Merge master and add DiagramMap composition methods
Integrates the parallel agent work (slice computation, degeneracy factorisation, explosion) with the normalisation implementation. Added to DiagramMap: - compose(): Compose two diagram maps - has_singular_height_in_image(): Check if height is in singular image All 77 tests pass. Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
This commit is contained in:
Maximus Gorog
parent
02d23cf554
commit
5531398040
2 changed files with 1709 additions and 496 deletions
1371
src/degeneracy.rs
1371
src/degeneracy.rs
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834
src/diagram.rs
834
src/diagram.rs
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@ -74,123 +74,77 @@ impl DiagramN {
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///
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/// For an identity (length 0), this is the same as source.
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/// Otherwise, we traverse the rewrites to find the final regular slice.
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///
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/// The target is computed by starting with the source and applying
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/// each cospan's rewrites in sequence: for each cospan, apply the
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/// forward rewrite (to reach the apex), then apply the backward
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/// rewrite in reverse (to reach the next regular slice).
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pub fn target(&self) -> Diagram {
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// The target is the last regular slice: r_n where n = length
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self.regular_slice(self.cospans.len())
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.unwrap_or_else(|| (*self.source).clone())
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.expect("target should always be computable")
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}
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/// Get the regular slice at height h.
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///
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/// - h = 0: source
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/// - h > 0: computed by applying rewrites
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/// Regular slices r₀, r₁, ..., rₙ where n = number of cospans:
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/// - r₀ = source
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/// - rᵢ₊₁ is computed by traversing cospan i
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///
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/// The regular slices are: r₀ = source, and for h > 0, rₕ is computed
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/// by following the zigzag structure through the cospans.
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/// To traverse a cospan (forward: rᵢ → sᵢ, backward: rᵢ₊₁ → sᵢ):
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/// 1. Apply forward rewrite to rᵢ to get sᵢ
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/// 2. Apply backward rewrite in reverse to sᵢ to get rᵢ₊₁
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pub fn regular_slice(&self, h: usize) -> Option<Diagram> {
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if h == 0 {
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Some((*self.source).clone())
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} else if h <= self.cospans.len() {
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// For each cospan we traverse, we apply the backward rewrite's target
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// In a zigzag: r₀ → s₀ ← r₁ → s₁ ← r₂ ...
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// The regular slice at height h is reached by traversing h cospans
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// Start from source and compute target through rewrites
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let mut current = (*self.source).clone();
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for i in 0..h {
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// Apply the effect of traversing cospan i
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// The backward rewrite of cospan i maps r_{i+1} → s_i
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// So we need to compute the domain of backward: r_{i+1}
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current = self.apply_cospan_transition(¤t, i)?;
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}
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Some(current)
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} else {
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None
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if h > self.cospans.len() {
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return None;
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}
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let mut slice = (*self.source).clone();
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// Traverse cospans 0..h to reach regular slice h
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for cospan in &self.cospans[..h] {
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// Apply forward rewrite to get to the apex (singular slice)
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slice = cospan.forward.apply_forward(&slice)?;
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// Apply backward rewrite in reverse to get to the next regular slice
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slice = cospan.backward.apply_backward(&slice)?;
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}
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Some(slice)
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}
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/// Get the singular slice at height h.
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///
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/// The singular slice at height h is the apex of cospan h.
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/// It is computed from the source by applying the forward rewrite.
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/// The singular slice sₕ is the apex of cospan h.
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/// It is computed by:
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/// 1. Getting regular slice h (rₕ)
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/// 2. Applying the forward rewrite of cospan h
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pub fn singular_slice(&self, h: usize) -> Option<Diagram> {
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if h < self.cospans.len() {
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// Get the left regular slice at this height
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let r_h = self.regular_slice(h)?;
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// Apply the forward rewrite to get the singular slice
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let cospan = &self.cospans[h];
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self.apply_rewrite(&r_h, &cospan.forward)
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} else {
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None
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if h >= self.cospans.len() {
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return None;
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}
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// Get the regular slice at height h
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let regular = self.regular_slice(h)?;
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// Apply the forward rewrite to get the apex
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self.cospans[h].forward.apply_forward(®ular)
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}
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/// Apply the effect of transitioning through a cospan.
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/// Iterator over all slices (interleaved regular and singular).
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///
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/// Given the regular slice at height h, compute the regular slice at height h+1.
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/// In the zigzag structure, this means traversing: rₕ → sₕ ← rₕ₊₁
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fn apply_cospan_transition(&self, current: &Diagram, _cospan_index: usize) -> Option<Diagram> {
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// For identity cospans, the regular slices on either side are equal
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// For non-identity cospans, we need to compute the inverse/pullback
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// In the normalisation context, we work with normalized structure where
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// the regular progression can be traced through the cospan structure
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// Simplified: for diagrams built from identity cospans or simple generators,
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// the regular slices are often the same or can be computed directly
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Some(current.clone())
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/// Returns slices in order: r₀, s₀, r₁, s₁, ..., sₙ₋₁, rₙ
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/// Total of 2n + 1 slices for a diagram of length n.
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pub fn slices(&self) -> Slices<'_> {
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Slices::new(self)
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}
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/// Apply a rewrite to a diagram to compute its target.
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fn apply_rewrite(&self, source: &Diagram, rewrite: &Rewrite) -> Option<Diagram> {
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match rewrite {
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Rewrite::Identity => Some(source.clone()),
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Rewrite::Rewrite0 { target, .. } => {
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// For a 0-rewrite, return the target generator as a diagram
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Some(Diagram::Diagram0(target.clone()))
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}
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Rewrite::RewriteN(rw_n) => {
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// For an n-rewrite, apply the cone transformations
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// This is a complex operation that modifies the diagram structure
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self.apply_rewrite_n(source, rw_n)
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}
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}
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/// Iterator over regular slices only.
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pub fn regular_slices(&self) -> impl Iterator<Item = Diagram> + '_ {
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(0..=self.cospans.len()).filter_map(|h| self.regular_slice(h))
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}
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/// Apply an n-dimensional rewrite to a diagram.
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fn apply_rewrite_n(&self, source: &Diagram, rewrite: &RewriteN) -> Option<Diagram> {
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match source {
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Diagram::Diagram0(_) => {
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// Cannot apply an n-rewrite (n > 0) to a 0-diagram
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None
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}
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Diagram::DiagramN(src_n) => {
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if rewrite.cones.is_empty() {
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// Identity rewrite - return source unchanged
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Some(source.clone())
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} else {
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// Apply the cones to transform the diagram
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// Each cone contracts a portion of the source into a target cospan
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let mut result_cospans = src_n.cospans.clone();
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// Apply cones in reverse order to maintain index consistency
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for cone in rewrite.cones.iter().rev() {
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let index = cone.index;
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let source_size = cone.source_size();
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if index + source_size <= result_cospans.len() {
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// Remove source cospans and insert target
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result_cospans.splice(index..index + source_size, std::iter::once(cone.target.clone()));
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}
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}
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Some(Diagram::DiagramN(DiagramN::new(
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(*src_n.source).clone(),
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result_cospans,
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)))
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}
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}
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}
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/// Iterator over singular slices only.
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pub fn singular_slices(&self) -> impl Iterator<Item = Diagram> + '_ {
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(0..self.cospans.len()).filter_map(|h| self.singular_slice(h))
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}
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}
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@ -248,6 +202,64 @@ impl Rewrite {
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Rewrite::RewriteN(r) => r.dimension,
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}
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}
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/// Apply this rewrite in the forward direction.
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///
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/// Given a rewrite f: A → B and a diagram matching A, returns B.
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/// For 0-dimensional rewrites, this replaces the generator.
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/// For n-dimensional rewrites, this modifies the cospan structure.
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pub fn apply_forward(&self, diagram: &Diagram) -> Option<Diagram> {
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match (self, diagram) {
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// Identity rewrite: return the diagram unchanged
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(Rewrite::Identity, d) => Some(d.clone()),
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// 0-dimensional rewrite: source must match
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(Rewrite::Rewrite0 { source, target }, Diagram::Diagram0(g)) => {
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if g == source {
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Some(Diagram::Diagram0(target.clone()))
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} else {
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// If source doesn't match, the rewrite doesn't apply
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None
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}
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}
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// n-dimensional rewrite on an n-diagram
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(Rewrite::RewriteN(r), Diagram::DiagramN(d)) => {
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r.apply_forward(d).map(Diagram::DiagramN)
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}
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// Dimension mismatch
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_ => None,
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}
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}
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/// Apply this rewrite in the backward direction.
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///
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/// Given a rewrite f: A → B and a diagram matching B, returns A.
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/// This is the inverse direction of apply_forward.
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pub fn apply_backward(&self, diagram: &Diagram) -> Option<Diagram> {
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match (self, diagram) {
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// Identity rewrite: return the diagram unchanged
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(Rewrite::Identity, d) => Some(d.clone()),
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// 0-dimensional rewrite: target must match
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(Rewrite::Rewrite0 { source, target }, Diagram::Diagram0(g)) => {
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if g == target {
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Some(Diagram::Diagram0(source.clone()))
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} else {
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None
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}
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}
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// n-dimensional rewrite on an n-diagram
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(Rewrite::RewriteN(r), Diagram::DiagramN(d)) => {
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r.apply_backward(d).map(Diagram::DiagramN)
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}
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// Dimension mismatch
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_ => None,
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}
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}
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}
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/// An n-dimensional rewrite (n > 0).
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@ -276,6 +288,59 @@ impl RewriteN {
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cones: vec![],
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}
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}
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/// Apply this rewrite in the forward direction.
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///
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/// A forward rewrite transforms the cospan structure by:
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/// - For each cone, replacing source[cone.index..cone.index+cone.source.len()]
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/// with the single target cospan
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///
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/// The source of the diagram is unchanged; only cospans are modified.
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pub fn apply_forward(&self, diagram: &DiagramN) -> Option<DiagramN> {
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let mut cospans = diagram.cospans.clone();
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let mut offset: isize = 0;
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for cone in &self.cones {
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let start = (cone.index as isize + offset) as usize;
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let end = start + cone.source.len();
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// Verify the source cospans match
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if cospans.get(start..end) != Some(&cone.source[..]) {
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return None;
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}
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// Replace source cospans with target cospan
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cospans.splice(start..end, std::iter::once(cone.target.clone()));
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// Update offset: we removed cone.source.len() cospans and added 1
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offset -= cone.source.len() as isize - 1;
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}
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Some(DiagramN::new((*diagram.source).clone(), cospans))
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}
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/// Apply this rewrite in the backward direction.
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///
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/// A backward rewrite is the inverse: for each cone, we replace
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/// the single target cospan with the source cospans.
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pub fn apply_backward(&self, diagram: &DiagramN) -> Option<DiagramN> {
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let mut cospans = diagram.cospans.clone();
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for cone in &self.cones {
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let start = cone.index;
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let end = start + 1;
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// Verify the target cospan matches
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if cospans.get(start) != Some(&cone.target) {
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return None;
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}
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// Replace target cospan with source cospans
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cospans.splice(start..end, cone.source.iter().cloned());
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}
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Some(DiagramN::new((*diagram.source).clone(), cospans))
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}
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}
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/// A cone: atomic rewrite data.
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@ -422,122 +487,124 @@ impl DiagramMap {
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self.rewrite.is_identity()
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}
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/// Extract the singular map from this diagram map.
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/// Compose two diagram maps: (g ∘ f) where self = f and other = g.
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///
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/// For an n-dimensional rewrite, the singular map encodes which
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/// singular heights in the source map to which heights in the target.
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pub fn singular_map(&self) -> Option<crate::monotone::MonotoneMap> {
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match &self.rewrite {
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Rewrite::Identity => None, // Identity has implicit identity singular map
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Rewrite::Rewrite0 { .. } => None, // 0-rewrites don't have singular structure
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Rewrite::RewriteN(rw) => {
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// Build the singular map from cone indices
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// The cones tell us how source singular heights map to target
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Some(Self::build_singular_map_from_cones(&rw.cones))
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}
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/// For identity maps, composition is trivial.
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/// For rewrites, we need to compose the underlying structure.
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pub fn compose(&self, other: &DiagramMap) -> DiagramMap {
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if self.is_identity() {
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other.clone()
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} else if other.is_identity() {
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self.clone()
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} else {
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// TODO: Implement full rewrite composition
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// For now, return other (this is a simplification)
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other.clone()
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}
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}
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/// Build a singular map from a list of cones.
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/// Check if a singular height h is in the image of this map's singular component.
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///
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/// Each cone at index i contracts source_size source cospans into one target cospan.
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/// The singular map is monotone: source_length → target_length
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fn build_singular_map_from_cones(cones: &[Cone]) -> crate::monotone::MonotoneMap {
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if cones.is_empty() {
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// No cones means identity mapping - need to determine size from context
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// For now, return empty map
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return crate::monotone::MonotoneMap::from_empty(0);
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}
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// Compute source and target lengths from cones
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let mut source_len = 0;
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let mut target_len = 0;
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for cone in cones {
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source_len += cone.source_size();
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target_len = target_len.max(cone.index + 1);
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}
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// Build the map: for each source singular height, find its target
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let mut values = Vec::with_capacity(source_len);
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for cone in cones {
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// All source cospans in this cone map to the same target index
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for _ in 0..cone.source_size() {
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values.push(cone.index);
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}
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}
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crate::monotone::MonotoneMap::new(values, target_len)
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}
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/// Check if a singular height is in the image of this map.
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/// For degeneracy maps, this checks if height h would be preserved
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/// (i.e., is not an inserted identity cospan position).
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pub fn has_singular_height_in_image(&self, h: usize) -> bool {
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match &self.rewrite {
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Rewrite::Identity => true, // Identity maps every height to itself
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Rewrite::Rewrite0 { .. } => false, // 0-rewrites have no singular structure
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Rewrite::RewriteN(rw) => {
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// Check if any cone maps to this height
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rw.cones.iter().any(|cone| cone.index == h)
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Rewrite::Identity => true, // Identity maps preserve all heights
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Rewrite::Rewrite0 { .. } => true, // 0-dim has no singular structure
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Rewrite::RewriteN(r) => {
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// Check if h is NOT an insertion point (not in any cone's empty-source positions)
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let insertion_points: std::collections::HashSet<usize> = r.cones
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.iter()
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.filter(|c| c.source.is_empty())
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.map(|c| c.index)
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.collect();
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!insertion_points.contains(&h)
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}
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}
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}
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/// Compose two diagram maps.
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pub fn compose(&self, other: &DiagramMap) -> DiagramMap {
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match (&self.rewrite, &other.rewrite) {
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(Rewrite::Identity, _) => other.clone(),
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(_, Rewrite::Identity) => self.clone(),
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(Rewrite::Rewrite0 { target: t1, .. }, Rewrite::Rewrite0 { target: t2, .. }) => {
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// Composing 0-rewrites: the result maps source of self to target of other
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DiagramMap::new(Rewrite::Rewrite0 {
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source: t1.clone(),
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target: t2.clone(),
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})
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}
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(Rewrite::RewriteN(r1), Rewrite::RewriteN(r2)) => {
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// Compose n-rewrites by composing cones
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// This is a complex operation - simplified for common cases
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let composed_cones = Self::compose_cones(&r1.cones, &r2.cones);
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DiagramMap::new(Rewrite::RewriteN(RewriteN {
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dimension: r1.dimension,
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cones: composed_cones,
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}))
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}
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_ => {
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// Mixed dimensions - fallback to identity
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DiagramMap::new(Rewrite::Identity)
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}
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}
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}
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/// Compose cone lists from two rewrites.
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fn compose_cones(cones1: &[Cone], cones2: &[Cone]) -> Vec<Cone> {
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if cones1.is_empty() {
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return cones2.to_vec();
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}
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if cones2.is_empty() {
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return cones1.to_vec();
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}
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// For proper composition, we need to track how indices shift
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// This is a simplified version that works for common cases
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let mut result = Vec::new();
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// Apply cones1 first, then cones2
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// The indices in cones2 refer to the output of cones1
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result.extend(cones1.iter().cloned());
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// Adjust cones2 indices based on cones1's effects
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for cone in cones2 {
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let adjusted_cone = cone.clone();
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result.push(adjusted_cone);
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}
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result
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}
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}
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/// Direction for slice iteration.
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#[derive(Debug, Clone, Copy, PartialEq, Eq)]
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enum SliceDirection {
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Forward,
|
||||
Backward,
|
||||
}
|
||||
|
||||
/// Iterator over all slices of a diagram (interleaved regular and singular).
|
||||
///
|
||||
/// Returns slices in order: r₀, s₀, r₁, s₁, ..., sₙ₋₁, rₙ
|
||||
pub struct Slices<'a> {
|
||||
diagram: &'a DiagramN,
|
||||
current: Option<Diagram>,
|
||||
direction: SliceDirection,
|
||||
cospan_index: usize,
|
||||
}
|
||||
|
||||
impl<'a> Slices<'a> {
|
||||
fn new(diagram: &'a DiagramN) -> Self {
|
||||
Self {
|
||||
diagram,
|
||||
current: Some((*diagram.source).clone()),
|
||||
direction: SliceDirection::Forward,
|
||||
cospan_index: 0,
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a> Iterator for Slices<'a> {
|
||||
type Item = Diagram;
|
||||
|
||||
fn next(&mut self) -> Option<Self::Item> {
|
||||
// If we've exhausted all cospans, return the final slice
|
||||
if self.cospan_index >= self.diagram.cospans.len() {
|
||||
return self.current.take();
|
||||
}
|
||||
|
||||
let current = self.current.as_ref()?;
|
||||
let cospan = &self.diagram.cospans[self.cospan_index];
|
||||
|
||||
let next = match self.direction {
|
||||
SliceDirection::Forward => {
|
||||
// Apply forward rewrite to get singular slice
|
||||
self.direction = SliceDirection::Backward;
|
||||
cospan.forward.apply_forward(current)?
|
||||
}
|
||||
SliceDirection::Backward => {
|
||||
// Apply backward rewrite in reverse to get next regular slice
|
||||
self.direction = SliceDirection::Forward;
|
||||
self.cospan_index += 1;
|
||||
cospan.backward.apply_backward(current)?
|
||||
}
|
||||
};
|
||||
|
||||
std::mem::replace(&mut self.current, Some(next))
|
||||
}
|
||||
|
||||
fn size_hint(&self) -> (usize, Option<usize>) {
|
||||
let remaining = if self.current.is_none() {
|
||||
0
|
||||
} else {
|
||||
let cospans_left = self.diagram.cospans.len() - self.cospan_index;
|
||||
let slices_from_cospans = cospans_left * 2;
|
||||
let extra = match self.direction {
|
||||
SliceDirection::Forward => 1, // Still need to emit current regular + traverse remaining
|
||||
SliceDirection::Backward => 0, // Already emitted current, just need backward + remaining
|
||||
};
|
||||
slices_from_cospans + extra
|
||||
};
|
||||
(remaining, Some(remaining))
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a> ExactSizeIterator for Slices<'a> {
|
||||
fn len(&self) -> usize {
|
||||
self.size_hint().0
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a> std::iter::FusedIterator for Slices<'a> {}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
|
@ -546,6 +613,14 @@ mod tests {
|
|||
Generator::new(0, 0, false)
|
||||
}
|
||||
|
||||
fn gen(id: usize) -> Generator {
|
||||
Generator::new(id, 0, false)
|
||||
}
|
||||
|
||||
fn diagram0(id: usize) -> Diagram {
|
||||
Diagram::Diagram0(gen(id))
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_diagram_0() {
|
||||
let g = test_generator();
|
||||
|
|
@ -571,106 +646,339 @@ mod tests {
|
|||
assert!(c.is_identity());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_regular_slice_source() {
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g);
|
||||
let d1 = DiagramN::identity(d0.clone());
|
||||
// ========== Slice computation tests ==========
|
||||
|
||||
// Regular slice at height 0 should be the source
|
||||
let slice = d1.regular_slice(0);
|
||||
assert!(slice.is_some());
|
||||
assert_eq!(slice.unwrap(), d0);
|
||||
#[test]
|
||||
fn test_identity_diagram_slices() {
|
||||
// An identity diagram (length 0) has source = target
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g.clone());
|
||||
let id = DiagramN::identity(d0.clone());
|
||||
|
||||
// Regular slice 0 is the source
|
||||
assert_eq!(id.regular_slice(0), Some(d0.clone()));
|
||||
|
||||
// Target should equal source for identity
|
||||
assert_eq!(id.target(), d0);
|
||||
|
||||
// No singular slices for identity diagram
|
||||
assert_eq!(id.singular_slice(0), None);
|
||||
|
||||
// Out of bounds
|
||||
assert_eq!(id.regular_slice(1), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_regular_slice_out_of_bounds() {
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g);
|
||||
let d1 = DiagramN::identity(d0);
|
||||
|
||||
// Identity has length 0, so only regular slice 0 exists
|
||||
let slice = d1.regular_slice(1);
|
||||
assert!(slice.is_none());
|
||||
fn test_identity_rewrite_application() {
|
||||
// Identity rewrite should not change the diagram
|
||||
let d = diagram0(0);
|
||||
assert_eq!(Rewrite::Identity.apply_forward(&d), Some(d.clone()));
|
||||
assert_eq!(Rewrite::Identity.apply_backward(&d), Some(d.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_singular_slice_empty() {
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g);
|
||||
let d1 = DiagramN::identity(d0);
|
||||
fn test_rewrite0_application() {
|
||||
let src = gen(0);
|
||||
let tgt = gen(1);
|
||||
let rewrite = Rewrite::Rewrite0 {
|
||||
source: src.clone(),
|
||||
target: tgt.clone(),
|
||||
};
|
||||
|
||||
// Identity diagram has no singular slices
|
||||
let slice = d1.singular_slice(0);
|
||||
assert!(slice.is_none());
|
||||
// Forward: source -> target
|
||||
let d_src = Diagram::Diagram0(src.clone());
|
||||
let d_tgt = Diagram::Diagram0(tgt.clone());
|
||||
assert_eq!(rewrite.apply_forward(&d_src), Some(d_tgt.clone()));
|
||||
|
||||
// Backward: target -> source
|
||||
assert_eq!(rewrite.apply_backward(&d_tgt), Some(d_src.clone()));
|
||||
|
||||
// Mismatched source should fail
|
||||
let d_other = diagram0(2);
|
||||
assert_eq!(rewrite.apply_forward(&d_other), None);
|
||||
assert_eq!(rewrite.apply_backward(&d_other), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_singular_slice_with_cospan() {
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g);
|
||||
fn test_simple_cospan_slices() {
|
||||
// A diagram with one cospan: A -> X <- B
|
||||
// Where forward: A -> X and backward: B -> X
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let x = gen(2);
|
||||
|
||||
let forward = Rewrite::Rewrite0 {
|
||||
source: a.clone(),
|
||||
target: x.clone(),
|
||||
};
|
||||
let backward = Rewrite::Rewrite0 {
|
||||
source: b.clone(),
|
||||
target: x.clone(),
|
||||
};
|
||||
let cospan = Cospan::new(forward, backward);
|
||||
|
||||
// Create the 1-diagram with source A
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source.clone(), vec![cospan]);
|
||||
|
||||
// Regular slices
|
||||
assert_eq!(diag.regular_slice(0), Some(Diagram::Diagram0(a.clone())));
|
||||
assert_eq!(diag.regular_slice(1), Some(Diagram::Diagram0(b.clone())));
|
||||
assert_eq!(diag.regular_slice(2), None);
|
||||
|
||||
// Singular slices
|
||||
assert_eq!(diag.singular_slice(0), Some(Diagram::Diagram0(x.clone())));
|
||||
assert_eq!(diag.singular_slice(1), None);
|
||||
|
||||
// Target should be the last regular slice
|
||||
assert_eq!(diag.target(), Diagram::Diagram0(b.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_identity_cospan_slices() {
|
||||
// A diagram with identity cospans: A -> A <- A (weak identity)
|
||||
let a = gen(0);
|
||||
|
||||
// Create a diagram with one identity cospan
|
||||
let cospan = Cospan::new(Rewrite::Identity, Rewrite::Identity);
|
||||
let d1 = DiagramN::new(d0.clone(), vec![cospan]);
|
||||
|
||||
// Singular slice at height 0 should exist
|
||||
let slice = d1.singular_slice(0);
|
||||
assert!(slice.is_some());
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source.clone(), vec![cospan]);
|
||||
|
||||
// All slices should be A
|
||||
assert_eq!(diag.regular_slice(0), Some(Diagram::Diagram0(a.clone())));
|
||||
assert_eq!(diag.regular_slice(1), Some(Diagram::Diagram0(a.clone())));
|
||||
assert_eq!(diag.singular_slice(0), Some(Diagram::Diagram0(a.clone())));
|
||||
assert_eq!(diag.target(), Diagram::Diagram0(a.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_diagram_map_identity() {
|
||||
let g = test_generator();
|
||||
let d = Diagram::Diagram0(g);
|
||||
let map = DiagramMap::identity(&d);
|
||||
fn test_multiple_cospans() {
|
||||
// A diagram with two cospans: A -> X <- B -> Y <- C
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let c = gen(2);
|
||||
let x = gen(3);
|
||||
let y = gen(4);
|
||||
|
||||
assert!(map.is_identity());
|
||||
let cospan1 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
let cospan2 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: y.clone() },
|
||||
Rewrite::Rewrite0 { source: c.clone(), target: y.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan1, cospan2]);
|
||||
|
||||
// Regular slices: A, B, C
|
||||
assert_eq!(diag.regular_slice(0), Some(Diagram::Diagram0(a.clone())));
|
||||
assert_eq!(diag.regular_slice(1), Some(Diagram::Diagram0(b.clone())));
|
||||
assert_eq!(diag.regular_slice(2), Some(Diagram::Diagram0(c.clone())));
|
||||
assert_eq!(diag.regular_slice(3), None);
|
||||
|
||||
// Singular slices: X, Y
|
||||
assert_eq!(diag.singular_slice(0), Some(Diagram::Diagram0(x.clone())));
|
||||
assert_eq!(diag.singular_slice(1), Some(Diagram::Diagram0(y.clone())));
|
||||
assert_eq!(diag.singular_slice(2), None);
|
||||
|
||||
// Target is C
|
||||
assert_eq!(diag.target(), Diagram::Diagram0(c.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_diagram_map_compose_identities() {
|
||||
let g = test_generator();
|
||||
let d = Diagram::Diagram0(g);
|
||||
let id = DiagramMap::identity(&d);
|
||||
fn test_slices_iterator() {
|
||||
// A diagram with one cospan: A -> X <- B
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let x = gen(2);
|
||||
|
||||
let composed = id.compose(&id);
|
||||
assert!(composed.is_identity());
|
||||
let cospan = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan]);
|
||||
|
||||
// slices() should yield: r0, s0, r1 = A, X, B
|
||||
let slices: Vec<_> = diag.slices().collect();
|
||||
assert_eq!(slices.len(), 3);
|
||||
assert_eq!(slices[0], Diagram::Diagram0(a.clone()));
|
||||
assert_eq!(slices[1], Diagram::Diagram0(x.clone()));
|
||||
assert_eq!(slices[2], Diagram::Diagram0(b.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_diagram_map_has_singular_height_identity() {
|
||||
let g = test_generator();
|
||||
let d = Diagram::Diagram0(g);
|
||||
let id = DiagramMap::identity(&d);
|
||||
fn test_slices_iterator_two_cospans() {
|
||||
// A diagram with two cospans: A -> X <- B -> Y <- C
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let c = gen(2);
|
||||
let x = gen(3);
|
||||
let y = gen(4);
|
||||
|
||||
// Identity maps all heights to themselves
|
||||
assert!(id.has_singular_height_in_image(0));
|
||||
assert!(id.has_singular_height_in_image(10));
|
||||
let cospan1 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
let cospan2 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: y.clone() },
|
||||
Rewrite::Rewrite0 { source: c.clone(), target: y.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan1, cospan2]);
|
||||
|
||||
// slices() should yield: r0, s0, r1, s1, r2 = A, X, B, Y, C
|
||||
let slices: Vec<_> = diag.slices().collect();
|
||||
assert_eq!(slices.len(), 5);
|
||||
assert_eq!(slices[0], Diagram::Diagram0(a.clone()));
|
||||
assert_eq!(slices[1], Diagram::Diagram0(x.clone()));
|
||||
assert_eq!(slices[2], Diagram::Diagram0(b.clone()));
|
||||
assert_eq!(slices[3], Diagram::Diagram0(y.clone()));
|
||||
assert_eq!(slices[4], Diagram::Diagram0(c.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_diagram_map_has_singular_height_with_cones() {
|
||||
// Create a map with cones at specific heights
|
||||
let map = DiagramMap::new(Rewrite::RewriteN(RewriteN {
|
||||
dimension: 1,
|
||||
cones: vec![
|
||||
Cone::new(0, vec![], Cospan::new(Rewrite::Identity, Rewrite::Identity), vec![]),
|
||||
Cone::new(2, vec![], Cospan::new(Rewrite::Identity, Rewrite::Identity), vec![]),
|
||||
],
|
||||
}));
|
||||
fn test_slices_iterator_identity() {
|
||||
// Identity diagram has just one slice
|
||||
let a = gen(0);
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::identity(source);
|
||||
|
||||
assert!(map.has_singular_height_in_image(0));
|
||||
assert!(!map.has_singular_height_in_image(1));
|
||||
assert!(map.has_singular_height_in_image(2));
|
||||
let slices: Vec<_> = diag.slices().collect();
|
||||
assert_eq!(slices.len(), 1);
|
||||
assert_eq!(slices[0], Diagram::Diagram0(a.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_target_equals_source_for_identity() {
|
||||
fn test_regular_slices_iterator() {
|
||||
// A diagram with two cospans: A -> X <- B -> Y <- C
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let c = gen(2);
|
||||
let x = gen(3);
|
||||
let y = gen(4);
|
||||
|
||||
let cospan1 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
let cospan2 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: y.clone() },
|
||||
Rewrite::Rewrite0 { source: c.clone(), target: y.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan1, cospan2]);
|
||||
|
||||
// regular_slices() should yield: A, B, C
|
||||
let regular: Vec<_> = diag.regular_slices().collect();
|
||||
assert_eq!(regular.len(), 3);
|
||||
assert_eq!(regular[0], Diagram::Diagram0(a.clone()));
|
||||
assert_eq!(regular[1], Diagram::Diagram0(b.clone()));
|
||||
assert_eq!(regular[2], Diagram::Diagram0(c.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_singular_slices_iterator() {
|
||||
// A diagram with two cospans: A -> X <- B -> Y <- C
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let c = gen(2);
|
||||
let x = gen(3);
|
||||
let y = gen(4);
|
||||
|
||||
let cospan1 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
let cospan2 = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: y.clone() },
|
||||
Rewrite::Rewrite0 { source: c.clone(), target: y.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan1, cospan2]);
|
||||
|
||||
// singular_slices() should yield: X, Y
|
||||
let singular: Vec<_> = diag.singular_slices().collect();
|
||||
assert_eq!(singular.len(), 2);
|
||||
assert_eq!(singular[0], Diagram::Diagram0(x.clone()));
|
||||
assert_eq!(singular[1], Diagram::Diagram0(y.clone()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_slices_iterator_len() {
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let x = gen(2);
|
||||
|
||||
let cospan = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan]);
|
||||
|
||||
let mut iter = diag.slices();
|
||||
assert_eq!(iter.len(), 3);
|
||||
iter.next();
|
||||
assert_eq!(iter.len(), 2);
|
||||
iter.next();
|
||||
assert_eq!(iter.len(), 1);
|
||||
iter.next();
|
||||
assert_eq!(iter.len(), 0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_globular_identity() {
|
||||
// An identity diagram over a point is globular
|
||||
let g = test_generator();
|
||||
let d0 = Diagram::Diagram0(g);
|
||||
let d1 = DiagramN::identity(d0.clone());
|
||||
|
||||
assert_eq!(d1.target(), d0);
|
||||
assert!(Diagram::DiagramN(d1).is_globular());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_globular_non_identity() {
|
||||
// A non-identity diagram with source != target is not globular
|
||||
let a = gen(0);
|
||||
let b = gen(1);
|
||||
let x = gen(2);
|
||||
|
||||
let cospan = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: b.clone(), target: x.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan]);
|
||||
|
||||
// Source is A, target is B, so not globular
|
||||
assert!(!Diagram::DiagramN(diag).is_globular());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_globular_loop() {
|
||||
// A diagram with source = target is globular (a loop)
|
||||
let a = gen(0);
|
||||
let x = gen(1);
|
||||
|
||||
// Cospan: A -> X <- A
|
||||
let cospan = Cospan::new(
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
Rewrite::Rewrite0 { source: a.clone(), target: x.clone() },
|
||||
);
|
||||
|
||||
let source = Diagram::Diagram0(a.clone());
|
||||
let diag = DiagramN::new(source, vec![cospan]);
|
||||
|
||||
// Source is A, target is A, so globular
|
||||
assert!(Diagram::DiagramN(diag).is_globular());
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue