Docs / Syntax / Minimalist / Probe / CyclicExpansion

Cyclic expansion

import Linglib.Syntax.Minimalist.Probe.CyclicExpansion · namespace Minimalist

A probe on a head searches the sister of the head, and as the head projects, the sister of each projection joins its search space. A probe on v between the arguments therefore meets the internal argument and then, once v projects over it, the external argument, Béjar & Rezac 2009's cyclic expansion, and a probe on T above both meets them in the reverse order. Reading the goals off a linearized object makes that order a consequence of where the head stands, instead of a stipulated list.

References

Declarations

L38–46

A probe meets exactly the tokens with a copy that a projection of its head c-commands, outside the positions closed to it.

theorem mem_cyclicGoalsL62–75
{hd : HeadFunction} {t : LinearizedSyntacticObject} {P : LexicalItem.Token → Prop} [DecidablePred P] {cut : Set Core.Order.TreePath} [DecidablePred fun (x : Core.Order.TreePath) => x ∈ cut] {a : Core.Order.TreePath} {x : LexicalItem.Token} :
x ∈ cyclicGoals hd t P cut a ↔ P x ∧ ∃ p ∈ projectionsOf hd t a, ∃ (q : Core.Order.TreePath), (q, x) ∈ positions (Sum.elim id id) ↑t ∧ (↑t).CCommands p q ∧ q ∉ cut

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