Encode state transitions in types using linear types

3 August 2017 — by Arnaud Spiwack

At the time of our first post on linear types, we were fresh out of the design phase to extend GHC with linear types. We had a prototype implementation, but it was just a proof of concept: there was precious little you could do with it.

A few months down the line, we are now in a very different place. We have pushed out a new paper, rewritten top to bottom. This one is chock-full of example applications of linear types. Today and in my next post in this series on linear types, I’d like to touch on two nifty uses of linear types from the paper.

But before I get started - I want to point out some recent progress on the linear-types branch in GHC. This branch is now a usable playground to experiment with linear types. Most of the basic features are there, but do expect some very rough edges and keep in mind that error messages still need to be improved. We provide a ready-made Docker image, so you don’t have to compile GHC yourself just to play with linear types. It’s all in the README: check it out!

I/O states, in your types

Say you want to communicate across a network. You use the socket library. You open the documentation and find that to use a TCP socket, on a server, you first need to bind the socket to an address. At this point the socket isn’t doing anything: you need to listen for incoming traffic. Now the socket receives messages from the network, specifically connection requests, which you must accept. An accept call returns a new socket which can receive a TCP stream.

That’s a bit of a headache! And you’ve got no safety net: the (simplified) type of bind is:

bind ::  Socket -> SocketAddress -> IO ()

The type of listen is:

listen :: Socket -> IO ()

These types are really not that helpful. In Haskell, we like our types to tell us what we can do with a value. But when I have a Socket, I can maybe bind it or listen to it, but certainly not both.

What we really need is that the type of a socket be indexed by the kind of things we can do with it. Something along the lines of:

data State = Unbound | Bound | Listening |data Socket (s :: State)

bind :: Socket Unbound -> IO ()
listen :: Socket Bound -> IO ()

Good! Now, what is the type of s in bind s? It must be Socket Unbound so that I can apply bind. Wait! When the bind call returns, s must not be Unbound anymore. It must be Bound. So… the type of s seems to change over time. This is the idea of typestates.

To implement a typestate for socket, maybe I could simply return a socket with its type changed like so:

bind :: Socket Unbound -> IO (Socket Bound)

do { s' <- bind s;}

I can then use s' as evidence that the socket has been bound. But I also have the old s still hanging about. And s claims to be unbound: we can go back in time. One has to be careful not to use s ever again to avoid ill effects: types have failed us once again.

What we need is the ability to consume the old s, to make it inaccessible. Which, coincidentally, is exactly what linear types enable. We just need to make IO a little bit more general, so that it can return both linear and non-linear values:

data IOL p a

-- An old friend, redefined.
type IO = IOL ω

-- `a ->_1 b = a ⊸ b` and `a ->_ω b = a -> b`
return :: a ->_p IOL p a
(>>=) :: IO p a(a ->_p IO q b)IO q b

and we can now have sockets with typestates:

socket :: IOL 1 (Socket Unbound)
bind   :: Socket UnboundSocketAddress -> IOL 1 (Socket Bound)
listen :: Socket BoundIOL 1 (Socket Listening)

What we’ve done here is precisely and safely captured the state of the socket at the type-level. The type tells you exactly what to do next with a socket. And GHC won’t let you reuse old states by accident. This is a prototypical example, demonstrating how linear types help us to be more precise about the use of resources, so that the type checker assists us in avoiding faulty resource use.

In the next post in the series, we’ll take a look at how linear types can pave the way towards safe zero-copy packed data exchange across clusters.

About the author

Arnaud Spiwack

Arnaud is Tweag's head of R&D. He described himself as a multi-classed Software Engineer/Constructive Mathematician. He can regularly be seen in the Paris office, but he doesn't live in Paris as he much prefers the calm and fresh air of his suburban town.

If you enjoyed this article, you might be interested in joining the Tweag team.

This article is licensed under a Creative Commons Attribution 4.0 International license.


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