80 lines
1.3 KiB
Plaintext
80 lines
1.3 KiB
Plaintext
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// Directed Graph: vertices and edges with source/target functions
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//
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// This is the canonical example of a "presheaf" - a functor from a small
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// category (the "walking arrow" • → •) to Set.
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theory Graph {
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V : Sort; // Vertices
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E : Sort; // Edges
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src : E -> V; // Source of an edge
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tgt : E -> V; // Target of an edge
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}
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// A simple triangle graph: A → B → C → A
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instance Triangle : Graph = {
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// Vertices
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A : V;
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B : V;
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C : V;
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// Edges
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ab : E;
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bc : E;
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ca : E;
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// Edge endpoints
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ab src = A;
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ab tgt = B;
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bc src = B;
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bc tgt = C;
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ca src = C;
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ca tgt = A;
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}
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// A self-loop: one vertex with an edge to itself
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instance Loop : Graph = {
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v : V;
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e : E;
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e src = v;
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e tgt = v;
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}
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// The "walking arrow": two vertices, one edge
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instance Arrow : Graph = {
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s : V;
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t : V;
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f : E;
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f src = s;
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f tgt = t;
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}
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// A more complex graph: diamond shape with two paths from top to bottom
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//
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// top
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// / \
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// left right
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// \ /
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// bottom
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//
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instance Diamond : Graph = {
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top : V;
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left : V;
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right : V;
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bottom : V;
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top_left : E;
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top_right : E;
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left_bottom : E;
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right_bottom : E;
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top_left src = top;
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top_left tgt = left;
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top_right src = top;
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top_right tgt = right;
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left_bottom src = left;
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left_bottom tgt = bottom;
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right_bottom src = right;
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right_bottom tgt = bottom;
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}
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