Hayes (1995): Metrical Stress Theory

This file formalizes the moraic-trochee analysis of Cairene Arabic stress in Section 4.1.3 of Hayes's book: the word is parsed from left to right into moraic trochees, a heavy syllable or two lights (13), and End Rule Right builds the word layer over the rightmost foot (16). parse is that construction over the post-extrametricality weight string, Tree.columns reads the stress off its grid, and the prominences of (12) follow, quantity moving the peak from the antepenult of kátaba to the penult of mudárris and a heavy syllable restarting the alternating count (parseCells_heavy). A single light syllable cannot form a foot, so the stray final light of an odd-parity word is beyond the reach of End Rule Right: promoting it would gap its grid column, which the Continuous Column Constraint of Section 3.4.2 forbids (promotedKataba_not_continuous), while the attested grid is continuous by construction.

Implementation notes

• The input is the weight profile after Consonant and Mora Extrametricality (14a–b), which demote a final CVC, and a final CV: of a Classical form, to light; those rules are upstream of the parse.

References

• [Hay95b]
• [Pri83]
• [McCP90]

The moraic-trochee parse

A heavy syllable (2 ≤ w, bimoraic) is its own foot, two lights make a trochee with the head on the left, and 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

Foot Construction (14c) parses a weight string from left to right into moraic trochees.

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]

theorem Hayes1995.parseCells_heavy {w : Prosody.Syllable.Weight} (hw : Prosody.Syllable.Weight.heavy ≤ w) (rest : Prosody.Yield) : parseCells (w :: rest) = Prosody.Tree.ft false [Prosody.Tree.σ w true] :: parseCells rest

A heavy syllable is a foot of its own and restarts the count, since it is necessarily followed by a foot boundary (Section 4.1.3, after (15)).

def Hayes1995.isFootChild : Prosody.Tree → Bool

Is this ω-daughter an f-level foot?

Equations

• Hayes1995.isFootChild (RoseTree.node a children) = decide (a.level = Prosody.Level.ft)

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

By End Rule Right (16), the first foot with no foot to its right is promoted to head foot.

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 builds a prosodic word over moraic trochees from left to right, with the rightmost foot heading the word.

Equations

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

Quantity-sensitive stress

The forms are those of (12), as their post-extrametricality weight profiles (1 light CV, 2 heavy). Tree.columns ∘ parse recovers the stress: the column of 3 is the primary, 2 a secondary, 1 unstressed.

def Hayes1995.kataba : Prosody.Yield

kátaba 'he wrote' (Classical) is all light.

Equations

• Hayes1995.kataba = [1, 1, 1]

def Hayes1995.mudarris : Prosody.Yield

mudárris 'teacher' has a heavy penult, the final CVC demoted to light.

Equations

• Hayes1995.mudarris = [1, 2, 1]

def Hayes1995.Pinkasara : Prosody.Yield

ʔinkásara 'it got broken' (Classical) has a heavy initial.

Equations

• Hayes1995.Pinkasara = [2, 1, 1, 1]

def Hayes1995.katabt : Prosody.Yield

katábt 'I wrote' has a superheavy final, heavy after Consonant Extrametricality.

Equations

• Hayes1995.katabt = [1, 2]

def Hayes1995.mudarrisit : Prosody.Yield

mudarrísit 'teacher (f. construct)' has a heavy second syllable and the final CVC light.

Equations

• Hayes1995.mudarrisit = [1, 2, 1, 1]

def Hayes1995.Padwiyatuhu : Prosody.Yield

ʔadwiyatúhu 'his drugs (nom.)' (Classical) has a heavy initial, then an even run of lights.

Equations

• Hayes1995.Padwiyatuhu = [2, 1, 1, 1, 1]

def Hayes1995.sajaratuhuma : Prosody.Yield

šaǰaratuhúma: 'their (dual) tree (nom.)' (Classical) has six lights, the final long-vowel syllable light by Mora Extrametricality.

Equations

• Hayes1995.sajaratuhuma = [1, 1, 1, 1, 1, 1]

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

kátaba has antepenultimate stress (12c.ii), (15d), parsing as (ká.ta)ba with the rightmost foot heading the antepenult and the final light stray.

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

mudárris has penultimate stress on a heavy penult (12b), (15b), parsing as mu(dár)ri.

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

The count restarts after a heavy, with secondary stress (12c.ii), (15d), so ʔinkásara parses as (ʔìn)(ká.sa)ra.

theorem Hayes1995.gridColumns_katabt : (parse katabt).columns = [1, 3]

katábt has final stress on a superheavy (12a), (15a), parsing as ka(tábt).

theorem Hayes1995.gridColumns_mudarrisit : (parse mudarrisit).columns = [1, 2, 3, 1]

mudarrísit has a stray initial light before a heavy (12c.i), (15c), parsing as mu(dàr)(rí.si)t.

theorem Hayes1995.gridColumns_Padwiyatuhu : (parse Padwiyatuhu).columns = [2, 2, 1, 3, 1]

ʔadwiyatúhu shows even parity after a heavy (12c.i), (15c), parsing as (ʔàd)(wì.ya)(tú.hu).

theorem Hayes1995.gridColumns_sajaratuhuma : (parse sajaratuhuma).columns = [2, 1, 2, 1, 3, 1]

šaǰaratuhúma: shows even parity from the left edge (12c.i), (15c), parsing as (šà.ja)(rà.tu)(hú.ma).

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

The head terminal of kátaba is the head syllable of its head foot, read off the grid's spine as an element rather than a height.

The Continuous Column Constraint blocks final promotion

End Rule Right would, naively, mark the rightmost column, the stray final light of kátaba. That column rests only on its syllable-layer beat: a word-layer mark over it would leave the foot layer empty beneath, the gapped column of (17) that the Continuous Column Constraint (9) of Section 3.4.2 rules out, so the mark falls on the rightmost foot head and the peak lands inward.

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

The attested grid of kátaba is a continuous staircase, with the primary column of three on the antepenult, the foot layer supporting it, and the stray final light flat.

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

The grid of kátaba satisfies the Continuous Column Constraint, as every grid read off a tree does (Prosody.Grid.ofTree_isContinuous).

def Hayes1995.promotedKataba : Prosody.Marks

If End Rule Right promoted the stray final light, (17), kátaba would have this grid, with a word-layer mark on the final column and 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 Continuous Column Constraint, since the final column of promotedKataba is marked on layer 2 with nothing on layer 1.

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

The peak retracts off the right edge. The final stray light of kátaba is strictly weaker than the primary, unlike the uniform right-strong words of [Pri83], whose grids peak at the edge.