Now, the p-calculus has a very interesting semantic: there are two semantics, there is a reduction, you can view it either as a reduction semantics, or as transition, label transition system semantics, like other process algebras.
So with the reduction semantics, it is closer inspired to the l-calculus, or to the so called chemical abstract machine. Essentially you have only one operation, which is the operation of communication.
You see, here you along the channel a, you communicate the name u, and so you replace all occurrences of x, with u, x is a bound variable, u is a name.
Now you can also, as all other process algebras, you have the behaviour of the usual connective, so this will be the parallel connective. This is other restriction operator behaves, it's similar to what happens is CCS, so you can always, even if x is a private name, you can still make a reduction within that private area. But, more than that, you have a rule of structural rule, which is very interesting: that allows to replace terms up to structural congruence, which is defined as follows.
