Documentation

Linglib.Phenomena.SocialMeaning.Studies.Labov2006

Cambridge University Press (2nd edition, 2006; first edition 1966).

The foundational study of quantitative sociolinguistics. Labov establishes that linguistic variation in NYC is not "free" but forms a highly structured system along two independent dimensions: social class (measured by a composite socioeconomic index) and contextual style (measured by degree of attention to speech).

Core contributions formalized here #

The department store study (Ch. 3): rapid anonymous survey showing (r) stratification across Saks, Macy's, and Klein employees (Table 3.4).
Table 7.8 — Class stratification of the five variables (Ch. 7, p. 140): the centerpiece data matrix. Five phonological variables — (r), (æh), (oh), (th), (dh) — measured across three class groups (SEC 0–2, 3–5, 6–9) and multiple contextual styles. All five show both class stratification and style shifting (with one notable exception: the lower class shows no style shifting for (oh)).
The (oh) real deviation (Ch. 7, p. 146): the lower class (0–2) shows no style shifting for (oh) and deviates from class stratification. This is the only "real deviation" in the five-variable system, providing evidence that (oh) is not socially significant for the lower class. Labov: "For the phonological variables, real deviations from class stratification are consistently and reciprocally associated with real deviations from stylistic stratification."
(ing) stratification (Ch. 10, Table 10.10): the (ing) variable as a Case I-A pattern — stable stigmatized feature with monotone class and style stratification. The sc3/sc4 anomaly in casual speech for older speakers (upper-middle SEC 9 uses more /in/ than lower-middle SEC 7–8) reflects the (ing) crossover in informal contexts.
Variable typology: all five phonological variables are markers (second-order indexicals showing style shifting). (r) is a change from above; (æh) and (oh) are changes from below; (th) and (dh) are stable.

The crossover pattern #

The most famous finding is the (r) crossover: in formal styles (D, D'), the lower-middle class (SEC 6–8) exceeds the upper-middle class (SEC 9) in use of the prestige variant, overshooting the target norm. This hypercorrection is characteristic of variables undergoing change from above. The crossover requires a finer class division (4+ groups) than Table 7.8's three-way split, so we formalize it as a structural concept via StratificationProfile.hasCrossover without stipulating the exact numbers from the finer-grained data.

inductive Labov2006.ClassGroup :

Three-group classification from Table 7.8 (p. 140). The 10-point SEC index collapsed into three roughly equal groups (N: 23, 28, 30 informants respectively).

lower : ClassGroup
working : ClassGroup
middle : ClassGroup

Instances For

@[implicit_reducible]

instance Labov2006.instDecidableEqClassGroup :

DecidableEq ClassGroup

Equations

Labov2006.instDecidableEqClassGroup x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Labov2006.instReprClassGroup.repr :

ClassGroup → ℕ → Std.Format

Equations

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

Instances For

@[implicit_reducible]

instance Labov2006.instReprClassGroup :

Repr ClassGroup

Equations

Labov2006.instReprClassGroup = { reprPrec := Labov2006.instReprClassGroup.repr }

def Labov2006.instInhabitedClassGroup.default :

Equations

Labov2006.instInhabitedClassGroup.default = Labov2006.ClassGroup.lower

Instances For

@[implicit_reducible]

instance Labov2006.instInhabitedClassGroup :

Inhabited ClassGroup

Equations

Labov2006.instInhabitedClassGroup = { default := Labov2006.instInhabitedClassGroup.default }

def Labov2006.ClassGroup.toNat :

ClassGroup → ℕ

Equations

Instances For

@[implicit_reducible]

instance Labov2006.instLTClassGroup :

Equations

Labov2006.instLTClassGroup = { lt := fun (a b : Labov2006.ClassGroup) => a.toNat < b.toNat }

@[implicit_reducible]

instance Labov2006.instLEClassGroup :

Equations

Labov2006.instLEClassGroup = { le := fun (a b : Labov2006.ClassGroup) => a.toNat ≤ b.toNat }

@[implicit_reducible]

instance Labov2006.instDecidableLtClassGroup (a b : ClassGroup) :

Decidable (a < b)

Equations

Labov2006.instDecidableLtClassGroup a b = a.toNat.decLt b.toNat

@[implicit_reducible]

instance Labov2006.instDecidableLeClassGroup (a b : ClassGroup) :

Decidable (a ≤ b)

Equations

Labov2006.instDecidableLeClassGroup a b = a.toNat.decLe b.toNat

inductive Labov2006.Store :

NYC department stores ranked by prestige.

saks : Store
macys : Store
klein : Store

Instances For

@[implicit_reducible]

instance Labov2006.instDecidableEqStore :

DecidableEq Store

Equations

Labov2006.instDecidableEqStore x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Labov2006.instReprStore :

Repr Store

Equations

Labov2006.instReprStore = { reprPrec := Labov2006.instReprStore.repr }

def Labov2006.instReprStore.repr :

Store → ℕ → Std.Format

Equations

Labov2006.instReprStore.repr Labov2006.Store.saks prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.Store.saks")).group prec✝
Labov2006.instReprStore.repr Labov2006.Store.macys prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.Store.macys")).group prec✝
Labov2006.instReprStore.repr Labov2006.Store.klein prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.Store.klein")).group prec✝

Instances For

def Labov2006.Store.toNat :

Store → ℕ

Store prestige ranking: Klein < Macy's < Saks.

Equations

Instances For

@[implicit_reducible]

instance Labov2006.instLTStore :

Equations

Labov2006.instLTStore = { lt := fun (a b : Labov2006.Store) => a.toNat < b.toNat }

@[implicit_reducible]

instance Labov2006.instDecidableLtStore (a b : Store) :

Decidable (a < b)

Equations

Labov2006.instDecidableLtStore a b = a.toNat.decLt b.toNat

structure Labov2006.DeptStoreResult :

Distribution of (r) for complete responses (Table 3.4). Values are percentage of total responses in each category. N: Saks 33, Macy's 48, Klein 34.

allR1 : ℚ
someR1 : ℚ
noR1 : ℚ

Instances For

def Labov2006.deptStore :

Store → DeptStoreResult

Equations

Labov2006.deptStore Labov2006.Store.saks = { allR1 := 24, someR1 := 46, noR1 := 30 }
Labov2006.deptStore Labov2006.Store.macys = { allR1 := 22, someR1 := 37, noR1 := 41 }
Labov2006.deptStore Labov2006.Store.klein = { allR1 := 6, someR1 := 12, noR1 := 82 }

Instances For

def Labov2006.anyR1 (s : Store) :

ℚ

Any (r-1) usage = allR1 + someR1.

Equations

Labov2006.anyR1 s = (Labov2006.deptStore s).allR1 + (Labov2006.deptStore s).someR1

Instances For

theorem Labov2006.deptStore_stratification :

anyR1 Store.saks > anyR1 Store.macys ∧ anyR1 Store.macys > anyR1 Store.klein

(r) stratification: Saks > Macy's > Klein in any (r-1) usage.

def Labov2006.thStopRate :

Store → ℚ

(th) stops in fourth: Saks 0%, Macy's 4%, Klein 15%. Parallel stratification on an independent variable.

Equations

Labov2006.thStopRate Labov2006.Store.saks = 0
Labov2006.thStopRate Labov2006.Store.macys = 4 / 100
Labov2006.thStopRate Labov2006.Store.klein = 15 / 100

Instances For

theorem Labov2006.thStop_stratification :

thStopRate Store.klein > thStopRate Store.macys ∧ thStopRate Store.macys > thStopRate Store.saks

Table 7.8 is the centerpiece of the book: five phonological variables measured across three class groups (SEC 0–2, 3–5, 6–9) and multiple contextual styles. Data verified against the 2nd edition PDF (p. 140).

Index conventions (important for interpreting directions):

(r): % (r-1) usage. Higher = more prestige form. 5 styles (A–D'). Increases with formality and class.
(æh): vowel height × 10 (scale 10–60). Higher = lower vowel = closer to standard. 4 styles (A–D).
(oh): same convention as (æh). 4 styles (A–D).
(th), (dh): % non-fricative (affricate + stop) forms × 100. Higher = more stigmatized. 3 styles (A–C).

def Labov2006.r_index :

ClassGroup → Phenomena.SocialMeaning.IndexicalField.ContextualStyle → ℚ

(r) index from Table 7.8. % (r-1) usage; higher = more prestige.

Equations

Instances For

theorem Labov2006.r_class_stratified :

(∀ (s : Phenomena.SocialMeaning.IndexicalField.ContextualStyle), r_index ClassGroup.middle s > r_index ClassGroup.working s) ∧ ∀ (s : Phenomena.SocialMeaning.IndexicalField.ContextualStyle), r_index ClassGroup.working s > r_index ClassGroup.lower s

(r) class stratification: middle > working > lower at every style. Higher class uses more of the prestige form (r-1) (Figure 7.1).

def Labov2006.aeh_A :

ClassGroup → ℚ

(æh) index from Table 7.8, per style. Vowel height × 10; higher = lower vowel = closer to standard. 4 styles (A–D); no minimal pair data.

Equations

Instances For

def Labov2006.aeh_B :

ClassGroup → ℚ

Equations

Instances For

def Labov2006.aeh_C :

ClassGroup → ℚ

Equations

Labov2006.aeh_C Labov2006.ClassGroup.lower = 29
Labov2006.aeh_C Labov2006.ClassGroup.working = 61 / 2
Labov2006.aeh_C Labov2006.ClassGroup.middle = 34

Instances For

def Labov2006.aeh_D :

ClassGroup → ℚ

Equations

Instances For

(æh) class stratification: middle > working > lower at styles A–C (higher index = closer to standard = less stigmatized; Figure 7.2). At Style D (word lists), lower and working converge (both 32).

theorem Labov2006.aeh_style_shift (g : ClassGroup) :

aeh_A g < aeh_B g ∧ aeh_B g < aeh_C g ∧ aeh_C g < aeh_D g

(æh) style shifting: every class shifts toward standard (higher) in more formal styles. A < B < C < D for all three classes.

def Labov2006.oh_A :

ClassGroup → ℚ

(oh) index from Table 7.8. Same convention as (æh): higher = closer to standard. 4 styles (A–D). The lower class (0–2) shows the "real deviation" — no style shifting and inverted class stratification.

Equations

Instances For

def Labov2006.oh_B :

ClassGroup → ℚ

Equations

Labov2006.oh_B Labov2006.ClassGroup.lower = 24
Labov2006.oh_B Labov2006.ClassGroup.working = 39 / 2
Labov2006.oh_B Labov2006.ClassGroup.middle = 47 / 2

Instances For

def Labov2006.oh_C :

ClassGroup → ℚ

Equations

Labov2006.oh_C Labov2006.ClassGroup.lower = 24
Labov2006.oh_C Labov2006.ClassGroup.working = 23
Labov2006.oh_C Labov2006.ClassGroup.middle = 53 / 2

Instances For

def Labov2006.oh_D :

ClassGroup → ℚ

Equations

Labov2006.oh_D Labov2006.ClassGroup.lower = 21
Labov2006.oh_D Labov2006.ClassGroup.working = 24
Labov2006.oh_D Labov2006.ClassGroup.middle = 59 / 2

Instances For

theorem Labov2006.oh_real_deviation :

oh_D ClassGroup.lower < oh_A ClassGroup.lower ∧ oh_D ClassGroup.middle > oh_A ClassGroup.middle ∧ oh_A ClassGroup.middle < oh_A ClassGroup.lower

The (oh) real deviation (@cite{labov-2006} Ch. 7, p. 146): the lower class does not treat (oh) as a socially significant variable.

Three key properties:

No style shift: lower class D (21) < A (23) — they move AWAY from standard in formal speech (the opposite of style shifting).
Middle class style shift: middle class shifts dramatically from 20 (A) to 29.5 (D), showing normal style correction.
Inverted class stratification: in casual speech (A), the middle class (20) has LOWER (oh) values (= more raised = more NYC) than the lower class (23), inverting the expected pattern where the lower class should be most NYC.

Labov: "it is oriented neither towards the class structure nor the stylistic structure."

theorem Labov2006.oh_regular_shift_working_middle :

oh_A ClassGroup.working < oh_D ClassGroup.working ∧ oh_A ClassGroup.middle < oh_D ClassGroup.middle

Despite the real deviation, the working and middle classes show regular style shifting for (oh): values increase from A to D (shifting toward standard in more formal styles).

def Labov2006.th_A :

ClassGroup → ℚ

(th) index from Table 7.8. % non-fricative forms × 100; higher = more stigmatized. 3 styles only (A–C).

Equations

Labov2006.th_A Labov2006.ClassGroup.lower = 78
Labov2006.th_A Labov2006.ClassGroup.working = 68
Labov2006.th_A Labov2006.ClassGroup.middle = 51 / 2

Instances For

def Labov2006.th_B :

ClassGroup → ℚ

Equations

Labov2006.th_B Labov2006.ClassGroup.lower = 65
Labov2006.th_B Labov2006.ClassGroup.working = 107 / 2
Labov2006.th_B Labov2006.ClassGroup.middle = 33 / 2

Instances For

def Labov2006.th_C :

ClassGroup → ℚ

Equations

Labov2006.th_C Labov2006.ClassGroup.lower = 87 / 2
Labov2006.th_C Labov2006.ClassGroup.working = 27
Labov2006.th_C Labov2006.ClassGroup.middle = 10

Instances For

(th) class stratification: lower > working > middle at every style. The three class lines show regular separation (Figure 7.4).

theorem Labov2006.th_style_shift (g : ClassGroup) :

th_A g > th_B g ∧ th_B g > th_C g

(th) style shifting: every class uses fewer stops in more formal styles. A > B > C for all three classes.

def Labov2006.dh_A :

ClassGroup → ℚ

(dh) index from Table 7.8. Same convention as (th). 3 styles (A–C).

Equations

Labov2006.dh_A Labov2006.ClassGroup.lower = 157 / 2
Labov2006.dh_A Labov2006.ClassGroup.working = 127 / 2
Labov2006.dh_A Labov2006.ClassGroup.middle = 59 / 2

Instances For

def Labov2006.dh_B :

ClassGroup → ℚ

Equations

Labov2006.dh_B Labov2006.ClassGroup.lower = 56
Labov2006.dh_B Labov2006.ClassGroup.working = 89 / 2
Labov2006.dh_B Labov2006.ClassGroup.middle = 33 / 2

Instances For

def Labov2006.dh_C :

ClassGroup → ℚ

Equations

Instances For

(dh) class stratification: lower > working > middle at every style. Roughly parallel separation through all three styles (Figure 7.5).

theorem Labov2006.dh_style_shift (g : ClassGroup) :

dh_A g > dh_B g ∧ dh_B g > dh_C g

(dh) style shifting: every class uses fewer stops in more formal styles. A > B > C for all three classes.

inductive Labov2006.NYCVariable :

The five phonological variables of the NYC study. All five show both class stratification and style shifting in Table 7.8, making them second-order indexicals (markers).

Instances For

@[implicit_reducible]

instance Labov2006.instDecidableEqNYCVariable :

DecidableEq NYCVariable

Equations

Labov2006.instDecidableEqNYCVariable x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Labov2006.instReprNYCVariable.repr :

NYCVariable → ℕ → Std.Format

Equations

Labov2006.instReprNYCVariable.repr Labov2006.NYCVariable.r prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.NYCVariable.r")).group prec✝
Labov2006.instReprNYCVariable.repr Labov2006.NYCVariable.aeh prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.NYCVariable.aeh")).group prec✝
Labov2006.instReprNYCVariable.repr Labov2006.NYCVariable.oh prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.NYCVariable.oh")).group prec✝
Labov2006.instReprNYCVariable.repr Labov2006.NYCVariable.th prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.NYCVariable.th")).group prec✝
Labov2006.instReprNYCVariable.repr Labov2006.NYCVariable.dh prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.NYCVariable.dh")).group prec✝

Instances For

@[implicit_reducible]

instance Labov2006.instReprNYCVariable :

Repr NYCVariable

Equations

Labov2006.instReprNYCVariable = { reprPrec := Labov2006.instReprNYCVariable.repr }

def Labov2006.variableBehavior :

NYCVariable → Phenomena.SocialMeaning.IndexicalField.VariableBehavior

Classification of each variable by indexical order and change status, following @cite{labov-2006} Ch. 7.

All five variables show style shifting (Table 7.8), making them markers (second-order). The lower class's "real deviation" for (oh) means (oh) is not a marker for that group, but the variable is a marker for the community overall.

The change status reflects the direction and social mechanism:

(r): new prestige feature spreading from highest-status group → change from above
(æh): raised variant spreading from interior groups, below conscious awareness → change from below
(oh): raised variant spreading from interior groups, below conscious awareness → change from below
(th), (dh): stable stigmatized features, no change in apparent time → stable

Equations

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

Instances For

theorem Labov2006.all_markers (v : NYCVariable) :

(variableBehavior v).isMarker

All five NYC variables are markers (second-order indexicals).

theorem Labov2006.r_changeFromAbove :

(variableBehavior NYCVariable.r).change = Phenomena.SocialMeaning.IndexicalField.ChangeStatus.changeFromAbove

(r) is undergoing change from above.

theorem Labov2006.th_stable :

(variableBehavior NYCVariable.th).change = Phenomena.SocialMeaning.IndexicalField.ChangeStatus.stable

(th) and (dh) are stable.

theorem Labov2006.dh_stable :

(variableBehavior NYCVariable.dh).change = Phenomena.SocialMeaning.IndexicalField.ChangeStatus.stable

theorem Labov2006.aeh_changeFromBelow :

(variableBehavior NYCVariable.aeh).change = Phenomena.SocialMeaning.IndexicalField.ChangeStatus.changeFromBelow

(æh) and (oh) are changes from below.

theorem Labov2006.oh_changeFromBelow :

(variableBehavior NYCVariable.oh).change = Phenomena.SocialMeaning.IndexicalField.ChangeStatus.changeFromBelow

structure Labov2006.INGDatum :

Average (ing) indexes by age and social class for adult white NYC informants (Table 10.10, p. 258). The index is percent /in/ forms (0–100). SC 1 = SEC 0–2, SC 2 = SEC 3–6, SC 3 = SEC 7–8, SC 4 = SEC 9.

Note: the SC grouping for (ing) differs from the three-way split in Table 7.8 (0–2 / 3–5 / 6–9). Table 10.10 splits the middle range differently (3–6 / 7–8) and isolates SEC 9 as its own group.

sc1 : ℚ
sc2 : ℚ
sc3 : ℚ
sc4 : ℚ

Instances For

def Labov2006.ing_A_young :

(ing) in Style A (casual speech), ages 20–39 (Table 10.10).

Equations

Labov2006.ing_A_young = { sc1 := 90, sc2 := 60, sc3 := 43, sc4 := 0 }

Instances For

def Labov2006.ing_A_older :

(ing) in Style A (casual speech), ages 40+ (Table 10.10).

Equations

Labov2006.ing_A_older = { sc1 := 85, sc2 := 48, sc3 := 21, sc4 := 23 }

Instances For

def Labov2006.ing_B_young :

(ing) in Style B (careful speech), ages 20–39 (Table 10.10).

Equations

Labov2006.ing_B_young = { sc1 := 75, sc2 := 45, sc3 := 50, sc4 := 2 }

Instances For

def Labov2006.ing_B_older :

(ing) in Style B (careful speech), ages 40+ (Table 10.10).

Equations

Labov2006.ing_B_older = { sc1 := 50, sc2 := 27, sc3 := 12, sc4 := 2 }

Instances For

theorem Labov2006.ing_A_young_stratified :

ing_A_young.sc1 > ing_A_young.sc2 ∧ ing_A_young.sc2 > ing_A_young.sc3 ∧ ing_A_young.sc3 > ing_A_young.sc4

(ing) is monotonically stratified in Style A for young speakers: lower class > working > lower-middle > upper-middle.

theorem Labov2006.ing_A_older_anomaly :

ing_A_older.sc1 > ing_A_older.sc2 ∧ ing_A_older.sc2 > ing_A_older.sc3 ∧ ing_A_older.sc4 > ing_A_older.sc3

(ing) stratification in Style A for older speakers: sc1 > sc2 > sc3, but sc4 (23) > sc3 (21) — upper-middle class (SEC 9) uses MORE /in/ than lower-middle class (SEC 7–8) in casual speech. This is the (ing) crossover: the lower-middle class hypercorrects even in casual speech (dropping /in/ below the upper-middle class rate), while the upper-middle class does not.

theorem Labov2006.ing_B_older_stratified :

ing_B_older.sc1 > ing_B_older.sc2 ∧ ing_B_older.sc2 > ing_B_older.sc3 ∧ ing_B_older.sc3 ≥ ing_B_older.sc4

(ing) is monotonically stratified in Style B for older speakers. Unlike Style A, there is no sc3/sc4 anomaly.

theorem Labov2006.ing_styleShift_older :

ing_A_older.sc1 > ing_B_older.sc1 ∧ ing_A_older.sc2 > ing_B_older.sc2 ∧ ing_A_older.sc3 > ing_B_older.sc3 ∧ ing_A_older.sc4 > ing_B_older.sc4

Style shifting: each class uses less /in/ in careful (B) than casual (A) speech, for older speakers.

inductive Labov2006.INGStyle :

A : INGStyle
B : INGStyle

Instances For

@[implicit_reducible]

instance Labov2006.instDecidableEqINGStyle :

DecidableEq INGStyle

Equations

Labov2006.instDecidableEqINGStyle x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Labov2006.instReprINGStyle.repr :

INGStyle → ℕ → Std.Format

Equations

Labov2006.instReprINGStyle.repr Labov2006.INGStyle.A prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGStyle.A")).group prec✝
Labov2006.instReprINGStyle.repr Labov2006.INGStyle.B prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGStyle.B")).group prec✝

Instances For

@[implicit_reducible]

instance Labov2006.instReprINGStyle :

Equations

Labov2006.instReprINGStyle = { reprPrec := Labov2006.instReprINGStyle.repr }

inductive Labov2006.INGClass :

Four-group SEC classification used in the (ing) data. (Different grouping from ClassGroup: SC2 = SEC 3–6.)

sc1 : INGClass
sc2 : INGClass
sc3 : INGClass
sc4 : INGClass

Instances For

@[implicit_reducible]

instance Labov2006.instDecidableEqINGClass :

DecidableEq INGClass

Equations

Labov2006.instDecidableEqINGClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Labov2006.instReprINGClass.repr :

INGClass → ℕ → Std.Format

Equations

Labov2006.instReprINGClass.repr Labov2006.INGClass.sc1 prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGClass.sc1")).group prec✝
Labov2006.instReprINGClass.repr Labov2006.INGClass.sc2 prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGClass.sc2")).group prec✝
Labov2006.instReprINGClass.repr Labov2006.INGClass.sc3 prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGClass.sc3")).group prec✝
Labov2006.instReprINGClass.repr Labov2006.INGClass.sc4 prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Labov2006.INGClass.sc4")).group prec✝

Instances For

@[implicit_reducible]

instance Labov2006.instReprINGClass :

Equations

Labov2006.instReprINGClass = { reprPrec := Labov2006.instReprINGClass.repr }

def Labov2006.INGClass.toNat :

INGClass → ℕ

Equations

Instances For

@[implicit_reducible]

instance Labov2006.instLTINGClass :

Equations

Labov2006.instLTINGClass = { lt := fun (a b : Labov2006.INGClass) => a.toNat < b.toNat }

@[implicit_reducible]

instance Labov2006.instDecidableLtINGClass (a b : INGClass) :

Decidable (a < b)

Equations

Labov2006.instDecidableLtINGClass a b = a.toNat.decLt b.toNat

def Labov2006.ingProfile_older :

Phenomena.SocialMeaning.IndexicalField.StratificationProfile INGClass INGStyle

Equations

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

Instances For

(ing) style shifting (StratificationProfile predicate): every class uses less /in/ in careful (B) than casual (A) speech.

(ing) class stratification in Style B: monotonically decreasing. sc1 > sc2 > sc3 ≥ sc4. Unlike Style A, no sc3/sc4 anomaly.

def Labov2006.ing_behavior :

Phenomena.SocialMeaning.IndexicalField.VariableBehavior

(ing) is a marker (second-order): it shows both social stratification and style shifting. Classified as Case I-A by @cite{labov-2006} — a stigmatized feature not involved in change.

Equations

Labov2006.ing_behavior = { order := Phenomena.SocialMeaning.IndexicalField.IndexicalOrder.second, change := Phenomena.SocialMeaning.IndexicalField.ChangeStatus.stable }

Instances For

theorem Labov2006.ing_isMarker :

ing_behavior.isMarker