Directional constraints as position-indexed blocks

[Lam22d]'s directional constraint evaluation, realized in the canonical constraint substrate. A directional constraint maps each candidate to a per-position violation vector compared lexicographically (Eisner 2000; [Lam22d]). The key observation ([Lam22d] §1.3) is that "a locus at position i relates to one at i+1 exactly as a higher-ranked constraint relates to a lower one … violation vectors are ordered lexicographically, which is exactly how candidates are ordered with respect to an entire constraint set in OT". So a directional constraint with single-segment loci over a length-preserving GEN is a position-indexed block of binary constraints, spliced into a ranking and compared under the canonical ViolationProfile lex order (Core.Optimization.Evaluation.lexLE_ofFn) — no new mechanism beyond the CON/ViolationProfile substrate already present.

directionalBlock n locus is that block: at each position i < n it flags whether locus i holds. Splice it into a ranking forward for left-to-right evaluation (⇒), or .reverse for right-to-left (⇐) — "the positions are reversed in the violation vector" ([Lam22d] §1.3, Fig 1.9).

Main definitions

• directionalBlock — the position-indexed block of binary constraints.

Consumers

• Tone.starFloatBlock — *FLOAT directional float deletion ([McPL26]).
• Lamont2022c.parseSigmaBlock — Parse(σ) directional footing ([Lam22b]).

Scope

This covers the single-segment-loci, length-preserving case — both current consumers (a floating tone / an unfooted syllable is a single position, and neither GEN changes the position count). [Lam22d]'s general formulation additionally handles multi-segment loci (the opposite-edge projection that rules out "locus folding", §2.3) and length-changing GEN (step-relative positions, fn. 10); those are deferred until a consumer exercises them.

def Constraints.directionalBlock {C : Type u_1} (n : ℕ) (locus : Fin n → C → Prop) [(i : Fin n) → DecidablePred (locus i)] : List (Constraint C)

A directional constraint with single-segment loci over length-preserving GEN ([Lam22d]): the position-indexed block of binary constraints i ↦ ⟦locus i⟧, for positions i < n. Spliced into a ranking and compared under the canonical lex profile this is directional EVAL — ⇒ (left-to-right) for the forward block, ⇐ for .reverse. The block's i-th coordinate is exactly the directional violation vector's i-th entry, so the spliced profile equals the directional one (Core.Optimization.Evaluation.lexLE_ofFn).

Equations

• Constraints.directionalBlock n locus = List.map (fun (i : Fin n) => Constraints.Constraint.binary (locus i)) (List.finRange n)