An algebraic Petri net (APN) is an evolution of the well known Petri net in which elements of user defined data types (called algebraic abstract data types (AADT)[1]) replace black tokens.
However, in the APN case, the semantics of the data types is given by an axiomatization enabling proofs and computations on it.
Algebraic Petri nets[3] were invented by Jacques Vautherin in 1985 in his PhD thesis and later improved by Wolfang Reisig.
[4] The formalism has two aspects : AADT can be themselves split in two parts: The following picture describes an algebraic Petri net model of the "dining philosophers problem".
The control part is composed of : In the example below only transition goEat is firable at the beginning.