open_hypergraphs/lax/
hypergraph.rs

1use crate::array::vec::{VecArray, VecKind};
2use crate::finite_function::*;
3
4use core::fmt::Debug;
5
6#[derive(Debug, Clone, Copy, PartialEq)]
7#[repr(transparent)]
8pub struct NodeId(pub usize);
9
10#[derive(Debug, Clone, Copy, PartialEq)]
11#[repr(transparent)]
12pub struct EdgeId(pub usize);
13
14#[derive(Debug, Clone)]
15pub struct Hyperedge {
16    pub sources: Vec<NodeId>,
17    pub targets: Vec<NodeId>,
18}
19
20pub type Interface = (Vec<NodeId>, Vec<NodeId>);
21
22/// A [`crate::lax::Hypergraph`] represents an "un-quotiented" hypergraph.
23///
24/// It can be thought of as a collection of disconnected operations and wires along with a
25/// *quotient map* which can be used with connected components to produce a `Hypergraph`.
26#[derive(Debug, Clone)]
27pub struct Hypergraph<O, A> {
28    /// Node labels. Defines a finite map from [`NodeId`] to node label
29    pub nodes: Vec<O>,
30
31    /// Edge labels. Defines a finite map from [`EdgeId`] to edge label
32    pub edges: Vec<A>,
33
34    /// Hyperedges map an *ordered list* of source nodes to an ordered list of target nodes.
35    pub adjacency: Vec<Hyperedge>,
36
37    // A finite endofunction on the set of nodes, identifying nodes to be quotiented.
38    // NOTE: this is a *graph* on the set of nodes.
39    pub quotient: (Vec<NodeId>, Vec<NodeId>),
40}
41
42impl<O, A> Hypergraph<O, A> {
43    /// The empty Hypergraph with no nodes or edges.
44    pub fn empty() -> Self {
45        Hypergraph {
46            nodes: vec![],
47            edges: vec![],
48            adjacency: vec![],
49            quotient: (vec![], vec![]),
50        }
51    }
52
53    pub fn from_strict(h: crate::hypergraph::Hypergraph<VecKind, O, A>) -> Self {
54        let mut adjacency = Vec::with_capacity(h.x.0.len());
55        for (sources, targets) in h.s.into_iter().zip(h.t.into_iter()) {
56            adjacency.push(Hyperedge {
57                sources: sources.table.iter().map(|i| NodeId(*i)).collect(),
58                targets: targets.table.iter().map(|i| NodeId(*i)).collect(),
59            })
60        }
61
62        Hypergraph {
63            nodes: h.w.0 .0,
64            edges: h.x.0 .0,
65            adjacency,
66            quotient: (vec![], vec![]),
67        }
68    }
69
70    pub fn discrete(nodes: Vec<O>) -> Self {
71        let mut h = Self::empty();
72        h.nodes = nodes;
73        h
74    }
75
76    /// Add a single node labeled `w` to the [`Hypergraph`]
77    pub fn new_node(&mut self, w: O) -> NodeId {
78        let index = self.nodes.len();
79        self.nodes.push(w);
80        NodeId(index)
81    }
82
83    /// Add a single hyperedge labeled `a` to the [`Hypergraph`]
84    /// it has sources and targets specified by `interface`
85    /// return which `EdgeId` corresponds to that new hyperedge
86    pub fn new_edge(&mut self, x: A, interface: Hyperedge) -> EdgeId {
87        let edge_idx = self.edges.len();
88        self.edges.push(x);
89        self.adjacency.push(interface);
90        EdgeId(edge_idx)
91    }
92
93    /// Append a "singleton" operation to the Hypergraph.
94    ///
95    /// 1. For each element t of `source_type` (resp. `target_type`), creates a node labeled t
96    /// 2. creates An edge labeled `x`, and sets its source/target nodes to those from step (1)
97    ///
98    /// Returns the index [`EdgeId`] of the operation in the [`Hypergraph`], and its source and
99    /// target nodes.
100    pub fn new_operation(
101        &mut self,
102        x: A,
103        source_type: Vec<O>,
104        target_type: Vec<O>,
105    ) -> (EdgeId, Interface) {
106        let sources: Vec<NodeId> = source_type.into_iter().map(|t| self.new_node(t)).collect();
107        let targets: Vec<NodeId> = target_type.into_iter().map(|t| self.new_node(t)).collect();
108        let interface = (sources.clone(), targets.clone());
109        let edge_id = self.new_edge(x, Hyperedge { sources, targets });
110        (edge_id, interface)
111    }
112
113    /// Identify a pair of nodes `(v, w)` by adding them to the quotient map.
114    ///
115    /// Note that if the labels of `v` and `w` are not equal, then this will not represent a valid
116    /// `Hypergraph`.
117    /// This is intentional so that typechecking and type inference can be deferred until after
118    /// construction of the `Hypergraph`.
119    pub fn unify(&mut self, v: NodeId, w: NodeId) {
120        // add nodes to the quotient graph
121        self.quotient.0.push(v);
122        self.quotient.1.push(w);
123    }
124
125    /// Add a new *source* node labeled `w` to edge `edge_id`.
126    pub fn add_edge_source(&mut self, edge_id: EdgeId, w: O) -> NodeId {
127        let node_id = self.new_node(w);
128        self.adjacency[edge_id.0].sources.push(node_id);
129        node_id
130    }
131
132    /// Add a new *target* node labeled `w` to edge `edge_id`
133    pub fn add_edge_target(&mut self, edge_id: EdgeId, w: O) -> NodeId {
134        let node_id = self.new_node(w);
135        self.adjacency[edge_id.0].targets.push(node_id);
136        node_id
137    }
138}
139
140impl<O: Clone + PartialEq, A: Clone + PartialEq> Hypergraph<O, A> {
141    /// Construct a [`Hypergraph`] by identifying nodes in the quotient map.
142    /// Mutably quotient this [`Hypergraph`], returning the coequalizer calculated from `self.quotient`.
143    ///
144    /// NOTE: this operation is unchecked; you should verify quotiented nodes have the exact same
145    /// type first, or this operation is undefined.
146    pub fn quotient(&mut self) -> FiniteFunction<VecKind> {
147        use std::mem::take;
148        let q = self.coequalizer();
149
150        self.nodes = coequalizer_universal(&q, &VecArray(take(&mut self.nodes)))
151            .unwrap()
152            .0;
153
154        // map hyperedges
155        for e in &mut self.adjacency {
156            e.sources.iter_mut().for_each(|x| *x = NodeId(q.table[x.0]));
157            e.targets.iter_mut().for_each(|x| *x = NodeId(q.table[x.0]));
158        }
159
160        // clear the quotient map (we just used it)
161        self.quotient = (vec![], vec![]); // empty
162
163        q // return the coequalizer used to quotient the hypergraph
164    }
165
166    pub fn to_hypergraph(&self) -> crate::prelude::Hypergraph<O, A> {
167        make_hypergraph(self)
168    }
169
170    fn coequalizer(&self) -> FiniteFunction<VecKind> {
171        // Compute the coequalizer (connected components) of the quotient graph
172        let s: FiniteFunction<VecKind> = FiniteFunction {
173            table: VecArray(self.quotient.0.iter().map(|x| x.0).collect()),
174            target: self.nodes.len(),
175        };
176
177        let t: FiniteFunction<VecKind> = FiniteFunction {
178            table: VecArray(self.quotient.1.iter().map(|x| x.0).collect()),
179            target: self.nodes.len(),
180        };
181
182        s.coequalizer(&t)
183            .expect("coequalizer must exist for any graph")
184    }
185}
186
187pub(crate) fn finite_function_coproduct(
188    v1: &[NodeId],
189    v2: &[NodeId],
190    target: usize,
191) -> Vec<NodeId> {
192    v1.iter()
193        .cloned()
194        .chain(v2.iter().map(|&s| NodeId(s.0 + target)))
195        .collect()
196}
197
198pub(crate) fn concat<T: Clone>(v1: &[T], v2: &[T]) -> Vec<T> {
199    v1.iter().cloned().chain(v2.iter().cloned()).collect()
200}
201
202impl<O: Clone, A: Clone> Hypergraph<O, A> {
203    pub(crate) fn coproduct(&self, other: &Hypergraph<O, A>) -> Hypergraph<O, A> {
204        let n = self.nodes.len();
205
206        let adjacency = self
207            .adjacency
208            .iter()
209            .cloned()
210            .chain(other.adjacency.iter().map(|edge| Hyperedge {
211                sources: edge.sources.iter().map(|&s| NodeId(s.0 + n)).collect(),
212                targets: edge.targets.iter().map(|&t| NodeId(t.0 + n)).collect(),
213            }))
214            .collect();
215
216        let quotient = (
217            finite_function_coproduct(&self.quotient.0, &other.quotient.0, n),
218            finite_function_coproduct(&self.quotient.1, &other.quotient.1, n),
219        );
220
221        Hypergraph {
222            nodes: concat(&self.nodes, &other.nodes),
223            edges: concat(&self.edges, &other.edges),
224            adjacency,
225            quotient,
226        }
227    }
228}
229
230/// Create a [`crate::hypergraph::Hypergraph`] by forgetting about the quotient map.
231fn make_hypergraph<O: Clone, A: Clone>(
232    h: &Hypergraph<O, A>,
233) -> crate::hypergraph::Hypergraph<VecKind, O, A> {
234    use crate::finite_function::*;
235    use crate::indexed_coproduct::*;
236    use crate::semifinite::*;
237
238    let s = {
239        let mut lengths = Vec::<usize>::with_capacity(h.edges.len());
240        let mut values = Vec::<usize>::new();
241        for e in h.adjacency.iter() {
242            lengths.push(e.sources.len());
243            values.extend(e.sources.iter().map(|x| x.0));
244        }
245
246        let sources = SemifiniteFunction(VecArray(lengths));
247        let values =
248            FiniteFunction::new(VecArray(values), h.nodes.len()).expect("invalid lax::Hypergraph!");
249        IndexedCoproduct::from_semifinite(sources, values).expect("valid IndexedCoproduct")
250    };
251
252    let t = {
253        let mut lengths = Vec::<usize>::with_capacity(h.edges.len());
254        let mut values = Vec::<usize>::new();
255        for e in h.adjacency.iter() {
256            lengths.push(e.targets.len());
257            values.extend(e.targets.iter().map(|x| x.0));
258        }
259
260        let sources = SemifiniteFunction(VecArray(lengths));
261        let values =
262            FiniteFunction::new(VecArray(values), h.nodes.len()).expect("invalid lax::Hypergraph!");
263        IndexedCoproduct::from_semifinite(sources, values).expect("valid IndexedCoproduct")
264    };
265
266    let w = SemifiniteFunction(VecArray(h.nodes.clone()));
267    let x = SemifiniteFunction(VecArray(h.edges.clone()));
268
269    crate::hypergraph::Hypergraph { s, t, w, x }
270}
open_hypergraphs/lax/hypergraph.rs

open_hypergraphs/lax/
hypergraph.rs
