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 Minimalism.Morphology.FissionOutput : Type

The result of Fission: two clitic positions.

• cl1Form : String

  Cl₁: bears person features

• cl2Form : String

  Cl₂: bears case features

instance Minimalism.Morphology.instReprFissionOutput : Repr FissionOutput

Equations

• Minimalism.Morphology.instReprFissionOutput = { reprPrec := Minimalism.Morphology.instReprFissionOutput.repr }

def Minimalism.Morphology.instReprFissionOutput.repr : FissionOutput → ℕ → Std.Format

Equations

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

instance Minimalism.Morphology.instBEqFissionOutput : BEq FissionOutput

Equations

• Minimalism.Morphology.instBEqFissionOutput = { beq := Minimalism.Morphology.instBEqFissionOutput.beq }

def Minimalism.Morphology.instBEqFissionOutput.beq : FissionOutput → FissionOutput → Bool

Equations

• Minimalism.Morphology.instBEqFissionOutput.beq { cl1Form := a, cl2Form := a_1 } { cl1Form := b, cl2Form := b_1 } = (a == b && a_1 == b_1)
• Minimalism.Morphology.instBEqFissionOutput.beq x✝¹ x✝ = false

instance Minimalism.Morphology.instDecidableEqFissionOutput : DecidableEq FissionOutput

Equations

• Minimalism.Morphology.instDecidableEqFissionOutput = Minimalism.Morphology.instDecidableEqFissionOutput.decEq

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

Equations

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

structure Minimalism.Morphology.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 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 Minimalism.Morphology.applyFission {Person : Type} (rule : FissionRule Person) (p : Person) (heads : List 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

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

structure Minimalism.Morphology.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 Minimalism.Morphology.fissionSatisfiesPF {Person : Type} (rule : FissionRule Person) (pf : PFMarkingCondition) (p : Person) (heads : List VerbHead) : Bool

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

Equations

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