Morphological Operators and Root Classification

[Luc94] [Boh04]

A morphological operator is a language-specific process (derivational or diagnostic-inflectional) that applies to a root subject to a structural condition on the root's entailments. The collection of operators that successfully apply to a root is the root's applicability profile under the inventory.

Partitioning roots by applicability profile recovers language-specific verb-stem classifications ([Boh04]'s 5-way Yukatek cut; [Luc94]'s 3-way salience cut) as derived equivalence classes rather than stipulated enums. Typological classes thereby become predictions of (root features × operator inventory), not architectural primitives.

Operators and inventories

structure Morphology.Derivation.DerivOp : Type

A morphological operator: a name and a structural condition on roots specifying when the operator can apply.

The condition is a propositional predicate over Root, typically phrased in terms of B&K-G feature signatures, with a bundled DecidablePred instance so the predicate can drive List.filter and other computational uses. Whether such conditions are descriptively adequate is itself an empirical question — encoding them this way exposes the choice.

• name : String
• applies : Verb.Root → Prop
• decApplies : DecidablePred self.applies

@[reducible, inline]

abbrev Morphology.Derivation.Inventory : Type

An inventory: a finite list of morphological operators.

Equations

• Morphology.Derivation.Inventory = List Morphology.Derivation.DerivOp

def Morphology.Derivation.Inventory.applicableNames (inv : Inventory) (r : Verb.Root) : List String

The names of the operators in the inventory that apply to a root — the root's applicability profile.

Equations

• inv.applicableNames r = List.map (fun (x : Morphology.Derivation.DerivOp) => x.name) (List.filter (fun (op : Morphology.Derivation.DerivOp) => decide (op.applies r)) inv)

def Morphology.Derivation.Inventory.Equivalent (inv : Inventory) (r₁ r₂ : Verb.Root) : Prop

Two roots are inventory-equivalent iff every operator in the inventory either applies to both or neither.

Equations

• inv.Equivalent r₁ r₂ = ∀ op ∈ inv, op.applies r₁ ↔ op.applies r₂

@[implicit_reducible]

instance Morphology.Derivation.Inventory.instDecidableEquivalent (inv : Inventory) (r₁ r₂ : Verb.Root) : Decidable (inv.Equivalent r₁ r₂)

Equations

• inv.instDecidableEquivalent r₁ r₂ = id inferInstance