Enum ShortPath

pub enum ShortPath<V, E> {
    Zero(V),
    One(E),
}

A path of length at most one.

We call a path of length at most one, i.e., a path of lenth zero or one, a short path. This is not standard terminology, though it is inspired by “short maps” between metric spaces, which are Lipschitz maps with Lipschitz constant at most 1.

Short paths are convertible into, and fallibly from, paths. Short paths might seem like an odd data structure, but are occasionally useful, such as in:

• finite categories defined by an explicit multiplication table, where every morphism is either a generator (path of length one) or an identity (path of length zero)
• augmented virtual double categories (Koudenburg 2020), where the codomain of a cell is by definition a short path, and relatedly unital virtual double categories

Variants

Zero(V)

Path of length zero.

One(E)

Path of length one.

Implementations

impl<Id> ShortPath<ModeApp<Id>, ModeApp<Id>>

pub fn apply(self, m: Modality) -> Self

Applies a modality.

pub fn apply_all(self, iter: impl IntoIterator<Item = Modality>) -> Self

Applies a sequence of modalities.

impl<V, E> ShortPath<V, E>

pub fn contained_in(&self, graph: &impl Graph<V = V, E = E>) -> bool

Is the path contained in the given graph?

pub fn src(&self, graph: &impl Graph<V = V, E = E>) -> V

where V: Clone,

Source of the path in the given graph.

pub fn tgt(&self, graph: &impl Graph<V = V, E = E>) -> V

where V: Clone,

Target of the path in the given graph.

pub fn as_edge(self, graph: &impl ReflexiveGraph<V = V, E = E>) -> E

Converts the short path into an edge in the given reflexive graph.

pub fn map<CodV, CodE>( self, fv: impl FnOnce(V) -> CodV, fe: impl FnOnce(E) -> CodE, ) -> ShortPath<CodV, CodE>

Maps over the short path.

Trait Implementations

impl<V: Clone, E: Clone> Clone for ShortPath<V, E>

fn clone(&self) -> ShortPath<V, E>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<V: Debug, E: Debug> Debug for ShortPath<V, E>

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

Formats the value using the given formatter.

impl<V, E> From<E> for ShortPath<V, E>

fn from(value: E) -> Self

Converts to this type from the input type.

impl<V, E> From<ShortPath<V, E>> for Path<V, E>

fn from(path: ShortPath<V, E>) -> Self

Converts to this type from the input type.

impl<V: PartialEq, E: PartialEq> PartialEq for ShortPath<V, E>

fn eq(&self, other: &ShortPath<V, E>) -> 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<V, E> TryFrom<Path<V, E>> for ShortPath<V, E>

type Error = ()

The type returned in the event of a conversion error.

fn try_from(path: Path<V, E>) -> Result<Self, Self::Error>

Performs the conversion.

impl<V: Eq, E: Eq> Eq for ShortPath<V, E>

impl<V, E> StructuralPartialEq for ShortPath<V, E>