Struct DblTree

pub struct DblTree<E, ProE, Sq>(pub OpenTree<ProE, DblNode<E, Sq>>);

A double tree, or pasting diagram in a virtual double category.

The underlying data structure of a double tree is a open tree whose nodes represent cells (or occasionally arrows) in the pasting diagram. Not just any tree constitutes a valid pasting. The domains/codomains and sources/targets of the cells must compatible, and spines can only appear in certain configurations.

Tuple Fields

0: OpenTree<ProE, DblNode<E, Sq>>

Implementations

impl<E, ProE, Sq> DblTree<E, ProE, Sq>

pub fn empty(p: ProE) -> Self

Constructs the empty or identity double tree.

pub fn single( sq: Sq, graph: &impl VDblGraph<E = E, ProE = ProE, Sq = Sq>, ) -> Self

Constructs a double tree with a single square from a virtual double graph.

pub fn two_level( squares: impl IntoIterator<Item = Sq>, base: Sq, graph: &impl VDblGraph<E = E, ProE = ProE, Sq = Sq>, ) -> Self

Constructs a double tree of height two.

pub fn dom<V>( &self, graph: &impl VDblGraph<V = V, E = E, ProE = ProE, Sq = Sq>, ) -> Path<V, ProE>

where ProE: Clone,

Domain of the tree in the given virtual double graph.

pub fn cod(&self, graph: &impl VDblGraph<E = E, ProE = ProE, Sq = Sq>) -> ProE

where ProE: Clone,

Codomain of the tree in the given virtual double graph.

pub fn src<V>( &self, graph: &impl VDblGraph<V = V, E = E, ProE = ProE, Sq = Sq>, ) -> Path<V, E>

where E: Clone,

Source of the tree in the given virtual double graph.

pub fn tgt<V>( &self, graph: &impl VDblGraph<V = V, E = E, ProE = ProE, Sq = Sq>, ) -> Path<V, E>

where E: Clone,

Target of the tree in the given virtual double graph.

pub fn arity( &self, graph: &impl VDblGraph<E = E, ProE = ProE, Sq = Sq>, ) -> usize

Arity of the cell specified by the double tree.

Note that this arity can differ from the arity of the underlying open tree due to the possibility of spines.

pub fn contained_in( &self, graph: &impl VDblGraph<E = E, ProE = ProE, Sq = Sq>, ) -> bool

where E: Eq + Clone, ProE: Eq + Clone,

Is the double tree contained in the given virtual double graph?

This includes checking whether the double tree is well-typed, i.e., that the domains and codomains, and sources and targets, of the cells are compatible.

pub fn is_isomorphic_to(&self, other: &Self) -> bool

where E: Eq, ProE: Eq, Sq: Eq,

Is the double tree isomorphic to another?

This method simply checks whether the underlying open trees are isomorphic.

pub fn map<CodE, CodSq>( self, fn_e: impl FnMut(E) -> CodE, fn_sq: impl FnMut(Sq) -> CodSq, ) -> DblTree<CodE, ProE, CodSq>

Maps over the edges and squares of the tree.

impl<V, E, ProE, Sq> DblTree<Path<V, E>, ProE, DblTree<E, ProE, Sq>>

pub fn flatten(self) -> DblTree<E, ProE, Sq>

Flattens a double tree of double trees into a single double tree.

Trait Implementations

impl<E: Clone, ProE: Clone, Sq: Clone> Clone for DblTree<E, ProE, Sq>

fn clone(&self) -> DblTree<E, ProE, Sq>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<E: Debug, ProE: Debug, Sq: Debug> Debug for DblTree<E, ProE, Sq>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<E, ProE, Sq> From<OpenTree<ProE, DblNode<E, Sq>>> for DblTree<E, ProE, Sq>

fn from(value: OpenTree<ProE, DblNode<E, Sq>>) -> Self

Converts to this type from the input type.

impl<E: PartialEq, ProE: PartialEq, Sq: PartialEq> PartialEq for DblTree<E, ProE, Sq>

fn eq(&self, other: &DblTree<E, ProE, Sq>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<E: Eq, ProE: Eq, Sq: Eq> Eq for DblTree<E, ProE, Sq>

impl<E, ProE, Sq> StructuralPartialEq for DblTree<E, ProE, Sq>