Moraic trochees in Cairene Arabic ([Hay95a] §4.1.3)

Cairene Arabic stress is quantity-sensitive: where the prominence peak lands depends on syllable weight. [Hay95a] (after Mitchell 1960, McCarthy 1979a) derives the pattern by parsing the word left to right into moraic trochees — a foot is either two light syllables (σ́σ) or one heavy (H́), bimoraic either way — and placing the main stress on the head of the rightmost foot (End Rule Right). A single light syllable cannot form a foot — independently supported by the absence of CV(C) content words in the language ([McCP90]) — so a word ending in an odd light syllable leaves it stray (unfooted).

parse is that algorithm on the weight string; reading the stress off the result with the metrical grid (Prosody.Tree.columns) recovers the attested prominences — primary 3, secondary 2, unstressed 1. Quantity moves the peak: all-light kataba is stressed on the antepenult, but a heavy penult (mudarris) draws stress to the penult. (The forms kataba and ʔinkasara are Cairene Classical; [Hay95a] shows these take the same stressing as colloquial Cairene, so the analysis is label-independent.)

The grid stress-test turns on the Continuous Column Constraint ([Pri83]; [Hay95a] §3.4.2 (9), formalised as Prosody.Grid.ofTree_isContinuous): End Rule Right cannot promote the stray final light syllable, because a column raised over an unfooted syllable would have a gap — a mark on a higher layer with none below — and the grid forbids that. So the peak retracts inward off the right edge, unlike the uniform words of [Pri83] whose peak sits at the edge. The input here is the post-extrametricality weight profile; consonant/mora extrametricality ([Hay95a] (14a–b)), which adjusts final-syllable weight, is upstream.

The moraic-trochee parse

Walk the weight string left to right. A heavy σ (2 ≤ w, bimoraic) is its own foot (H́); two lights make a trochee (σ́σ), head on the left; a light with no light to pair with is left stray. Foot heads are marked as the parse builds them; markHeadFoot then promotes the rightmost foot to head foot — End Rule Right.

def Hayes1995.parseCells : Prosody.Yield → List Prosody.Tree

Parse a (post-extrametricality) weight string into moraic-trochee cells, left to right: a heavy σ is a monosyllabic foot, two lights a trochee, a lone light a stray σ. Every foot marks its own head σ; the head foot is selected by markHeadFoot.

Equations

• One or more equations did not get rendered due to their size.
• Hayes1995.parseCells [] = []
• Hayes1995.parseCells [w] = if Prosody.Syllable.Weight.heavy ≤ w then [Prosody.Tree.ft false [Prosody.Tree.σ w true]] else [Prosody.Tree.σ w]

def Hayes1995.isFootChild : Prosody.Tree → Bool

Is this ω-daughter an f-level foot?

Equations

• Hayes1995.isFootChild (RoseTree.node a children) = a.isFt

def Hayes1995.markHeadFoot : List Prosody.Tree → List Prosody.Tree

End Rule Right: mark the rightmost foot as the head foot. The first foot with no foot to its right (scanning left to right) is promoted; everything else is left untouched.

Equations

• One or more equations did not get rendered due to their size.
• Hayes1995.markHeadFoot [] = []

def Hayes1995.parse (y : Prosody.Yield) : Prosody.Tree

The Cairene parse ([Hay95a] §4.1.3): a prosodic word over moraic trochees built left to right, the rightmost foot heading the word.

Equations

• Hayes1995.parse y = Prosody.Tree.om (Hayes1995.markHeadFoot (Hayes1995.parseCells y))

Quantity-sensitive stress

The forms are [Hay95a]'s, given as their post-extrametricality weight profiles (1 = light CV, 2 = heavy CVC/CVV). Reading Tree.columns ∘ parse recovers the attested stress: the column of 3 is the primary, 2 a secondary, 1 unstressed.

def Hayes1995.kataba : Prosody.Yield

kataba ka.ta.ba 'he wrote' — all light (Cairene Classical).

Equations

• Hayes1995.kataba = [1, 1, 1]

def Hayes1995.mudarris : Prosody.Yield

mudarri(s) mu.dar.ri 'teacher' — heavy penult (colloquial).

Equations

• Hayes1995.mudarris = [1, 2, 1]

def Hayes1995.Pinkasara : Prosody.Yield

ʔinkasara ʔin.ka.sa.ra 'it got broken' — heavy initial (Cairene Classical).

Equations

• Hayes1995.Pinkasara = [2, 1, 1, 1]

theorem Hayes1995.gridColumns_kataba : (parse kataba).columns = [3, 1, 1]

Antepenultimate stress ([Hay95a] (15d), (16d)): all-light kataba parses as (ká.ta)ba, the rightmost foot heading the antepenult; the final light is stray.

theorem Hayes1995.gridColumns_mudarris : (parse mudarris).columns = [1, 3, 1]

Penultimate stress ([Hay95a] (12b), (15b)): with a heavy penult, mudarris parses as mu(dár)ri — the heavy is its own foot, rightmost, so quantity pulls the peak one syllable rightward off the antepenult.

theorem Hayes1995.gridColumns_Pinkasara : (parse Pinkasara).columns = [2, 3, 1, 1]

Restarting the count after a heavy, with secondary stress ([Hay95a] (15d), (16d)): ʔinkasara parses as (ʔìn)(ká.sa)ra — the heavy initial is its own foot (secondary 2), the count restarts, the next two lights foot, and the antepenult ka takes primary 3.

theorem Hayes1995.headTerminals_kataba : (parse kataba).headTerminals = [Prosody.Tree.σ 1 true]

The head terminal is the antepenult head σ ([LP77]): kataba's head terminal — its primary stress, Liberman & Prince's head terminal — is the head syllable of the rightmost (head) foot, read off the grid's live column as an element, not just a height (cf. gridColumns_kataba's [3, 1, 1]).

The Continuous Column Constraint blocks final promotion

Why the peak does not sit at the right edge. End Rule Right would, naively, mark the rightmost column — the stray final light. But that column rests only on its syllable-layer beat: raising a word-layer mark over it leaves the foot layer empty beneath, a gapped column the Continuous Column Constraint rules out ([Hay95a] §3.4.2 (9), §4.1.3 (17)). So the mark retracts to the rightmost foot head, and the peak lands inward. The attested grid is continuous by construction (Prosody.Grid.ofTree_isContinuous); the promotion is not.

theorem Hayes1995.toGrid_kataba : Prosody.Grid.ofTree (parse kataba) = [[true, true, true], [true, false, false], [true, false, false]]

The attested grid of kataba: a continuous staircase, the primary column of three on the antepenult, the foot layer (true row 1) supporting it, the stray final light flat.

theorem Hayes1995.cairene_grid_continuous : (Prosody.Grid.ofTree (parse kataba)).IsContinuous

The grid is well-formed ([Hay95a] §3.4.2 (9)): kataba's grid satisfies the Continuous Column Constraint — a consumer of the derived Prosody.Grid.ofTree_isContinuous, here doing the work that makes the inward peak the only legal reading.

def Hayes1995.promotedKataba : Prosody.Marks

The grid kataba would have if End Rule Right promoted the stray final light: a word-layer mark on the final column ([hayes-1995] (17), (x)(x.)) with no foot-layer mark beneath.

Equations

• Hayes1995.promotedKataba = [[true, true, true], [true, false, false], [false, false, true]]

theorem Hayes1995.promotedKataba_not_continuous : ¬promotedKataba.IsContinuous

Promoting the final light violates the CCC ([Hay95a] (16d), (17)): the final column of promotedKataba is marked on layer 2 with nothing on layer 1 — a gap. This is exactly why End Rule Right cannot reach the edge, and the peak retracts inward.

theorem Hayes1995.kataba_final_below_peak : (List.getLast? (parse kataba).columns).getD 0 < (parse kataba).columns.peak

The peak retracts off the right edge ([Hay95a] (16d)): the final stray light of kataba is strictly weaker than the primary — unlike a uniform right-strong word ([Pri83]), whose grid peaks at the edge. The blocked promotion above is why.