Hayes (1989): Compensatory Lengthening in Moraic Phonology

@cite{hayes-1989}

Bruce Hayes. "Compensatory Lengthening in Moraic Phonology." Linguistic Inquiry 20(2): 253–306.

This study file formalizes the empirical core of Hayes 1989: the typology of compensatory lengthening (CL) and its three central arguments for moraic theory over segmental prosodic theories (X theory, CV theory).

Core Claims Formalized

1. CL is governed by a prosodic frame provided by moraic structure (not by constraints on association line rearrangements).

2. Onset Deletion Asymmetry: CL from coda deletion is common (38 rules, 26 languages); CL from onset deletion is unattested. Moraic theory derives this from the universal non-moraicity of onsets.

3. Weight Prerequisite: CL occurs only in languages with a syllable weight distinction. Moraic theory derives this from language-specific moraic structure: only languages with bimoraic syllables have morae to strand.

4. Moraic Conservation: CL conserves total mora count. This follows automatically from the representations — no stipulation needed.

Languages Covered

• Latin (s-deletion: *kasnus → ka:nus; onset s-deletion: *smereo → mereo)
• Middle English (vowel loss: ⟨talə⟩ → [ta:l])
• Lardil (no WBP: CL impossible — derived from syllableToMoraic)
• Estonian (trimoraic syllables, Q1/Q2/Q3 quantity system)

def Hayes1989.kasnus_σ₁ : Phonology.Moraic.MoraicSyllable

Latin underlying form *kasnus 'gray': σ₁ = ⟨kas⟩ (C=onset, a=nucleus[1μ], s=coda[1μ with WBP]) σ₂ = ⟨nus⟩

With WBP, the coda ⟨s⟩ bears one mora, making σ₁ heavy.

Equations

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def Hayes1989.kasnus_σ₂ : Phonology.Moraic.MoraicSyllable

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def Hayes1989.kasnus : Phonology.Moraic.MoraicForm

Equations

• Hayes1989.kasnus = { syllables := [Hayes1989.kasnus_σ₁, Hayes1989.kasnus_σ₂] }

theorem Hayes1989.kasnus_σ₁_heavy : kasnus_σ₁.toSyllWeight = Phonology.Syllable.SyllWeight.heavy

σ₁ of *kasnus is heavy (2 morae: nucleus + coda with WBP).

theorem Hayes1989.kasnus_s_deletion_strands : (Phonology.Moraic.CL.deleteMoraic kasnus_σ₁ 1).snd = 1

After ⟨s⟩-deletion from σ₁, one mora is stranded.

def Hayes1989.kaanus_σ₁ : Phonology.Moraic.MoraicSyllable

After spreading, the vowel ⟨a⟩ becomes long (2 morae). Result: σ₁ = [kaː] with 2 morae — still heavy.

Equations

• Hayes1989.kaanus_σ₁ = match Phonology.Moraic.CL.deleteMoraic Hayes1989.kasnus_σ₁ 1 with | (σ_del, stranded) => Phonology.Moraic.CL.spreadToFill σ_del stranded Phonology.Moraic.CL.SpreadDir.left

theorem Hayes1989.kaanus_σ₁_heavy : kaanus_σ₁.toSyllWeight = Phonology.Syllable.SyllWeight.heavy

theorem Hayes1989.kasnus_conservation : kasnus_σ₁.moraCount = kaanus_σ₁.moraCount

Moraic conservation: *kasnus σ₁ and ka:nus σ₁ have the same mora count.

def Hayes1989.kosmis_σ₁ : Phonology.Moraic.MoraicSyllable

Latin *kosmis → ko:mis 'courteous': same pattern.

Equations

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theorem Hayes1989.kosmis_conservation : kosmis_σ₁.moraCount = (Phonology.Moraic.CL.spreadToFill (Phonology.Moraic.CL.deleteMoraic kosmis_σ₁ 1).fst (Phonology.Moraic.CL.deleteMoraic kosmis_σ₁ 1).snd Phonology.Moraic.CL.SpreadDir.left).moraCount

def Hayes1989.smereo_σ₁ : Phonology.Moraic.MoraicSyllable

Latin *smereo → mereo: ⟨s⟩ deletes word-initially (onset position). Since onset ⟨s⟩ has no mora, no CL occurs.

Equations

• Hayes1989.smereo_σ₁ = { onset := [Hayes1989.s✝], moraic := [{ seg := Hayes1989.e✝, morae := Phonology.Moraic.MoraCount.one }] }

theorem Hayes1989.smereo_onset_no_cl : (Phonology.Moraic.CL.deleteOnset smereo_σ₁ 0).moraCount = smereo_σ₁.moraCount

Onset deletion does not change the mora count.

theorem Hayes1989.smereo_remains_light : (Phonology.Moraic.CL.deleteOnset smereo_σ₁ 0).toSyllWeight = Phonology.Syllable.SyllWeight.light

The mora count after onset deletion is still 1 (light syllable).

def Hayes1989.tale_σ₁ : Phonology.Moraic.MoraicSyllable

Middle English ⟨talə⟩ 'tale' (original disyllabic form): σ₁ = ⟨ta⟩ (open, light), σ₂ = ⟨lə⟩ (open, light).

When word-final schwa deletes, Parasitic Delinking removes σ₂'s structure, stranding a mora. Spreading from the left fills it, lengthening ⟨a⟩.

Equations

• Hayes1989.tale_σ₁ = { onset := [Hayes1989.t✝], moraic := [{ seg := Hayes1989.a✝, morae := Phonology.Moraic.MoraCount.one }] }

def Hayes1989.tale_σ₂ : Phonology.Moraic.MoraicSyllable

Equations

• Hayes1989.tale_σ₂ = { onset := [Hayes1989.l✝], moraic := [{ seg := Hayes1989.e✝, morae := Phonology.Moraic.MoraCount.one }] }

def Hayes1989.tale_input : Phonology.Moraic.MoraicForm

Equations

• Hayes1989.tale_input = { syllables := [Hayes1989.tale_σ₁, Hayes1989.tale_σ₂] }

theorem Hayes1989.tale_input_morae : tale_input.totalMorae = 2

Input ⟨talə⟩ has 2 total morae (one per syllable).

theorem Hayes1989.tale_schwa_strands : (Phonology.Moraic.CL.deleteMoraic tale_σ₂ 0).snd = 1

After schwa deletion from σ₂, one mora is stranded.

def Hayes1989.tale_output : Phonology.Moraic.MoraicSyllable

CL result: ⟨a⟩ becomes long, ⟨l⟩ resyllabifies as coda. Output σ = [taːl] with 2 morae.

Equations

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theorem Hayes1989.tale_conservation : tale_input.totalMorae = tale_output.moraCount

Conservation: input total morae = output morae.

def Hayes1989.lardil_cvc : Phonology.Moraic.MoraicSyllable

In a language without WBP (e.g., Lardil), syllableToMoraic produces non-moraic codas. Deleting the coda strands zero morae → no CL.

Equations

• Hayes1989.lardil_cvc = Phonology.Moraic.syllableToMoraic { wbp := false } { onset := [Hayes1989.t✝], nucleus := [Hayes1989.a✝], coda := [Hayes1989.k✝] }

theorem Hayes1989.lardil_cvc_is_light : lardil_cvc.toSyllWeight = Phonology.Syllable.SyllWeight.light

theorem Hayes1989.lardil_no_cl_from_coda : (Phonology.Moraic.CL.deleteMoraic lardil_cvc 1).snd = 0

def Hayes1989.latin_cvc : Phonology.Moraic.MoraicSyllable

In a language with WBP (e.g., Latin), syllableToMoraic produces moraic codas. Deleting the coda strands one mora → CL is possible.

Equations

• Hayes1989.latin_cvc = Phonology.Moraic.syllableToMoraic { wbp := true } { onset := [Hayes1989.t✝], nucleus := [Hayes1989.a✝], coda := [Hayes1989.k✝] }

theorem Hayes1989.latin_cvc_is_heavy : latin_cvc.toSyllWeight = Phonology.Syllable.SyllWeight.heavy

theorem Hayes1989.latin_cl_from_coda : (Phonology.Moraic.CL.deleteMoraic latin_cvc 1).snd = 1

theorem Hayes1989.weight_determines_cl : (Phonology.Moraic.CL.deleteMoraic latin_cvc 1).snd ≠ (Phonology.Moraic.CL.deleteMoraic lardil_cvc 1).snd

The weight prerequisite: the difference between Latin (CL possible) and Lardil (CL impossible) is exactly the WBP parameter.

def Hayes1989.estonian_q1 : Phonology.Moraic.MoraicSyllable

Estonian Q1/Q2/Q3 (short/long/overlong) syllables demonstrate the three-way weight distinction that moraic theory encodes directly as 1μ/2μ/3μ.

Equations

• Hayes1989.estonian_q1 = { onset := [Hayes1989.k✝], moraic := [{ seg := Hayes1989.a✝, morae := Phonology.Moraic.MoraCount.one }] }

def Hayes1989.estonian_q2 : Phonology.Moraic.MoraicSyllable

Equations

• Hayes1989.estonian_q2 = { onset := [Hayes1989.k✝], moraic := [{ seg := Hayes1989.a✝, morae := Phonology.Moraic.MoraCount.two }] }

def Hayes1989.estonian_q3 : Phonology.Moraic.MoraicSyllable

Equations

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theorem Hayes1989.q1_is_light : estonian_q1.toSyllWeight = Phonology.Syllable.SyllWeight.light

theorem Hayes1989.q2_is_heavy : estonian_q2.toSyllWeight = Phonology.Syllable.SyllWeight.heavy

theorem Hayes1989.q3_is_superheavy : estonian_q3.toSyllWeight = Phonology.Syllable.SyllWeight.superheavy

theorem Hayes1989.q3_to_q2_loses_one_mora : estonian_q3.moraCount = estonian_q2.moraCount + 1

Q3 → Q2 grade shift: removing the third mora. The moraic account: Q3 has 3 morae, Q2 has 2. The shift is simply "remove the third mora," which automatically eliminates gemination when the third mora belonged to a geminate consonant.

def Hayes1989.paat_ti_q3 : Phonology.Moraic.MoraicSyllable

Estonian gemination loss: Q3 ⟨paːt.ti⟩ → Q2 ⟨paː.ti⟩. σ₁ goes from 3μ to 2μ; the geminate loses its second mora.

Equations

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def Hayes1989.paa_ti_q2 : Phonology.Moraic.MoraicSyllable

Equations

• Hayes1989.paa_ti_q2 = { onset := [Hayes1989.k✝], moraic := [{ seg := Hayes1989.a✝, morae := Phonology.Moraic.MoraCount.two }] }

theorem Hayes1989.gemination_loss_removes_mora : paat_ti_q3.moraCount = paa_ti_q2.moraCount + 1

def Hayes1989.kaanus_form : Phonology.Moraic.MoraicForm

The full phonological pipeline for Latin ka:nus after CL: moraic syllabification → weight profile → prosodic word.

This demonstrates the chain that moraic theory creates: segments + WBP → MoraicSyllable → SyllWeight → PrWd

CL output: σ₁ = [ka:] (bimoraic = heavy), σ₂ = [nus] (bimoraic = heavy). Weight profile: [H, H].

Equations

• Hayes1989.kaanus_form = { syllables := [Hayes1989.kaanus_σ₁, Hayes1989.kasnus_σ₂] }

theorem Hayes1989.kaanus_weight_profile : kaanus_form.toPrWd = { syllables := [Phonology.Syllable.SyllWeight.heavy, Phonology.Syllable.SyllWeight.heavy] }

CL output has the weight profile [heavy, heavy].

theorem Hayes1989.kaanus_satisfies_minword : kaanus_form.toPrWd.satisfiesMinWord = true

CL output satisfies the bimoraic minimal word constraint (4μ ≥ 2μ).

theorem Hayes1989.tale_minword_preserved : tale_input.toPrWd.satisfiesMinWord = true ∧ { syllables := [tale_output] }.toPrWd.satisfiesMinWord = true

Middle English: CL preserves the bimoraic minimum across syllable restructuring. Input ⟨talə⟩ = [L, L] (2μ); output [ta:l] = [H] (2μ). Both satisfy the bimoraic minimum.

This follows from Moraic Conservation (Rule (64), @cite{hayes-1989}): CL does not change total mora count, so it cannot cause a minimal word violation that wasn't already present.