Enum DblNode

pub enum DblNode<E, ProE, Sq> {
    Cell(Sq),
    Id(ProE),
    Spine(E),
}

A node in a double tree.

To be more precise, this enum is the type of a value carried by a node in a double tree.

Variants

Cell(Sq)

A generic cell, given by a square in a virtual double graph.

Id(ProE)

The identity cell on a pro-edge in a virtual double graph.

Any node with an identity as its value should be a leaf node. While not logically required, we enforce this invariant to obtain a normal form for pastings in VDCs.

Spine(E)

An edge dangling from a nullary cell.

In a well-formed double tree, a spine node can be a child only of a nullary cell or of another spine node. Spines represent the operation of precomposing a nullary cell with an arrow to obtain another nullary cell, a degenerate case of composition in a virtual double category.

Implementations

impl<E, ProE, Sq> DblNode<E, ProE, Sq>

pub fn is_cell(&self) -> bool

Is the node a generic cell?

pub fn is_id(&self) -> bool

Is the node an identity?

pub fn is_spine(&self) -> bool

Is the node a spine?

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

where ProE: Clone,

Domain of node in the given virtual double graph.

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

where ProE: Clone,

Codomain of node 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 node 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 node in the given virtual double graph.

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

Arity of node in the given virtual double graph.

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

Is the node contained in the given virtual double graph?

Trait Implementations

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

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

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

Formats the value using the given formatter.

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

fn eq(&self, other: &DblNode<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 DblNode<E, ProE, Sq>

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