See the [variance](../variance.html) chapter of this guide for more info on how
the type checker handles variance.

<a id="free-vs-bound"></a>

## What is a "free region" or a "free variable"? What about "bound region"?

Let's describe the concepts of free vs bound in terms of program
variables, since that's the thing we're most familiar with.

- Consider this expression, which creates a closure: `|a, b| a + b`.
  Here, the `a` and `b` in `a + b` refer to the arguments that the closure will
  be given when it is called. We say that the `a` and `b` there are **bound** to
  the closure, and that the closure signature `|a, b|` is a **binder** for the
  names `a` and `b` (because any references to `a` or `b` within refer to the
  variables that it introduces).
- Consider this expression: `a + b`. In this expression, `a` and `b` refer to
  local variables that are defined *outside* of the expression. We say that
  those variables **appear free** in the expression (i.e., they are **free**,
  not **bound** (tied up)).

So there you have it: a variable "appears free" in some
expression/statement/whatever if it refers to something defined
outside of that expressions/statement/whatever. Equivalently, we can
then refer to the "free variables" of an expression – which is just
the set of variables that "appear free".

So what does this have to do with regions? Well, we can apply the
analogous concept to type and regions. For example, in the type `&'a
u32`, `'a` appears free.  But in the type `for<'a> fn(&'a u32)`, it
does not.

# Further Reading About Compilers

> Thanks to `mem`, `scottmcm`, and `Levi` on the official Discord for the
> recommendations, and to `tinaun` for posting a link to a [twitter thread from
> Graydon Hoare](https://web.archive.org/web/20181230012554/https://twitter.com/graydon_pub/status/1039615569132118016)
> which had some more recommendations!
>
> Other sources: https://gcc.gnu.org/wiki/ListOfCompilerBooks
>
> If you have other suggestions, please feel free to open an issue or PR.

## Books
- [Types and Programming Languages](https://www.cis.upenn.edu/~bcpierce/tapl/)
- [Programming Language Pragmatics](https://www.cs.rochester.edu/~scott/pragmatics/)
- [Practical Foundations for Programming Languages](https://www.cs.cmu.edu/~rwh/pfpl/)
- [Compilers: Principles, Techniques, and Tools, 2nd Edition](https://www.pearson.com/us/higher-education/program/Aho-Compilers-Principles-Techniques-and-Tools-2nd-Edition/PGM167067.html)
- [Garbage Collection: Algorithms for Automatic Dynamic Memory Management](https://www.cs.kent.ac.uk/people/staff/rej/gcbook/)
- [Linkers and Loaders](https://www.amazon.com/Linkers-Kaufmann-Software-Engineering-Programming/dp/1558604960) (There are also free versions of this, but the version we had linked seems to be offline at the moment.)
- [Advanced Compiler Design and Implementation](https://www.goodreads.com/book/show/887908.Advanced_Compiler_Design_and_Implementation)
- [Building an Optimizing Compiler](https://www.goodreads.com/book/show/2063103.Building_an_Optimizing_Compiler)
- [Crafting Interpreters](http://www.craftinginterpreters.com/)

## Courses
- [University of Oregon Programming Languages Summer School archive](https://www.cs.uoregon.edu/research/summerschool/archives.html)

## Wikis
- [Wikipedia](https://en.wikipedia.org/wiki/List_of_programming_languages_by_type)
- [Esoteric Programming Languages](https://esolangs.org/wiki/Main_Page)
- [Stanford Encyclopedia of Philosophy](https://plato.stanford.edu/index.html)
- [nLab](https://ncatlab.org/nlab/show/HomePage)

## Misc Papers and Blog Posts
- [Programming in Martin-Löf's Type Theory](https://www.cse.chalmers.se/research/group/logic/book/)
- [Polymorphism, Subtyping, and Type Inference in MLsub](https://dl.acm.org/doi/10.1145/3093333.3009882)