Struct ModalDblTheory

pub struct ModalDblTheory<Id, S = RandomState> { /* private fields */ }

A modal double theory.

Implementations

impl<Id, S> ModalDblTheory<Id, S>

where Id: Eq + Clone + Hash, S: BuildHasher,

pub fn add_ob_type(&mut self, id: Id)

Adds a generating object type to the theory.

pub fn add_mor_type( &mut self, id: Id, src: ModalObType<Id>, tgt: ModalObType<Id>, )

Adds a generating morphism type to the theory.

pub fn add_ob_op(&mut self, id: Id, dom: ModalObType<Id>, cod: ModalObType<Id>)

Adds a generating object operation to the theory.

pub fn add_mor_op( &mut self, id: Id, dom: Path<ModalObType<Id>, ModalMorType<Id>>, cod: ModalMorType<Id>, src: ModalObOp<Id>, tgt: ModalObOp<Id>, )

Adds a generating morphism operation to the theory.

pub fn add_special_mor_op( &mut self, id: Id, src: ModalObOp<Id>, tgt: ModalObOp<Id>, )

Adds a morphism operation with nullary domain and unit codomain.

pub fn equate_ob_ops(&mut self, lhs: ModalObOp<Id>, rhs: ModalObOp<Id>)

Equate two object operations in the theory.

Trait Implementations

impl<Id: Debug, S: Debug> Debug for ModalDblTheory<Id, S>

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

Formats the value using the given formatter.

impl<Id: Default, S: Default> Default for ModalDblTheory<Id, S>

fn default() -> ModalDblTheory<Id, S>

Returns the “default value” for a type.

impl<Id, S> VDCWithComposites for ModalDblTheory<Id, S>

where Id: Eq + Clone + Hash, S: BuildHasher,

fn composite_ext(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Cell>

Gets the chosen cell witnessing a composite of proarrows, if there is one.

fn composite(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Pro>

Gets the chosen composite for a path of proarrows, if there is one.

fn through_composite( &self, _cell: Self::Cell, _range: Range<usize>, ) -> Option<Self::Cell>

Factorizes a cell through a composite of proarrows.

fn has_composite(&self, path: &Path<Self::Ob, Self::Pro>) -> bool

Does the path of proarrows have a chosen composite?

fn has_unit(&self, x: &Self::Ob) -> bool

Does the object have a chosen unit?

fn composite2_ext(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Cell>

Gets the chosen cell witnessing a composite of two proarrows, if there is one.

fn composite2(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Pro>

Gets the chosen composite for a pair of consecutive proarrows, if there is one.

fn unit_ext(&self, x: Self::Ob) -> Option<Self::Cell>

Gets the chosen extension cell for an object, if there is one.

fn unit(&self, x: Self::Ob) -> Option<Self::Pro>

Gets the chosen unit for an object, if there is one.

fn through_unit(&self, cell: Self::Cell, index: usize) -> Option<Self::Cell>

Factorizes a cell through the unit proarrow for an object.

impl<Id, S> VDblCategory for ModalDblTheory<Id, S>

where Id: Eq + Clone + Hash, S: BuildHasher,

type Ob = ModeApp<Id>

Type of objects in the VDC.

type Arr = Path<ModeApp<Id>, ModeApp<ModalOp<Id>>>

Type of arrows (tight morphisms) in the VDC.

type Pro = ShortPath<ModeApp<Id>, ModeApp<Id>>

Type of proarrows (loose morphisms) in the VDC.

type Cell = DblTree<Path<ModeApp<Id>, ModeApp<ModalOp<Id>>>, ShortPath<ModeApp<Id>, ModeApp<Id>>, ModalNode<Id>>

Type of cells in the VDC;

fn has_ob(&self, x: &Self::Ob) -> bool

Does the object belong to the VDC?

fn has_arrow(&self, f: &Self::Arr) -> bool

Does the arrow belong to the VDC?

fn has_proarrow(&self, m: &Self::Pro) -> bool

Does the proarrow belong to the VDC?

fn has_cell(&self, tree: &Self::Cell) -> bool

Does the cell belong to the VDC?

fn dom(&self, f: &Self::Arr) -> Self::Ob

Gets the domain of an arrow.

fn cod(&self, f: &Self::Arr) -> Self::Ob

Gets the codomain of an arrow.

fn src(&self, m: &Self::Pro) -> Self::Ob

Gets the source of a proarrow.

fn tgt(&self, m: &Self::Pro) -> Self::Ob

Gets the target of a proarrow.

fn cell_dom(&self, tree: &Self::Cell) -> Path<Self::Ob, Self::Pro>

Gets the domain of a cell, a path of proarrows.

fn cell_cod(&self, tree: &Self::Cell) -> Self::Pro

Gets the codomain of a cell, a single proarrow.

fn cell_src(&self, tree: &Self::Cell) -> Self::Arr

Gets the source of a cell, an arrow.

fn cell_tgt(&self, tree: &Self::Cell) -> Self::Arr

Gets the target of a cell, an edge.

fn arity(&self, tree: &Self::Cell) -> usize

Gets the arity of a cell.

fn compose(&self, path: Path<Self::Ob, Self::Arr>) -> Self::Arr

Composes a path of arrows in the VDC.

fn compose_cells( &self, tree: DblTree<Self::Arr, Self::Pro, Self::Cell>, ) -> Self::Cell

Composes a tree of cells in the VDC.

fn compose2(&self, f: Self::Arr, g: Self::Arr) -> Self::Arr

Composes a pair of arrows with compatible (co)domains.

fn id(&self, x: Self::Ob) -> Self::Arr

Constructs the identity arrow at an object.

fn compose_cells2( &self, αs: impl IntoIterator<Item = Self::Cell>, β: Self::Cell, ) -> Self::Cell

where Self: Sized,

Composes a two-layer pasting of cells.

fn id_cell(&self, m: Self::Pro) -> Self::Cell

Constructs the identity cell on a proarrow.

impl<Id, S> Validate for ModalDblTheory<Id, S>

where Id: Eq + Clone + Hash, S: BuildHasher,

type ValidationError = InvalidDblTheory<Id>

The type of a validation error.

fn validate(&self) -> Result<(), NonEmpty<Self::ValidationError>>

Validates the object.