Maori Negation Fragment

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

Maori expresses standard negation with the word kāhore (also written kaahore). WALS classifies the negator's morpheme type as wordUnclear — in this isolating language, it is unclear whether kāhore is a verb or a particle.

Asymmetric A/Fin

WALS classifies Maori negation as asymmetric (A/Fin): the negator functions as a quasi-auxiliary that changes the finiteness structure. In the affirmative, the lexical verb is preceded by a TAM particle (e.g., kei te progressive). Under negation, kāhore takes the position of the TAM particle and the verb appears in a nominalized form with e...ana or bare.

Examples

	Affirmative	Negative
Progressive	Kei te kai ia	Kāhore ia e kai ana
Past	I kai ia	Kāhore ia i kai

def Fragments.Maori.Negation.negWord : String

The standard negation word.

Equations

• Fragments.Maori.Negation.negWord = "kāhore"

structure Fragments.Maori.Negation.NegExample : Type

A Maori negation example.

• affirmative : String
• negative : String
• glossAff : String
• glossNeg : String
• tamLabel : String
• symmetric : Bool

  Is this construction symmetric?

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

Equations

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

instance Fragments.Maori.Negation.instReprNegExample : Repr NegExample

Equations

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

instance Fragments.Maori.Negation.instBEqNegExample : BEq NegExample

Equations

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

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

Equations

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

def Fragments.Maori.Negation.progressive : NegExample

Progressive: Kei te kai ia → Kāhore ia e kai ana. Asymmetric: TAM particle replaced by negator, verb nominalized.

Equations

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

def Fragments.Maori.Negation.past : NegExample

Past: I kai ia → Kāhore ia i kai. Asymmetric: negator replaces TAM position.

Equations

• Fragments.Maori.Negation.past = { affirmative := "I kai ia", negative := "Kāhore ia i kai", glossAff := "PST eat 3SG", glossNeg := "NEG 3SG PST eat", tamLabel := "past", symmetric := false }

def Fragments.Maori.Negation.allExamples : List NegExample

Equations

• Fragments.Maori.Negation.allExamples = [Fragments.Maori.Negation.progressive, Fragments.Maori.Negation.past]

Verification

theorem Fragments.Maori.Negation.negWord_is_kahore : negWord = "kāhore"

theorem Fragments.Maori.Negation.all_examples_count : allExamples.length = 2

theorem Fragments.Maori.Negation.all_asymmetric : (allExamples.all fun (e : NegExample) => !e.symmetric) = true

All constructions are asymmetric (A/Fin).

theorem Fragments.Maori.Negation.all_negative_contain_kahore : (allExamples.all fun (e : NegExample) => Fragments.Maori.Negation.hasSubstr✝ e.negative "Kāhore") = true

All negative examples contain the negator Kāhore.