136 lines
2.9 KiB
Plaintext
136 lines
2.9 KiB
Plaintext
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// Petri Net: a bipartite graph between places and transitions
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//
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// Petri nets model concurrent systems. Places hold tokens, transitions
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// fire when their input places have tokens, consuming inputs and
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// producing outputs.
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//
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// This encoding uses explicit "arc" sorts for input/output connections,
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// which is more faithful to the categorical semantics (a span).
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theory PetriNet {
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P : Sort; // Places
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T : Sort; // Transitions
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In : Sort; // Input arcs (from place to transition)
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Out : Sort; // Output arcs (from transition to place)
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// Input arc endpoints
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in/place : In -> P;
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in/trans : In -> T;
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// Output arc endpoints
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out/trans : Out -> T;
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out/place : Out -> P;
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}
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// A simple producer-consumer net:
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//
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// (ready) --[produce]--> (buffer) --[consume]--> (done)
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//
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instance ProducerConsumer : PetriNet = {
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// Places
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ready : P;
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buffer : P;
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done : P;
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// Transitions
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produce : T;
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consume : T;
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// Input arcs
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i1 : In;
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i1 in/place = ready;
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i1 in/trans = produce;
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i2 : In;
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i2 in/place = buffer;
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i2 in/trans = consume;
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// Output arcs
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o1 : Out;
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o1 out/trans = produce;
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o1 out/place = buffer;
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o2 : Out;
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o2 out/trans = consume;
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o2 out/place = done;
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}
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// Mutual exclusion: two processes competing for a shared resource
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//
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// (idle1) --[enter1]--> (crit1) --[exit1]--> (idle1)
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// ^ |
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// | (mutex) |
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// | v
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// (idle2) --[enter2]--> (crit2) --[exit2]--> (idle2)
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//
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instance MutualExclusion : PetriNet = {
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// Places for process 1
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idle1 : P;
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crit1 : P;
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// Places for process 2
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idle2 : P;
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crit2 : P;
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// Shared mutex token
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mutex : P;
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// Transitions
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enter1 : T;
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exit1 : T;
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enter2 : T;
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exit2 : T;
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// Process 1 enters: needs idle1 AND mutex
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i_enter1_idle : In;
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i_enter1_idle in/place = idle1;
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i_enter1_idle in/trans = enter1;
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i_enter1_mutex : In;
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i_enter1_mutex in/place = mutex;
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i_enter1_mutex in/trans = enter1;
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o_enter1 : Out;
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o_enter1 out/trans = enter1;
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o_enter1 out/place = crit1;
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// Process 1 exits: releases mutex
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i_exit1 : In;
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i_exit1 in/place = crit1;
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i_exit1 in/trans = exit1;
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o_exit1_idle : Out;
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o_exit1_idle out/trans = exit1;
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o_exit1_idle out/place = idle1;
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o_exit1_mutex : Out;
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o_exit1_mutex out/trans = exit1;
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o_exit1_mutex out/place = mutex;
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// Process 2 enters: needs idle2 AND mutex
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i_enter2_idle : In;
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i_enter2_idle in/place = idle2;
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i_enter2_idle in/trans = enter2;
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i_enter2_mutex : In;
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i_enter2_mutex in/place = mutex;
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i_enter2_mutex in/trans = enter2;
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o_enter2 : Out;
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o_enter2 out/trans = enter2;
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o_enter2 out/place = crit2;
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// Process 2 exits: releases mutex
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i_exit2 : In;
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i_exit2 in/place = crit2;
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i_exit2 in/trans = exit2;
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o_exit2_idle : Out;
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o_exit2_idle out/trans = exit2;
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o_exit2_idle out/place = idle2;
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o_exit2_mutex : Out;
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o_exit2_mutex out/trans = exit2;
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o_exit2_mutex out/place = mutex;
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}
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