Struct OpenHypergraph 

pub struct OpenHypergraph<K: ArrayKind, O, A> {
    pub s: FiniteFunction<K>,
    pub t: FiniteFunction<K>,
    pub h: Hypergraph<K, O, A>,
}

Open Hypergraphs

Invariants

We must have the following invariants:

These are checked by the OpenHypergraph::validate method

Panics

Most operations assume the invariants hold, and will panic if not.

Fields

s: FiniteFunction<K>

t: FiniteFunction<K>

h: Hypergraph<K, O, A>

Implementations

impl<K: ArrayKind, O, A> OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O>, K::Type<A>: Array<K, A>,

pub fn new( s: FiniteFunction<K>, t: FiniteFunction<K>, h: Hypergraph<K, O, A>, ) -> Result<Self, InvalidOpenHypergraph<K>>

pub fn validate(self) -> Result<Self, InvalidOpenHypergraph<K>>

pub fn singleton( x: A, a: SemifiniteFunction<K, O>, b: SemifiniteFunction<K, O>, ) -> OpenHypergraph<K, O, A>

pub fn tensor_operations( operations: Operations<K, O, A>, ) -> OpenHypergraph<K, O, A>

pub fn source(&self) -> SemifiniteFunction<K, O>

pub fn target(&self) -> SemifiniteFunction<K, O>

pub fn identity(w: SemifiniteFunction<K, O>) -> OpenHypergraph<K, O, A>

pub fn spider( s: FiniteFunction<K>, t: FiniteFunction<K>, w: SemifiniteFunction<K, O>, ) -> Option<Self>

Trait Implementations

impl<K: ArrayKind, O, A> Arrow for OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

type Object = SemifiniteFunction<K, O>

fn source(&self) -> Self::Object

fn target(&self) -> Self::Object

fn identity(w: Self::Object) -> Self

the identity morphism on a

fn compose(&self, other: &Self) -> Option<Self>

Compose morphisms in diagrammatic order: self ; other

impl<K: ArrayKind, O, A> BitOr<&OpenHypergraph<K, O, A>> for &OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

type Output = OpenHypergraph<K, O, A>

The resulting type after applying the | operator.

fn bitor(self, rhs: &OpenHypergraph<K, O, A>) -> OpenHypergraph<K, O, A>

Performs the | operation.

impl<K: ArrayKind, O, A> Clone for OpenHypergraph<K, O, A>

where K::Type<O>: Clone, K::Type<A>: Clone, K::Type<K::I>: Clone,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<K: ArrayKind, O: Debug, A: Debug> Debug for OpenHypergraph<K, O, A>

where K::Index: Debug, K::Type<K::I>: Debug, K::Type<O>: Debug, K::Type<A>: Debug,

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

Formats the value using the given formatter.

impl<K: ArrayKind, O, A> Monoidal for OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

fn unit() -> Self::Object

the monoidal unit object

fn tensor(&self, other: &Self) -> Self

f \otimes g of two morphisms

impl<K: ArrayKind, O, A> Shr<&OpenHypergraph<K, O, A>> for &OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

type Output = Option<OpenHypergraph<K, O, A>>

The resulting type after applying the >> operator.

fn shr(self, rhs: &OpenHypergraph<K, O, A>) -> Option<OpenHypergraph<K, O, A>>

Performs the >> operation.

impl<K: ArrayKind, O, A> Spider<K> for OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

fn dagger(&self) -> Self

Given an Arrow with type f : A → B, construct its dagger f† : B → A by using Hypergraph structure to bend sources to targets and vice-versa.

fn spider( s: FiniteFunction<K>, t: FiniteFunction<K>, w: Self::Object, ) -> Option<Self>

Construct a spider using a type w, and source s and target t interface maps.

fn half_spider(s: FiniteFunction<K>, w: Self::Object) -> Option<Self>

Construct a “half-spider”: a spider whose t leg is identity.

impl<K: ArrayKind, O, A> SymmetricMonoidal for OpenHypergraph<K, O, A>

where K::Type<K::I>: NaturalArray<K>, K::Type<O>: Array<K, O> + PartialEq, K::Type<A>: Array<K, A>,

fn twist(a: Self::Object, b: Self::Object) -> Self

Construct the symmetry \sigma_{a,b} from a and b.