67 lines
1.8 KiB
Plaintext
67 lines
1.8 KiB
Plaintext
// Test Trace theory with axioms using product codomains
|
|
|
|
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;
|
|
}
|
|
|
|
// Trace theory with axioms
|
|
theory (N : PetriNet instance) Trace {
|
|
F : Sort;
|
|
F/of : F -> N/T;
|
|
|
|
W : Sort;
|
|
W/src : W -> [firing : F, arc : N/out];
|
|
W/tgt : W -> [firing : F, arc : N/in];
|
|
|
|
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];
|
|
|
|
// Axiom: wires are injective on source
|
|
// forall w1, w2 : W. w1 W/src = w2 W/src |- w1 = w2;
|
|
// (Commented out - requires product codomain equality in premises)
|
|
|
|
// Axiom: every arc endpoint must be wired or terminated
|
|
// forall f : F, arc : N/out. arc N/out/src = f F/of |-
|
|
// (exists w : W. w W/src = [firing: f, arc: arc]) \/
|
|
// (exists o : output_terminal. o output_terminal/src = [firing: f, arc: arc]);
|
|
// (Commented out - requires product codomain values in conclusions)
|
|
}
|
|
|
|
// Simple net for testing
|
|
instance SimpleNet : PetriNet = {
|
|
A : P;
|
|
B : P;
|
|
t : T;
|
|
arc_in : in;
|
|
arc_in in/src = A;
|
|
arc_in in/tgt = t;
|
|
arc_out : out;
|
|
arc_out out/src = t;
|
|
arc_out out/tgt = B;
|
|
}
|
|
|
|
// Test that the basic theory without axioms still works
|
|
instance SimpleTrace : SimpleNet Trace = {
|
|
f1 : F;
|
|
f1 F/of = SimpleNet/t;
|
|
|
|
it : input_terminal;
|
|
it input_terminal/of = SimpleNet/A;
|
|
it input_terminal/tgt = [firing: f1, arc: SimpleNet/arc_in];
|
|
|
|
ot : output_terminal;
|
|
ot output_terminal/of = SimpleNet/B;
|
|
ot output_terminal/src = [firing: f1, arc: SimpleNet/arc_out];
|
|
}
|