# Sessions

We have seen that Ferrite programs have the Rust type Session<A>, where the type A must implement the Protocol trait. A Ferrite program of type Session<A> starts with an empty linear context, and offers the protocol A. More generally, it is also possible to define partial Ferrite programs with non-empty linear context. In such cases, these programs would have the Rust type PartialSession<C, A>.

## Partial Sessions

A partial Ferrite program of type PartialSession<C, A> have a linear context C which implements Context, and offers the session type A. The linear context C may be non-empty, and if so the partial program must fully consume the linear context before it can terminate.

In the special case when the linear context is empty, the partial program is then equivalent to the full Ferrite program. In fact, the type Session<A> is defined to be a type alias of PartialSession<(), A>, or PartialSession<HList![], A>.

When we write our Ferrite program, the program is actually made of many fragments of PartialSession that are composed together. For example, the program fragment wait(a, terminate()) in hello_client has the Rust type PartialSession<HList![End], End>, and the program fragment receive_value_from(a, wait(a, terminate())) has the Rust type PartialSession<HList![SendValue<String, End>], End>.

Ferrite constructs such as receive_value_from implements the typing rules of how the linear context and the offered protocol should be updated before and after the given Ferrite expression. For example, given that the channel variable a refers to the first element of the linear context, the Rust expression receive_value_from(a, cont) should have the type in the form PartialSession<HList![SendValue<T, A>], B>, and the continuation expression cont should have the Rust type in the form PartialSession<HList![A], B>. i.e. receive_value_from updates the protocol of the first channel in the linear context from SendValue<T, A> to A for any protocol A.

## Closed Ferrite Programs

Now that we have learned about PartialSession, a question that might arise is why don't we just define hello_client to have the type PartialSession<HList![ReceiveValue<String, End>], End> instead of Session<ReceiveChannel<ReceiveValue<String, End>, End>>? The reason is because a partial session has free variables that are not captured by the program. Consider the following invalid program:

let hello_client_incorrect

The channel variable a is not defined anywhere, or in other words we have a free variable a, hence the program would not compile. We can think of defining partial sessions directly being equivalent to defining Rust expressions containing free variables such as x + 1. Without the surrounding code, we wouldn't able to know where x is from and whether the expression is valid with a given x. To make such expression to be valid, we would instead define a closure that captures the free variable x, forming the closed expression |x| { x + 1 }.
The same principle also applies to Ferrite programs. In practice, we would write Ferrite programs having the Session type instead of PartialSession so that there are no free channel variables that escape the program.