// Full Petri Net Reachability Vision Test
// From 2025-12-12_12:10_VanillaPetriNetRechability.md

theory PetriNet {
  P : Sort;
  T : Sort;
  in : Sort;
  out : Sort;
  in/src : in -> P;
  in/tgt : in -> T;
  out/src : out -> T;
  out/tgt : out -> P;
}

theory (N : PetriNet instance) Marking {
  token : Sort;
  token/of : token -> N/P;
}

theory (N : PetriNet instance) ReachabilityProblem {
  initial_marking : N Marking instance;
  target_marking : N Marking instance;
}

// Simplified Trace theory without disjunctions for now
theory (N : PetriNet instance) SimpleTrace {
  F : Sort;
  F/of : F -> N/T;

  input_terminal : Sort;
  output_terminal : Sort;
  input_terminal/of : input_terminal -> N/P;
  output_terminal/of : output_terminal -> N/P;
  input_terminal/tgt : input_terminal -> [firing : F, arc : N/in];
  output_terminal/src : output_terminal -> [firing : F, arc : N/out];

  // Simplified ax5: every firing+arc gets an output terminal
  ax5 : forall f : F, arc : N/out. |- exists o : output_terminal. o output_terminal/src = [firing: f, arc: arc];

  // Simplified ax6: every firing+arc gets an input terminal
  ax6 : forall f : F, arc : N/in. |- exists i : input_terminal. i input_terminal/tgt = [firing: f, arc: arc];
}

instance ExampleNet : PetriNet = {
  A : P;
  B : P;
  ab : T;
  ab_in : in;
  ab_in in/src = A;
  ab_in in/tgt = ab;
  ab_out : out;
  ab_out out/src = ab;
  ab_out out/tgt = B;
}

// Test nested instance elaboration
instance problem0 : ExampleNet ReachabilityProblem = {
  initial_marking = {
    tok : token;
    tok token/of = ExampleNet/A;
  };
  target_marking = {
    tok : token;
    tok token/of = ExampleNet/B;
  };
}

// Test chase with SimpleTrace
instance trace0 : ExampleNet SimpleTrace = chase {
  f1 : F;
  f1 F/of = ExampleNet/ab;
}