# Session Types

This chapter provides some supplementary overview of session types, the type theory that Ferrite is based on. In the discussion we will talk about some concepts related to logic and type theory. For readers who are unfamiliar with these topics, feel free to skip this chapter and move on to the next chapter.

## Background on Session Types

So far we have been talking about session types without going into details what it is. Broadly speaking, session types can refer to a branch of type systems used to model structured communication-based programming. Session types are also known as behavioural types, since the types describe the behaviour of a program.

From the theoretical perspective, session types establish a correspondence with linear logic. This makes session-typed languages slightly different from functional languages such as Rust and Haskell, which have their roots in lambda calculus and intuitionistic logic.

Throughout this book, we will learn about various concepts of session types from the perspective of a Rust programmer. While this may not be a comprehensive overview of session types themselves, we aim to cover enough of the basics so that you can explore more deeply into session types through other resources.

## Linear, Affine, and Structural Rules

One notable distiction between session types and Rust is that session typed variables are linear, while Rust variables are affine by default. We will try to understand what that really means.

A common explanation of linear vs affine is that linear variables must be used exactly once, while affine variables can be used at most once. However that is not entirely accurate.

To be more precise, type theorists differentiate different kinds of type systems based on which structural rules are allowed in the type system:

• In a normal type system like Haskell, variables are allowed to be used more than once (contraction). Variables are also allowed to be discarded (weakening).

• In an affine type system like Rust, variables are not allowed to be used more than once (no contraction), unless they specifically implement Copy or Clone. However variables are still allowed to be discarded (weakening).

• In a linear type system like Ferrite, variables are not allowed to be used more than once (no contraction), and variables are not allowed to be discarded (no weakening).

As we have seen in the previous chapter, Ferrite programs like hello_client interact with channel variables multiple times, with the session type of the channel changing every time after interaction. Under linear typing rules, we cannot make multiple copies of the channel, and we also cannot discard the channel until it is explicitly terminated.

## Intuitionistic vs Classical Linear Logic

Since session types cover a family of programming languages, readers with some familiarity with session types may notice that Ferrite's implementation is quite different from some other session types implementations in the wild, such as session-types and sesh.

Ferrite's implementation of session types is based on intuitionistic linear logic. This is in contrast with the classical linear logic formulation that is used by some other session types implementations.

From the programmers' perspective, there are some key differences when using the intuitionistic formulation of session types in Ferrite. For example, you may notice that there is no need for dualization in Ferrite. This means that the session type signature remain the same from the perspective of both the provider and the client.

As illustrated in the previous chapter, while the provider hello_provider sends a string value through a channel with the session type SendValue<String, End>, the client hello_client receives a value from a channel of the same session type.

In comparison, with classical formulation, we would instead have to explicitly dualize the session type. As a result, the session type of the channel given to hello_client would instead have the session type ReceiveValue<String, End>.

Both intuitionistic and classical formulation of session types share the same foundation, viewed from different angles. From the perspective of a type theorist, it may be more convenient to formulate proofs with the help of dualization in the classical formulation.

From the perspective of a programmer, it may be more intuitive to understand session types in the intuitionistic formulation. Intuitionistic session types have closer semantics with lambda calculus, and this makes it easier for programmers to bridge the concepts with their existing knowledge in functional programming.

We leave it to informed readers to decide whether the intuitionistic formulation of Ferrite provides better intuition for programming in session types. For the purpose of this book, it is only important for us to clarify the distinctions, so that readers are better informed when comparing Ferrite with other session types implementations.