Fission (Distributed Morphology)

@cite{halle-marantz-1993}

Fission is a postsyntactic operation that splits a single terminal node into two morphological exponents. This module provides the generic framework; language-specific instantiations live in Fragments/.

The key parameters of any Fission rule:

1. Structural context: What verb-head configuration licenses Fission?
2. Person condition: Which person categories trigger Fission?
3. Realization: How is the split terminal spelled out?

structure Morphology.DM.Fission.FissionOutput : Type

The result of Fission: two clitic positions.

• cl1Form : String

  Cl₁: bears person features

• cl2Form : String

  Cl₂: bears case features

@[implicit_reducible]

instance Morphology.DM.Fission.instReprFissionOutput : Repr FissionOutput

Equations

• Morphology.DM.Fission.instReprFissionOutput = { reprPrec := Morphology.DM.Fission.instReprFissionOutput.repr }

def Morphology.DM.Fission.instReprFissionOutput.repr : FissionOutput → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Morphology.DM.Fission.instDecidableEqFissionOutput : DecidableEq FissionOutput

Equations

• Morphology.DM.Fission.instDecidableEqFissionOutput = Morphology.DM.Fission.instDecidableEqFissionOutput.decEq

def Morphology.DM.Fission.instDecidableEqFissionOutput.decEq (x✝ x✝¹ : FissionOutput) : Decidable (x✝ = x✝¹)

Equations

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

structure Morphology.DM.Fission.FissionRule (Person : Type) : Type

A Fission rule parameterized over a person category type.

Language-specific modules instantiate this with their own person type, structural context, and realization function.

• contextOk : List Minimalist.VerbHead → Bool

  Structural context check (e.g., inchoative = vGO ∧ vBE).

• personOk : Person → Bool

  Person/number condition (e.g., [+PART, +SING]).

• realize : Person → FissionOutput

  Realization: map person category to the two clitic forms.

def Morphology.DM.Fission.applyFission {Person : Type} (rule : FissionRule Person) (p : Person) (heads : List Minimalist.VerbHead) : Option FissionOutput

Apply Fission given a rule, a person category, and a verb-head list. Returns none if either the structural or person condition fails.

Equations

• Morphology.DM.Fission.applyFission rule p heads = if (rule.contextOk heads && rule.personOk p) = true then some (rule.realize p) else none

structure Morphology.DM.Fission.PFMarkingCondition : Type

A PF well-formedness condition: checks whether a list of overt clitic forms satisfies a language-specific phonological requirement (e.g., anticausative marking in Spanish).

• isSatisfied : List String → Bool

def Morphology.DM.Fission.fissionSatisfiesPF {Person : Type} (rule : FissionRule Person) (pf : PFMarkingCondition) (p : Person) (heads : List Minimalist.VerbHead) : Bool

When Fission produces a clitic that satisfies a PF condition, another overt marker (e.g., SE) may be optional.

Equations

• Morphology.DM.Fission.fissionSatisfiesPF rule pf p heads = match Morphology.DM.Fission.applyFission rule p heads with | some output => pf.isSatisfied [output.cl1Form] | none => false