zigzag-engine/examples/inspect_half_braid.rs

//! Inspect the categorical structure of half_braid.json
//!
//! Run with: cargo run --example inspect_half_braid

use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::import::load_homotopy_diagram_n;

fn describe_diagram(d: &Diagram, indent: usize) -> String {
    let prefix = "  ".repeat(indent);
    match d {
        Diagram::Diagram0(g) => {
            format!("{}0-diagram: generator id={}, dim={}", prefix, g.id, g.dimension)
        }
        Diagram::DiagramN(dn) => {
            let dim = d.dimension();
            let mut lines = vec![format!(
                "{}{}-diagram with {} cospans:",
                prefix,
                dim,
                dn.cospans.len()
            )];
            lines.push(format!("{}  source:", prefix));
            lines.push(describe_diagram(dn.source(), indent + 2));
            if !dn.cospans.is_empty() {
                lines.push(format!("{}  target:", prefix));
                lines.push(describe_diagram(&dn.target(), indent + 2));
            }
            lines.join("\n")
        }
    }
}

fn main() {
    let json = fs::read_to_string("fixtures/half_braid.json")
        .expect("Failed to read half_braid.json");
    let half_braid = load_homotopy_diagram_n(&json)
        .expect("Failed to parse");

    let half_braid_d = Diagram::DiagramN(half_braid.clone());

    println!("=== HALF_BRAID CATEGORICAL STRUCTURE ===\n");

    // The half_braid itself is a 3-diagram
    println!("half_braid is a {}-diagram with {} cospans\n",
        half_braid_d.dimension(), half_braid.cospans.len());

    // Its source (a 2-diagram)
    let source_2d = half_braid.source();
    println!("SOURCE of half_braid (the 2-diagram it transforms FROM):");
    println!("{}\n", describe_diagram(source_2d, 1));

    // Its target (a 2-diagram)
    let target_2d = half_braid.target();
    println!("TARGET of half_braid (the 2-diagram it transforms TO):");
    println!("{}\n", describe_diagram(&target_2d, 1));

    // Are source and target the same?
    println!("Are source and target equal? {}\n", source_2d == &target_2d);

    // Look at the source 2-diagram structure
    if let Diagram::DiagramN(src) = source_2d {
        println!("=== SOURCE 2-DIAGRAM SLICES ===");
        println!("This 2-diagram has {} cospans (singular heights)\n", src.cospans.len());

        // Regular slices
        for i in 0..=src.cospans.len() {
            if let Some(slice) = src.regular_slice(i) {
                println!("Regular slice r{}: {}", i, describe_diagram(&slice, 0));
            }
        }
        println!();

        // Singular slices
        for i in 0..src.cospans.len() {
            if let Some(slice) = src.singular_slice(i) {
                println!("Singular slice s{}: {}", i, describe_diagram(&slice, 0));
            }
        }
    }

    println!("\n=== INTERPRETATION ===");
    println!("Generator 0 (dim=0): The base object x");
    println!("Generator 1 (dim=2): The scalar s (a 2-cell: id_x → id_x)");
    println!();
    println!("The SOURCE 2-diagram is 'two scalars stacked':");
    println!("  - 2 cospans means 2 singular heights (s0, s1)");
    println!("  - Each singular height is where a scalar (2-cell) lives");
    println!();
    println!("The half_braid 3-diagram is the Eckmann-Hilton homotopy:");
    println!("  - It shows the two scalars 'sliding past' each other");
    println!("  - Source = target (as 2-diagrams, they're the same configuration)");
    println!("  - But the 3-diagram is NON-trivial: it's the braiding coherence");
}