Root Arity

[Coo19]: the central division of labor in Mayan root typology is that roots determine internal arguments while functional heads (v/Voice⁰) determine external arguments. Root arity — whether a root obligatorily projects a theme — is orthogonal to change entailment and to the B&K-G feature signature, and is the dimension behind the Mayan "root transitive" class: [Coo19]'s √TV for Chuj, [Luc94]'s agent-patient salient (=∅) class for Yucatec ("these roots require two arguments and refer to events involving the action of one entity on another").

Arity captures complement projection, not semantic type: an unaccusative's sole argument is semantically theme-like, but the root does not project it as a complement.

Main declarations

• Root.Arity — selectsTheme (√TV) vs noTheme

inductive Verb.Root.Arity : Type

Root-level argument selection ([Coo19]): does the root obligatorily take an internal (theme) argument? selectsTheme is Coon's √TV — the Mayan root-transitive class; noTheme covers √ITV, √NOM, √POS.

• selectsTheme : Arity
• noTheme : Arity

@[implicit_reducible]

instance Verb.Root.instDecidableEqArity : DecidableEq Arity

Equations

• Verb.Root.instDecidableEqArity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Verb.Root.instFintypeArity : Fintype Arity

Equations

• Verb.Root.instFintypeArity = { elems := { val := ↑Verb.Root.Arity.enumList, nodup := Verb.Root.Arity.enumList_nodup }, complete := Verb.Root.instFintypeArity._proof_1 }

def Verb.Root.instReprArity.repr : Arity → ℕ → Std.Format

Equations

• Verb.Root.instReprArity.repr Verb.Root.Arity.selectsTheme prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Verb.Root.Arity.selectsTheme")).group prec✝
• Verb.Root.instReprArity.repr Verb.Root.Arity.noTheme prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Verb.Root.Arity.noTheme")).group prec✝

@[implicit_reducible]

instance Verb.Root.instReprArity : Repr Arity

Equations

• Verb.Root.instReprArity = { reprPrec := Verb.Root.instReprArity.repr }

def Verb.Root.Arity.hasInternalArg : Arity → Bool

Does this root arity entail an obligatory internal argument?

Equations

• Verb.Root.Arity.selectsTheme.hasInternalArg = true
• Verb.Root.Arity.noTheme.hasInternalArg = false