open_hypergraphs/lax/
open_hypergraph.rs

1//! Cospans of Hypergraphs.
2use super::hypergraph::*;
3use crate::array::vec::VecKind;
4
5/// A lax OpenHypergraph is a cospan of lax hypergraphs:
6/// a hypergraph equipped with two finite maps representing the *interfaces*.
7#[derive(Debug, Clone)]
8#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
9#[cfg_attr(
10    feature = "serde",
11    serde(
12        bound = "O: serde::Serialize + serde::de::DeserializeOwned, A: serde::Serialize + serde::de::DeserializeOwned"
13    )
14)]
15pub struct OpenHypergraph<O, A> {
16    pub sources: Vec<NodeId>,
17    pub targets: Vec<NodeId>,
18    pub hypergraph: Hypergraph<O, A>,
19}
20
21// Imperative-specific methods
22impl<O, A> OpenHypergraph<O, A> {
23    /// The empty OpenHypergraph with no nodes and no edges.
24    ///
25    /// In categorical terms, this is the identity map at the unit object.
26    pub fn empty() -> Self {
27        OpenHypergraph {
28            sources: vec![],
29            targets: vec![],
30            hypergraph: Hypergraph::empty(),
31        }
32    }
33
34    pub fn from_strict(f: crate::strict::open_hypergraph::OpenHypergraph<VecKind, O, A>) -> Self {
35        let sources = f.s.table.0.into_iter().map(NodeId).collect();
36        let targets = f.t.table.0.into_iter().map(NodeId).collect();
37        let hypergraph = Hypergraph::from_strict(f.h);
38        OpenHypergraph {
39            sources,
40            targets,
41            hypergraph,
42        }
43    }
44
45    /// Create a new node in the hypergraph labeled `w`.
46    pub fn new_node(&mut self, w: O) -> NodeId {
47        self.hypergraph.new_node(w)
48    }
49
50    pub fn new_edge(&mut self, x: A, interface: Hyperedge) -> EdgeId {
51        self.hypergraph.new_edge(x, interface)
52    }
53
54    /// Create a new "operation" in the hypergraph.
55    /// Concretely, `f.new_operation(x, s, t)` mutates `f` by adding:
56    ///
57    /// 1. a new hyperedge labeled `x`
58    /// 2. `len(s)` new nodes, with the `i`th node labeled `s[i]`
59    /// 3. `len(t)` new nodes, with the `i`th node labeled `t[i]`
60    ///
61    /// Returns the new hyperedge ID and the [`NodeId`]s of the source/target nodes.
62    ///
63    /// This is a convenience wrapper for [`Hypergraph::new_operation`]
64    pub fn new_operation(
65        &mut self,
66        x: A,
67        source_type: Vec<O>,
68        target_type: Vec<O>,
69    ) -> (EdgeId, Interface) {
70        self.hypergraph.new_operation(x, source_type, target_type)
71    }
72
73    /// An [`OpenHypergraph`] consisting of a single operation.
74    pub fn singleton(x: A, source_type: Vec<O>, target_type: Vec<O>) -> Self {
75        let mut f = Self::empty();
76        let (_, (s, t)) = f.new_operation(x, source_type, target_type);
77        f.sources = s;
78        f.targets = t;
79        f
80    }
81
82    /// Compute an open hypergraph by calling `to_hypergraph` on the internal `Hypergraph`.
83    pub fn unify(&mut self, v: NodeId, w: NodeId) {
84        self.hypergraph.unify(v, w);
85    }
86
87    pub fn add_edge_source(&mut self, edge_id: EdgeId, w: O) -> NodeId {
88        self.hypergraph.add_edge_source(edge_id, w)
89    }
90
91    pub fn add_edge_target(&mut self, edge_id: EdgeId, w: O) -> NodeId {
92        self.hypergraph.add_edge_target(edge_id, w)
93    }
94}
95
96impl<O: Clone + PartialEq, A: Clone> OpenHypergraph<O, A> {
97    /// Apply the quotient map to identify nodes in the internal [`Hypergraph`].
98    /// This deletes the internal quotient map, resulting in a *strict* [`OpenHypergraph`].
99    pub fn quotient(&mut self) {
100        // mutably quotient self.hypergraph, returning the coequalizer q
101        let q = self.hypergraph.quotient();
102
103        // note: this is composition of finite functions `q >> self.sources`,
104        // but we do it mutably in-place.
105        self.sources
106            .iter_mut()
107            .for_each(|x| *x = NodeId(q.table[x.0]));
108        self.targets
109            .iter_mut()
110            .for_each(|x| *x = NodeId(q.table[x.0]));
111    }
112
113    /// Convert this *lax* [`OpenHypergraph`] to a strict [`crate::strict::OpenHypergraph`] by
114    /// quotienting.
115    pub fn to_strict(mut self) -> crate::strict::OpenHypergraph<VecKind, O, A> {
116        use crate::array::vec::VecArray;
117        use crate::finite_function::FiniteFunction;
118        use crate::strict::open_hypergraph::OpenHypergraph;
119
120        self.quotient();
121
122        let target = self.hypergraph.nodes.len();
123
124        let s = {
125            let table = self.sources.iter().map(|x| x.0).collect();
126            FiniteFunction::new(VecArray(table), target).expect("Valid by construction")
127        };
128
129        let t = {
130            let table = self.targets.iter().map(|x| x.0).collect();
131            FiniteFunction::new(VecArray(table), target).expect("Valid by construction")
132        };
133
134        let h = self.hypergraph.to_hypergraph();
135
136        OpenHypergraph::new(s, t, h).expect("any valid lax::Hypergraph must be quotientable!")
137    }
138
139    // Old name for `to_strict`. Provided for backwards compatibility
140    #[deprecated(since = "0.2.4", note = "renamed to_strict")]
141    pub fn to_open_hypergraph(self) -> crate::strict::OpenHypergraph<VecKind, O, A> {
142        self.to_strict()
143    }
144}
open_hypergraphs/lax/open_hypergraph.rs

open_hypergraphs/lax/
open_hypergraph.rs
