open_hypergraphs/lax/
open_hypergraph.rs

1//! Cospans of Hypergraphs.
2use super::hypergraph::*;
3use crate::strict::vec::{FiniteFunction, 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, PartialEq)]
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: impl Into<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    /// Delete the specified edges from the hypergraph.
88    ///
89    /// Panics if any edge id is out of bounds.
90    pub fn delete_edges(&mut self, edge_ids: &[EdgeId]) {
91        self.hypergraph.delete_edges(edge_ids);
92    }
93
94    /// Delete the specified nodes from the hypergraph, and renumber the source/target interfaces.
95    ///
96    /// Panics if any node id is out of bounds.
97    pub fn delete_nodes(&mut self, node_ids: &[NodeId]) {
98        let new_index = self.hypergraph.delete_nodes_witness(node_ids);
99        self.sources = self
100            .sources
101            .iter()
102            .filter_map(|n| new_index[n.0].map(NodeId))
103            .collect();
104        self.targets = self
105            .targets
106            .iter()
107            .filter_map(|n| new_index[n.0].map(NodeId))
108            .collect();
109    }
110
111    pub fn add_edge_source(&mut self, edge_id: EdgeId, w: O) -> NodeId {
112        self.hypergraph.add_edge_source(edge_id, w)
113    }
114
115    pub fn add_edge_target(&mut self, edge_id: EdgeId, w: O) -> NodeId {
116        self.hypergraph.add_edge_target(edge_id, w)
117    }
118
119    /// Set the nodes of the OpenHypergraph, possibly changing types.
120    /// Returns None if new nodes array had different length.
121    pub fn with_nodes<T, F: FnOnce(Vec<O>) -> Vec<T>>(self, f: F) -> Option<OpenHypergraph<T, A>> {
122        self.hypergraph
123            .with_nodes(f)
124            .map(|hypergraph| OpenHypergraph {
125                sources: self.sources,
126                targets: self.targets,
127                hypergraph,
128            })
129    }
130
131    /// Map the node labels of this OpenHypergraph, possibly changing their type
132    pub fn map_nodes<F: Fn(O) -> T, T>(self, f: F) -> OpenHypergraph<T, A> {
133        OpenHypergraph {
134            sources: self.sources,
135            targets: self.targets,
136            hypergraph: self.hypergraph.map_nodes(f),
137        }
138    }
139
140    /// Set the edges of the OpenHypergraph, possibly changing types.
141    /// Returns None if new edges array had different length.
142    pub fn with_edges<T, F: FnOnce(Vec<A>) -> Vec<T>>(self, f: F) -> Option<OpenHypergraph<O, T>> {
143        self.hypergraph
144            .with_edges(f)
145            .map(|hypergraph| OpenHypergraph {
146                sources: self.sources,
147                targets: self.targets,
148                hypergraph,
149            })
150    }
151
152    /// Map the edge labels of this OpenHypergraph, possibly changing their type
153    pub fn map_edges<F: Fn(A) -> T, T>(self, f: F) -> OpenHypergraph<O, T> {
154        OpenHypergraph {
155            sources: self.sources,
156            targets: self.targets,
157            hypergraph: self.hypergraph.map_edges(f),
158        }
159    }
160}
161
162impl<O, A> OpenHypergraph<O, A> {
163    pub fn identity(a: Vec<O>) -> Self {
164        let mut f = OpenHypergraph::empty();
165        f.sources = (0..a.len()).map(NodeId).collect();
166        f.targets = (0..a.len()).map(NodeId).collect();
167        f.hypergraph.nodes = a;
168        f
169    }
170
171    pub fn spider(s: FiniteFunction, t: FiniteFunction, w: Vec<O>) -> Option<Self> {
172        // s and t must have target equal to the number of supplied nodes
173        if s.target != t.target || s.target != w.len() {
174            return None;
175        }
176
177        let mut f = OpenHypergraph::empty();
178        f.hypergraph.nodes = w;
179        f.sources = s.table.0.into_iter().map(NodeId).collect();
180        f.targets = t.table.0.into_iter().map(NodeId).collect();
181        Some(f)
182    }
183}
184
185impl<O: Clone, A: Clone> OpenHypergraph<O, A> {
186    pub fn tensor(&self, other: &Self) -> Self {
187        let hypergraph = Hypergraph::coproduct(&self.hypergraph, &other.hypergraph);
188
189        // renumber all nodes
190        let n = self.hypergraph.nodes.len();
191
192        let sources = self
193            .sources
194            .iter()
195            .cloned()
196            .chain(other.sources.iter().map(|&i| NodeId(i.0 + n)))
197            .collect();
198
199        let targets = self
200            .targets
201            .iter()
202            .cloned()
203            .chain(other.targets.iter().map(|&i| NodeId(i.0 + n)))
204            .collect();
205
206        OpenHypergraph {
207            sources,
208            targets,
209            hypergraph,
210        }
211    }
212}
213
214impl<O: Clone + PartialEq, A: Clone> OpenHypergraph<O, A> {
215    /// Apply the quotient map to identify nodes in the internal [`Hypergraph`],
216    /// returning the computed coequalizer.
217    pub fn quotient(&mut self) -> Result<FiniteFunction, FiniteFunction> {
218        // mutably quotient self.hypergraph, returning the coequalizer q
219        let q = self.hypergraph.quotient()?;
220
221        // note: this is composition of finite functions `q >> self.sources`,
222        // but we do it mutably in-place.
223        self.sources
224            .iter_mut()
225            .for_each(|x| *x = NodeId(q.table[x.0]));
226        self.targets
227            .iter_mut()
228            .for_each(|x| *x = NodeId(q.table[x.0]));
229
230        Ok(q)
231    }
232
233    /// Deprecated alias for [`Self::quotient`]
234    #[deprecated(since = "0.2.10", note = "use OpenHypergraph::quotient")]
235    pub fn quotient_witness(&mut self) -> Result<FiniteFunction, FiniteFunction> {
236        self.quotient()
237    }
238
239    /// Convert this *lax* [`OpenHypergraph`] to a strict [`crate::strict::OpenHypergraph`] by
240    /// quotienting.
241    pub fn to_strict(mut self) -> crate::strict::OpenHypergraph<VecKind, O, A> {
242        use crate::array::vec::VecArray;
243        use crate::finite_function::FiniteFunction;
244        use crate::strict::open_hypergraph::OpenHypergraph;
245
246        self.quotient().unwrap();
247
248        let target = self.hypergraph.nodes.len();
249
250        let s = {
251            let table = self.sources.iter().map(|x| x.0).collect();
252            FiniteFunction::new(VecArray(table), target).expect("Valid by construction")
253        };
254
255        let t = {
256            let table = self.targets.iter().map(|x| x.0).collect();
257            FiniteFunction::new(VecArray(table), target).expect("Valid by construction")
258        };
259
260        let h = self.hypergraph.to_hypergraph();
261
262        OpenHypergraph::new(s, t, h).expect("any valid lax::Hypergraph must be quotientable!")
263    }
264
265    // Old name for `to_strict`. Provided for backwards compatibility
266    #[deprecated(since = "0.2.4", note = "renamed to_strict")]
267    pub fn to_open_hypergraph(self) -> crate::strict::OpenHypergraph<VecKind, O, A> {
268        self.to_strict()
269    }
270}
open_hypergraphs/lax/open_hypergraph.rs

open_hypergraphs/lax/
open_hypergraph.rs
