IsAreal europeanReference (isoglossFor SAEFeature.definiteIndefiniteArticles)

Definite + indefinite articles (Map 107.1) is areal at the strict 1/2 threshold: ubiquitous in the area, absent from cofamilial/adjacent/world samples.

theorem Phenomena.ArealTypology.Studies.Haspelmath2001.havePerfect_isAreal : Theories.Diachronic.Areal.IsAreal europeanReference (isoglossFor SAEFeature.havePerfect)

The 'have'-perfect (Map 107.3) is areal at the strict 1/2 threshold.

theorem Phenomena.ArealTypology.Studies.Haspelmath2001.particleComp_isAreal : Theories.Diachronic.Areal.IsAreal europeanReference (isoglossFor SAEFeature.particleComparative)

Particle comparatives (Map 107.9) are areal at the strict 1/2 threshold.

theorem Phenomena.ArealTypology.Studies.Haspelmath2001.french_in_nucleus : SAELanguage.French ∈ sae.nucleus

French sits in the SAE cluster nucleus: it exhibits all 12 diagnostic features (the maximum cluster score).

theorem Phenomena.ArealTypology.Studies.Haspelmath2001.german_in_nucleus : SAELanguage.German ∈ sae.nucleus

German sits in the SAE cluster nucleus alongside French — @cite{haspelmath-2001} §4's Charlemagne Sprachbund core.

theorem Phenomena.ArealTypology.Studies.Haspelmath2001.sae_features_card : sae.features.card = 12

The SAE feature inventory has 12 features, matching Maps 107.1–107.12 of @cite{haspelmath-2001}.