Imbabura Quechua Negation Fragment

@cite{miestamo-2005} @cite{dryer-haspelmath-2013}

Imbabura Quechua expresses standard negation with the preverbal particle mana, optionally reinforced by the suffix -chu on the verb.

SymAsy: Symmetric and Asymmetric (A/NonReal)

WALS classifies Imbabura Quechua as both symmetric and asymmetric:

• Symmetric: in some constructions, mana simply negates without further structural change.

• Asymmetric (A/NonReal): in other constructions, negation triggers obligatory -chu marking on the verb. -chu is a validator enclitic that also appears in polar interrogatives; it expresses assertion authority and certainty (@cite{miestamo-2005} p. 158). Its use in negatives introduces a non-realized category absent from affirmatives.

The A/NonReal asymmetry is paradigmatic: the negative paradigm obligatorily includes a validator category (-chu) that the affirmative lacks. The clause structure itself does not change (no constructional asymmetry).

def Fragments.Quechua.Negation.negParticle : String

The standard negation particle.

Equations

• Fragments.Quechua.Negation.negParticle = "mana"

def Fragments.Quechua.Negation.chuSuffix : String

The validator enclitic triggered in negative (and interrogative) contexts. Glossed as VAL (validator); shared with polar questions.

Equations

• Fragments.Quechua.Negation.chuSuffix = "-chu"

structure Fragments.Quechua.Negation.NegExample : Type

An Imbabura Quechua negation example.

• affirmative : String
• negative : String
• glossAff : String
• glossNeg : String
• requiresChu : Bool

  Does this construction require -chu?

• symmetric : Bool

  Is this construction symmetric?

instance Fragments.Quechua.Negation.instReprNegExample : Repr NegExample

Equations

• Fragments.Quechua.Negation.instReprNegExample = { reprPrec := Fragments.Quechua.Negation.instReprNegExample.repr }

def Fragments.Quechua.Negation.instReprNegExample.repr : NegExample → Nat → Std.Format

Equations

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

def Fragments.Quechua.Negation.instBEqNegExample.beq : NegExample → NegExample → Bool

Equations

• One or more equations did not get rendered due to their size.
• Fragments.Quechua.Negation.instBEqNegExample.beq x✝¹ x✝ = false

instance Fragments.Quechua.Negation.instBEqNegExample : BEq NegExample

Equations

• Fragments.Quechua.Negation.instBEqNegExample = { beq := Fragments.Quechua.Negation.instBEqNegExample.beq }

def Fragments.Quechua.Negation.present : NegExample

Simple present: asymmetric (requires -chu, A/NonReal).

Equations

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

def Fragments.Quechua.Negation.progressive : NegExample

Progressive: symmetric (mana alone suffices).

Equations

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

def Fragments.Quechua.Negation.past : NegExample

Past: asymmetric (requires -chu).

Equations

• Fragments.Quechua.Negation.past = { affirmative := "shamurca", negative := "mana shamurca-chu", glossAff := "come-PST", glossNeg := "NEG come-PST-VAL", requiresChu := true, symmetric := false }

def Fragments.Quechua.Negation.allExamples : List NegExample

Equations

• Fragments.Quechua.Negation.allExamples = [Fragments.Quechua.Negation.present, Fragments.Quechua.Negation.progressive, Fragments.Quechua.Negation.past]

Verification

theorem Fragments.Quechua.Negation.negParticle_is_mana : negParticle = "mana"

theorem Fragments.Quechua.Negation.chuSuffix_is_chu : chuSuffix = "-chu"

theorem Fragments.Quechua.Negation.example_count : allExamples.length = 3

theorem Fragments.Quechua.Negation.symasy_distribution : (List.filter (fun (x : NegExample) => x.symmetric) allExamples).length = 1 ∧ (List.filter (fun (e : NegExample) => !e.symmetric) allExamples).length = 2

Mixed: some symmetric, some asymmetric = SymAsy.

theorem Fragments.Quechua.Negation.asymmetric_iff_chu : (allExamples.all fun (e : NegExample) => e.symmetric == !e.requiresChu) = true

Asymmetric constructions are exactly those requiring -chu.