Docs / Syntax / DependencyGrammar / Stemma

Stemmas

import Linglib.Syntax.DependencyGrammar.Stemma · namespace DependencyGrammar

A stemma is a dependency tree as it is drawn: a head with its dependents to its left and to its right, each dependent attached by a relation and heading a stemma of its own. Reading a stemma from left to right spells out its sentence, and numbering the words of that sentence turns the stemma into a dependency graph on positions, in which each word's head is the head it hangs from. That graph is a tree and projective: a stemma never draws crossing arcs.

Main definitions

DependencyGrammar.Stemma: the stemmas with relations in L.
Stemma.yield: the sentence a stemma spells out.
Stemma.toGraph, Stemma.toTree: the dependency graph on the positions of the sentence, and the same graph bundled as a tree.

Implementation notes

The graph records, for each position, the position of its head and the relation to it (Stemma.heads), so no position has two heads by construction.

TODO

The converse: every projective tree is the graph of a stemma.

References

Tesnière 1959, Éléments de syntaxe structurale

Declarations

A stemma is a head word with its dependents to its left and to its right, in order, each attached by a relation in L and heading a stemma of its own.

inductive Stemma L47–50

(L : Type u_1) :

Type u_1

node {L : Type u_1} (head : Morphology.Word) (left right : List (L × Stemma L)) : Stemma L

Used by Stemma.leaf, Stemma.yield, Stemma.yieldDeps, Stemma.size, Stemma.sizeDeps, Stemma.headIndex, Stemma.heads, Stemma.headsDeps, Stemma.length_yield, Stemma.length_yieldDeps, Stemma.headIndex_lt_size, Stemma.instNeZeroNatSize, Stemma.toGraph, Stemma.length_heads, Stemma.length_headsDeps, Stemma.getElem?_heads_headIndex, Stemma.toGraph_adj, Stemma.isTree_toGraph, Stemma.isProjective_toGraph, Stemma.toTree

Used in OsborneLi2023

L56–57

The sentence a stemma spells out: its left dependents, its head, its right dependents.

def Stemma.yield L61–63

{L : Type u_1} :

Stemma L → List Morphology.Word

(Stemma.node w l r).yield = Stemma.yieldDeps l ++ w :: Stemma.yieldDeps r

Built from ,

Used by Stemma.yieldDeps, Stemma.length_yield

The dependency graph on the positions of a stemma's sentence: an arc from each word's head to the word, labelled with its relation, rooted at the stemma's head.

def Stemma.toGraph L123–129

{L : Type u_1} (s : Stemma L) :

Graph L s.size

The definition is too large to print here; read it in the source.

Built from ,

Used by Stemma.toGraph_adj, Stemma.isTree_toGraph, Stemma.isProjective_toGraph, Stemma.toTree

Used in OsborneLi2023

L133–138