Tagalog Nasal Substitution Data @cite{zuraw-2010}

Empirical data for Tagalog nasal substitution (@cite{zuraw-2010}), the running case study in @cite{magri-2025}'s analysis of constraint interaction in probabilistic phonology.

The process

When a nasal-final prefix (maŋ- or paŋ-) is concatenated with an obstruent-initial stem, the nasal and the obstruent may coalesce into a single consonant retaining the nasality of the former and the place of the latter (@cite{zuraw-2010}):

• maŋ+bigáj → mamigáj 'to distribute' (nasal substitution)
• paŋ+tabój → pantabój 'to goad' (place assimilation, no substitution)

Data organization

• § 1: Stem consonants — the six stem-initial obstruents from @cite{zuraw-2010}'s factorial typology
• § 2: Dictionary rates — text-verified substitution rates from the Tagalog dictionary study
• § 3–7: 2×2 square — @cite{magri-2025}'s arrangement of four underlying concatenations for probabilistic analysis

inductive Fragments.Tagalog.Phonology.StemC : Type

The six stem-initial obstruents in the nasal substitution typology. Coalescence maps each to its homorganic nasal: p→m, t→n, k→ŋ, b→m, d→n, g→ŋ.

• p : StemC
• t : StemC
• k : StemC
• b : StemC
• d : StemC
• g : StemC

instance Fragments.Tagalog.Phonology.instDecidableEqStemC : DecidableEq StemC

Equations

• Fragments.Tagalog.Phonology.instDecidableEqStemC x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Tagalog.Phonology.instBEqStemC.beq : StemC → StemC → Bool

Equations

• Fragments.Tagalog.Phonology.instBEqStemC.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Tagalog.Phonology.instBEqStemC : BEq StemC

Equations

• Fragments.Tagalog.Phonology.instBEqStemC = { beq := Fragments.Tagalog.Phonology.instBEqStemC.beq }

instance Fragments.Tagalog.Phonology.instReprStemC : Repr StemC

Equations

• Fragments.Tagalog.Phonology.instReprStemC = { reprPrec := Fragments.Tagalog.Phonology.instReprStemC.repr }

def Fragments.Tagalog.Phonology.instReprStemC.repr : StemC → ℕ → Std.Format

Equations

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

inductive Fragments.Tagalog.Phonology.SubSt : Type

Whether nasal substitution applies.

• yes : SubSt
• no : SubSt

instance Fragments.Tagalog.Phonology.instDecidableEqSubSt : DecidableEq SubSt

Equations

• Fragments.Tagalog.Phonology.instDecidableEqSubSt x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Fragments.Tagalog.Phonology.instBEqSubSt : BEq SubSt

Equations

• Fragments.Tagalog.Phonology.instBEqSubSt = { beq := Fragments.Tagalog.Phonology.instBEqSubSt.beq }

def Fragments.Tagalog.Phonology.instBEqSubSt.beq : SubSt → SubSt → Bool

Equations

• Fragments.Tagalog.Phonology.instBEqSubSt.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Fragments.Tagalog.Phonology.instReprSubSt.repr : SubSt → ℕ → Std.Format

Equations

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instance Fragments.Tagalog.Phonology.instReprSubSt : Repr SubSt

Equations

• Fragments.Tagalog.Phonology.instReprSubSt = { reprPrec := Fragments.Tagalog.Phonology.instReprSubSt.repr }

@[reducible, inline]

abbrev Fragments.Tagalog.Phonology.NSCand : Type

A candidate is a stem consonant paired with a substitution decision.

Equations

• Fragments.Tagalog.Phonology.NSCand = (Fragments.Tagalog.Phonology.StemC × Fragments.Tagalog.Phonology.SubSt)

def Fragments.Tagalog.Phonology.dictRate_p : ℚ

Dictionary substitution rate for voiceless labial p (253/263 ≈ 96.2%). Text-verified from @cite{zuraw-2010}'s discussion of the Tagalog dictionary study.

Equations

• Fragments.Tagalog.Phonology.dictRate_p = 253 / 263

def Fragments.Tagalog.Phonology.dictRate_b : ℚ

Dictionary substitution rate for voiced labial b (177/277 ≈ 63.9%). Text-verified from @cite{zuraw-2010}'s discussion of the Tagalog dictionary study.

Equations

• Fragments.Tagalog.Phonology.dictRate_b = 177 / 277

theorem Fragments.Tagalog.Phonology.dict_voicing_labial : dictRate_p > dictRate_b

Voicing effect in dictionary data (labial place): voiceless p has a higher substitution rate than voiced b.

inductive Fragments.Tagalog.Phonology.NasalSubInput : Type

The four underlying concatenations from @cite{magri-2025}'s 2×2 square arrangement. These cross two prefixes (maŋ-, paŋ-) with two of the six stem consonants (b, k).

• mang_b : NasalSubInput
• mang_k : NasalSubInput
• pang_b : NasalSubInput
• pang_k : NasalSubInput

instance Fragments.Tagalog.Phonology.instDecidableEqNasalSubInput : DecidableEq NasalSubInput

Equations

• Fragments.Tagalog.Phonology.instDecidableEqNasalSubInput x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Fragments.Tagalog.Phonology.instBEqNasalSubInput : BEq NasalSubInput

Equations

• Fragments.Tagalog.Phonology.instBEqNasalSubInput = { beq := Fragments.Tagalog.Phonology.instBEqNasalSubInput.beq }

def Fragments.Tagalog.Phonology.instBEqNasalSubInput.beq : NasalSubInput → NasalSubInput → Bool

Equations

• Fragments.Tagalog.Phonology.instBEqNasalSubInput.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Fragments.Tagalog.Phonology.instReprNasalSubInput.repr : NasalSubInput → ℕ → Std.Format

Equations

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instance Fragments.Tagalog.Phonology.instReprNasalSubInput : Repr NasalSubInput

Equations

• Fragments.Tagalog.Phonology.instReprNasalSubInput = { reprPrec := Fragments.Tagalog.Phonology.instReprNasalSubInput.repr }

inductive Fragments.Tagalog.Phonology.NasalSubOutput : Type

The two surface variants for each underlying form.

• yes : NasalSubOutput

  YES: nasal substitution applies — nasal and obstruent coalesce.

• no : NasalSubOutput

  NO: nasal substitution does not apply — place assimilation only.

instance Fragments.Tagalog.Phonology.instDecidableEqNasalSubOutput : DecidableEq NasalSubOutput

Equations

• Fragments.Tagalog.Phonology.instDecidableEqNasalSubOutput x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Tagalog.Phonology.instBEqNasalSubOutput.beq : NasalSubOutput → NasalSubOutput → Bool

Equations

• Fragments.Tagalog.Phonology.instBEqNasalSubOutput.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Tagalog.Phonology.instBEqNasalSubOutput : BEq NasalSubOutput

Equations

• Fragments.Tagalog.Phonology.instBEqNasalSubOutput = { beq := Fragments.Tagalog.Phonology.instBEqNasalSubOutput.beq }

def Fragments.Tagalog.Phonology.instReprNasalSubOutput.repr : NasalSubOutput → ℕ → Std.Format

Equations

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

instance Fragments.Tagalog.Phonology.instReprNasalSubOutput : Repr NasalSubOutput

Equations

• Fragments.Tagalog.Phonology.instReprNasalSubOutput = { reprPrec := Fragments.Tagalog.Phonology.instReprNasalSubOutput.repr }

instance Fragments.Tagalog.Phonology.instFintypeNasalSubInput : Fintype NasalSubInput

Equations

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

instance Fragments.Tagalog.Phonology.instFintypeNasalSubOutput : Fintype NasalSubOutput

Equations

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@[reducible, inline]

abbrev Fragments.Tagalog.Phonology.NasalSubCandidate : Type

Input–output pair for constraint evaluation.

Equations

• Fragments.Tagalog.Phonology.NasalSubCandidate = (Fragments.Tagalog.Phonology.NasalSubInput × Fragments.Tagalog.Phonology.NasalSubOutput)

def Fragments.Tagalog.Phonology.nasalSubSquare : Theories.Phonology.HarmonicGrammar.Square NasalSubInput

The 2×2 square of underlying forms: prefix × stem-initial obstruent.

Equations

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

def Fragments.Tagalog.Phonology.starNC : NasalSubCandidate → ℕ

C₁ = *NC: one violation for every nasal–obstruent sequence. Violated by NO (place assimilation preserves the NC sequence).

Equations

• Fragments.Tagalog.Phonology.starNC (fst, Fragments.Tagalog.Phonology.NasalSubOutput.no) = 1
• Fragments.Tagalog.Phonology.starNC (fst, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 0

def Fragments.Tagalog.Phonology.starNCvoiceless : NasalSubCandidate → ℕ

C₂ = *NC̥: one violation for nasal followed by voiceless obstruent. Violated by NO only for voiceless stems (k).

Equations

• Fragments.Tagalog.Phonology.starNCvoiceless (Fragments.Tagalog.Phonology.NasalSubInput.mang_k, Fragments.Tagalog.Phonology.NasalSubOutput.no) = 1
• Fragments.Tagalog.Phonology.starNCvoiceless (Fragments.Tagalog.Phonology.NasalSubInput.pang_k, Fragments.Tagalog.Phonology.NasalSubOutput.no) = 1
• Fragments.Tagalog.Phonology.starNCvoiceless x✝ = 0

def Fragments.Tagalog.Phonology.starStemVelar : NasalSubCandidate → ℕ

C₃ = *[stemη]: one violation when stem starts with a velar nasal. Violated by YES for k-initial stems (coalesced ŋ is velar).

Equations

• Fragments.Tagalog.Phonology.starStemVelar (Fragments.Tagalog.Phonology.NasalSubInput.mang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.starStemVelar (Fragments.Tagalog.Phonology.NasalSubInput.pang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.starStemVelar x✝ = 0

def Fragments.Tagalog.Phonology.starStemVelarCoronal : NasalSubCandidate → ℕ

C₄ = *[stemη]∕n: one violation when stem starts with a velar or coronal nasal. In the b vs k square, this coincides with C₃ (bilabial m is neither velar nor coronal).

Equations

• Fragments.Tagalog.Phonology.starStemVelarCoronal (Fragments.Tagalog.Phonology.NasalSubInput.mang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.starStemVelarCoronal (Fragments.Tagalog.Phonology.NasalSubInput.pang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.starStemVelarCoronal x✝ = 0

def Fragments.Tagalog.Phonology.unifMang : NasalSubCandidate → ℕ

C₅ = UNIFORMITY(maŋ): one violation when the maŋ- prefix coalesces with the stem-initial obstruent. Only relevant for maŋ- forms.

Equations

• Fragments.Tagalog.Phonology.unifMang (Fragments.Tagalog.Phonology.NasalSubInput.mang_b, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.unifMang (Fragments.Tagalog.Phonology.NasalSubInput.mang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.unifMang x✝ = 0

def Fragments.Tagalog.Phonology.unifPang : NasalSubCandidate → ℕ

C₆ = UNIFORMITY(paŋ): one violation when the paŋ- prefix coalesces. Only relevant for paŋ- forms.

Equations

• Fragments.Tagalog.Phonology.unifPang (Fragments.Tagalog.Phonology.NasalSubInput.pang_b, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.unifPang (Fragments.Tagalog.Phonology.NasalSubInput.pang_k, Fragments.Tagalog.Phonology.NasalSubOutput.yes) = 1
• Fragments.Tagalog.Phonology.unifPang x✝ = 0

def Fragments.Tagalog.Phonology.constraints : Fin 6 → NasalSubCandidate → ℕ

The six constraints as a Fin 6-indexed family.

Equations

• Fragments.Tagalog.Phonology.constraints ⟨0, isLt⟩ = Fragments.Tagalog.Phonology.starNC
• Fragments.Tagalog.Phonology.constraints ⟨1, isLt⟩ = Fragments.Tagalog.Phonology.starNCvoiceless
• Fragments.Tagalog.Phonology.constraints ⟨2, isLt⟩ = Fragments.Tagalog.Phonology.starStemVelar
• Fragments.Tagalog.Phonology.constraints ⟨3, isLt⟩ = Fragments.Tagalog.Phonology.starStemVelarCoronal
• Fragments.Tagalog.Phonology.constraints ⟨4, isLt⟩ = Fragments.Tagalog.Phonology.unifMang
• Fragments.Tagalog.Phonology.constraints ⟨5, isLt⟩ = Fragments.Tagalog.Phonology.unifPang

def Fragments.Tagalog.Phonology.violDiffProfile : Fin 6 → NasalSubInput → ℤ

Violation difference Δₖ(x) = Cₖ(x, NO) − Cₖ(x, YES) for each underlying form x and constraint k. Positive Δ favors YES.

Equations

• Fragments.Tagalog.Phonology.violDiffProfile ⟨0, isLt⟩ x✝ = 1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨1, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.mang_k = 1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨1, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.pang_k = 1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨1, isLt⟩ x✝ = 0
• Fragments.Tagalog.Phonology.violDiffProfile ⟨2, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.mang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨2, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.pang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨2, isLt⟩ x✝ = 0
• Fragments.Tagalog.Phonology.violDiffProfile ⟨3, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.mang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨3, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.pang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨3, isLt⟩ x✝ = 0
• Fragments.Tagalog.Phonology.violDiffProfile ⟨4, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.mang_b = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨4, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.mang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨4, isLt⟩ x✝ = 0
• Fragments.Tagalog.Phonology.violDiffProfile ⟨5, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.pang_b = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨5, isLt⟩ Fragments.Tagalog.Phonology.NasalSubInput.pang_k = -1
• Fragments.Tagalog.Phonology.violDiffProfile ⟨5, isLt⟩ x✝ = 0

def Fragments.Tagalog.Phonology.nasalSubRate : NasalSubInput → ℚ

Empirical rates of nasal substitution from @cite{zuraw-2010} type frequencies, arranged per @cite{magri-2025}'s 2×2 square (@cite{zuraw-hayes-2017}). The four cells correspond to the two extreme prefixes (maŋ-other = highest rate, paŋ-res = lowest) crossed with /b/ (voiced) and /k/ (voiceless).

Equations

• Fragments.Tagalog.Phonology.nasalSubRate Fragments.Tagalog.Phonology.NasalSubInput.mang_b = 916 / 1000
• Fragments.Tagalog.Phonology.nasalSubRate Fragments.Tagalog.Phonology.NasalSubInput.mang_k = 993 / 1000
• Fragments.Tagalog.Phonology.nasalSubRate Fragments.Tagalog.Phonology.NasalSubInput.pang_b = 434 / 1000
• Fragments.Tagalog.Phonology.nasalSubRate Fragments.Tagalog.Phonology.NasalSubInput.pang_k = 909 / 1000

def Fragments.Tagalog.Phonology.deltaR : Fin 6 → NasalSubInput → ℝ

The violation differences cast to ℝ, for use with me_predicts_hz.

Equations

• Fragments.Tagalog.Phonology.deltaR k x = ↑(Fragments.Tagalog.Phonology.violDiffProfile k x)

theorem Fragments.Tagalog.Phonology.violDiff_independence : Theories.Phonology.HarmonicGrammar.ViolDiffIndependence deltaR nasalSubSquare

Violation difference independence: the violation differences Δₖ satisfy ViolDiffIndependence on the nasal substitution square.

• C₁–C₄ (markedness): Δₖ is the same for /maŋ+X/ and /paŋ+X/ (insensitive to prefix = row)
• C₅–C₆ (faithfulness): Δₖ is the same for /X+b/ and /X+k/ (insensitive to stem = column)

This is a data-level property of the constraint violation profiles, used by both @cite{zuraw-hayes-2017} and @cite{magri-2025}.