Pi calculus can be transformed from lambda calculus by replacing a variable constructor with stream constructor. But the language and protocol accessing this stream could vary from backend to backend with respect to design requirements.

`∀ (x: Input) -> Output`

Pi calculus is also known as a process calculus that can be used to model of distributed system over a channel transport. Each process presented as coinductive program and is able to be runned both in parallel and sequentially. Processes are communicating by inductive protocols known as session types over physical channels that can be corecursive streams (linear types), random access arrays (static lifetime) or other effectful disciplines. Process calculus is used to model distributed systems such as Erlang or application based protocols.

The process calculus itself should be backed with number of infinity streams, represented as processor cores. The parallel system of reactive shcedulers that cycle the list of AST trees filled with calculus instructions.

## Language Axioms

```
Inductive PiCalculus :=
| Send | Recv
| Spawn | Kill
| Sequential | Parallel
| Stop | Start
| Pub | Sub.
```

# Calculus