95 lines
2.1 KiB
Plaintext
95 lines
2.1 KiB
Plaintext
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// Petri Net Reachability Vision Test
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// Based on 2025-12-12 design document
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// Basic Petri net structure
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theory PetriNet {
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// Places
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P : Sort;
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// Transitions
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T : Sort;
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// Arcs (input to transitions, output from transitions)
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in : Sort;
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out : Sort;
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in/src : in -> P;
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in/tgt : in -> T;
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out/src : out -> T;
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out/tgt : out -> P;
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}
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// A marking is a multiset of tokens, each at a place
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theory (N : PetriNet instance) Marking {
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token : Sort;
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token/of : token -> N/P;
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}
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// A reachability problem is: can we get from initial marking to target?
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theory (N : PetriNet instance) ReachabilityProblem {
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initial_marking : N Marking instance;
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target_marking : N Marking instance;
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}
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// A trace is a sequence of firings connected by wires
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theory (N : PetriNet instance) Trace {
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// Firings of transitions
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F : Sort;
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F/of : F -> N/T;
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// Wires connect firing outputs to firing inputs
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W : Sort;
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W/src : W -> [firing : F, arc : N/out];
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W/tgt : W -> [firing : F, arc : N/in];
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// Terminals are unconnected arc endpoints (to/from the initial/target markings)
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input_terminal : Sort;
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output_terminal : Sort;
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input_terminal/of : input_terminal -> N/P;
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output_terminal/of : output_terminal -> N/P;
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input_terminal/tgt : input_terminal -> [firing : F, arc : N/in];
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output_terminal/src : output_terminal -> [firing : F, arc : N/out];
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}
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// Example Petri net: A <--ab/ba--> B, (A,B) --abc--> C
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instance ExampleNet : PetriNet = {
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A : P;
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B : P;
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C : P;
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ab : T;
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ba : T;
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abc : T;
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ab_in : in;
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ab_in in/src = A;
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ab_in in/tgt = ab;
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ab_out : out;
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ab_out out/src = ab;
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ab_out out/tgt = B;
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ba_in : in;
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ba_in in/src = B;
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ba_in in/tgt = ba;
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ba_out : out;
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ba_out out/src = ba;
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ba_out out/tgt = A;
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abc_in1 : in;
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abc_in1 in/src = A;
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abc_in1 in/tgt = abc;
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abc_in2 : in;
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abc_in2 in/src = B;
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abc_in2 in/tgt = abc;
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abc_out : out;
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abc_out out/src = abc;
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abc_out out/tgt = C;
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}
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// Reachability problem: Can we reach B from A?
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instance problem0 : ExampleNet ReachabilityProblem = {
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initial_marking = {
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t : token;
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t token/of = ExampleNet/A;
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};
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target_marking = {
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t : token;
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t token/of = ExampleNet/B;
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};
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}
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