# The Jurisdiction of Heaven

With yesterdays feels safely out of the way, let’s turn our attention back to the one of the finer things in life: functional programming. If you’re a fan of the feels, consider filing a bug against me; until you do, I’m going to assume my “peeps” want gnarly haskell stuff.

You probably don’t know it, but I’m writing a vim clone in Haskell (don’t worry, this post isn’t about vim after this paragraph.) One of the huge problems with vim that neovim and others are trying to solve is that the vim codebase is crunchy. Bram is very hesitant to merge pull requests as of late, since the code is such a mess of spaghetti that it’s hard to tell a priori what is going to tear down beloved piece of text-editing infrastructure. vim is written in C, and unfortunately C is very amenable to this kind of situation. In addition, vimscript is atrocious. This got me thinking, is there a way we can solve all of these problems simultaneously?

The answer, as you might expect, is Haskell. We can exploit the typesystem to enforce a no-spaghetti policy, and we can rewrite vimscript as a domain specific language using free monads. Additionally, Haskell composes well, which is nice for implementing a lot of vim features.

Unfortunately, text editors are programs that are chalked full of state[citation needed], and, as you might remember, Haskell isn’t a huge fan of state. Lenses and the State monad can alleviate a lot of the potential issues with trying to work with state, but as I dug deeper and deeper into what I wanted to accomplish, I quickly realized something. The typesystem had no mechanism for some of the constraints I wanted to express.

Consider this. The State monad gives us a single datum as state, with which we need to encapsulate our entire world (which for simplicity we will express in this post as being of type data World.) For our purposes, the world will only contain the current editor mode, and a collection of buffers:

data Buffer =
Buffer
{ _bFilename :: FilePath
, _bContent  :: String
}
makeLenses ''Buffer

data World =
World
{ _wBuffers :: [Buffer]
, _wCurrent :: Int
, _wMode    :: Mode
}
makeLenses ''World

The leading underscores are a convention when working with lenses; makeLenses will generate non-prefixed lenses for each of our records. In order to avoid spaghetti state (where anybody can do anything to any piece of the state), it would be nice to be able to be able to restrict functions to a subtree of the state. A bug in the change operator shouldn’t be able to close inactive buffers, for example.

A few minutes of googling later, I found the Control.Lens.Zoom1 package, which provides zoom :: Lens s r -> State r -> State s2. zoom lifts a Lens s r over a State s monad, which as you might expect from the name, behaves just like zooming on a microscope. It lets you look at a deeper piece of state without needing to pay attention to any of the underlying context.

So I hooked up all the necessary infrastructure to use zoom, and after some wrangling, got it to typecheck. I ran it. It worked. But there was a conceptual problem: zooming turns out to not be what I wanted.

Remember that a zoom ignores the underlying context; which means when we zoom into our Buffer record, we can no longer determine what the value of wMode (the editor mode) is. It turns out zoom enforces too strong a constraint – that the only piece of state you’re allowed to read is the bit you’re allowed to write. But this isn’t useful to us: we want to be able to read the whole state, but only write over the piece we’ve been restricted to.

Despair. I spent a day trying to hook up some monad transformer stacks of various combinations of StateT and ReaderT, hoping to be able to use the MonadReader instance to give me access to the whole state, but zoom over the MonadState. I actually managed to get an implementation of this “working”, but it had some issues – the most egregious of which was that writing state would desynchronize get and view lensesCurrentlyRestrictedOver <$> ask, even though conceptually they should have been the same thing. Eventually it became painfully clear that zoom wasn’t the right tool for the job. Even more painful was that it appeared that no tool was right for the job. Somehow, nobody had never (published) needing to do what I wanted. I’m pretty sure about this; I spent several hours googling. So I decided to write my own monad to do what I wanted. Behold, Jurisdiction s r a: type RLens r s = Lens s s r r newtype Jurisdiction s r a = Jurisdiction { runJurisdiction' :: RLens r s -> s -> (a, s, RLens r s) } deriving (Functor) Jurisdiction s r is a monad (which we’ll derive in a bit) you can interpret as a State r monad combined with a Reader s instance, except that get and view restrictions <$> ask always remain synchronized. What this means is that we can now express our buffer constraint earlier as Jurisdiction World Buffer – any function whose type is this can read the entire World, but only write to a restricted Buffer subset of that world.

This was the first monad I’ve ever implemented, and conceptually I wasn’t really clear on what I needed to do. So I closely followed Bartosz Milewski’s great tutorial on implementing the State monad, which is pretty much what I wanted. But because I’m lazy, I used deriving Functor. No judgment.

I had to do some mental gymnastics to figure out what this monad actually is, but the answer is “it’s a function RLens r s -> s -> (a s, RLens r s) that composes with itself.” Thats why we’re going to keep seeing Jurisdiction $\l s -> in the forthcoming code snippets. I guess this makes sense when you look at its only record, runJurisdiction', but this took me a few days to wrap my mind around. I wrote my monad instance by following Milewski’s code, and then randomly making changes until it typechecked with Jurisdiction s r. I had originally written a bunch of text here explaining the code with inline snippets, but that felt gratuitous, so instead I’ll skip past all of the different Monad* instances and jump into the bits that make Jurisdiction interesting. If you’re curious in the implementation, you can check it out on github However, the MonadState instance has some inside baseball that is worth taking a look at. instance MonadState r (Jurisdiction s r) where get = Jurisdiction$ \l s -> (view l s, s,         l)
put v = Jurisdiction $\l s -> ((), set l v s, l) Recall that the first element of our resulting tuple is the result of our monad, the second is the state contained in it, and the third is the current lens which acts as a filter over what we’re allowed to touch. get pulls our state through the lens l at the very last second, so there’s no chance for it to get out of sync with the state. Likewise, set pushes the state through the lens in order to change its value. But just because Jurisdiction is now a MonadState and a MonadReader (a very boring implementation3) doesn’t actually mean it’s useful yet. So far we have no means of restricting the scope of our jurisdiction, and without that, it’s just a clunky State. Instead, we introduce restrict, which takes a lens into our restricted scope from our current scope, and a Jurisdiction in that restricted scope, giving us back one in the unrestricted scope. At first glance, this might sound like our types are backwards; relative to the callee, restrict is actually widening their scope. We want to widen restricted scopes so they apply to the entire state by the time they’ve made it to the point where the user will call runJurisdiction. But to calling code, restrict behaves as intended, it takes the current scope and runs something with less scope. Confused yet? I was the first three times I tried to write this function. So let’s take a look at the code. restrict :: RLens r' r -> Jurisdiction s r' a -> Jurisdiction s r a restrict l' j = Jurisdiction$ \l s ->
let (a, s', _) = runJurisdiction' j (l . l') s
in (a, s', l)

The moving part here is is the composition of our lenses. Recall l is the current lens, and l' is a lens relative to it. These two lenses therefore compose, and thusly we get that restrict composes with itself for free. This is a good thing; we’d be in trouble if it didn’t. When we run our restricted Jurisdiction, we simply swap out our lens with the composed lens, which will necessary narrow its scope. Cool!

I want to say here that I checked all the monad and functor laws, but I didn’t actually. I couldn’t be fucked, but I’d be very surprised if I had violated them somewhere.

Anyway, everything seems to be in place now, all that’s left is a friendly interface for users to call. Because the lens is an implementation detail, and we should always start the state with unrestricted access, we hide it. Coincidentally, this is why our runJurisdiction' has had the trailing prime; my motives are revealed at last!

runJurisdiction :: JurisdictionT s s a
-> s
-> (a, s)
runJurisdiction j = (\(a, s, l) -> (a, s)) \$ runJurisdiction' j id

With what seemed like everything in order, I went back to my little vim clone and went to try it out. Because my underlying state is always going to be World, I made a new type:

type Eden r a = Jurisdiction World r a

and went on to write a command to put me into insert mode.

enterInsertMode :: Eden Mode ()
enterInsertMode = put INSERT

The actual test was a little more involved than this (it loaded a prompt and let you run commands in a big loop), but it is more than enough to demonstrate the point. What I really like about this is that it’s now self-evident that our constraint is satisfied; enterInsertMode has literally no way to express anything except how to change the mode. In my mind, this is a huge win for functional programming; if you can’t express something in the language, there’s no way for it to go wrong.

Basking in my success, I went to write appendToBuffer:

appendToBuffer :: String -> Eden Buffer ()
appendToBuffer str = proclaims bContent (++ str)

where proclaims is a helper function4 which gets the current value, applies a function to it, and puts the result back. So far, so good, but then something bad happened. How do I get a lens to the current buffer?

A quick google search led me to the ix function. I hopefully (and naively) tried restrict (wBuffers . ix 0) as a test to see if I could get the first element of my list, but to no avail. GHC complained that my lens type in Jurisdiction now needed to be an Applicative, when a Functor had been good enough before this foray.

So I listened to GHC, and changed all of my constraints to require Applicative lenses. It felt dirty, but as they say, make it typecheck and worry about the consequences later. I made it typecheck, but the consequences were bad. The compiler had crunched the types and the results were in: any scope I wanted to restrict to now needed to be an instance of Monoid. The good news was that [Buffer] is a Monoid. The bad news is that most things aren’t.

This was unacceptable. I reverted my changes, and looked for another way. Expanding out the RLens [r] r type, I found that it was (Functor f) => (r -> f r) -> [r] -> f [r]. If only, I thought, I could find a function of this form, it might behave as the proper lens. There were a few magical hours of trying to conditionally filter over a list to see if I had the right index, but all was for naught. In fact, even a trivial implementation of this function is surprisingly hard. Give it a try; I’d love to see what you come up with.

In a moment of insight, I realized there was a function I had seen during my perusal of the Control.Lens library that I’d forgotten about. It was called at, and I had passed it over because it didn’t typecheck with [a]. at’s semantics allow it to insert or delete from its container if the key doesn’t exist, or if you return a None. Obviously this doesn’t work for [a], as it’s impossible to meaningfully insert at index 1000 into an empty list.

But the insight remained. Maybe _wBuffers :: [Buffer] had the wrong type! I eagerly changed it to _wBuffers :: IntMap Buffer, and lo and behold, at typechecked, though appendToBuffer needed some changes:

{-# LANGUAGE LambdaCase #-}
appendToBuffer :: String -> Eden (Maybe Buffer) ()
appendToBuffer str = get >>= put . Just . \case
-- there's a nicer way to do this but I'm doing it from memory
Just x  -> x { _bContents = (view bContents x) ++ str }
Nothing -> emptyBuffer { _bContents = str }

All of a sudden, we get some cool magic for free! We can create buffers where none existed before. What might be more interesting is now the user can close the first buffer but keep the number ordering on the remaining ones. This is something that vim does, and we’ve accidentally implemented it by doing no extra work.

If that’s not divine mandate that this project is the right and holy implementation of vim, I don’t know what is.

If you’re interested in seeing the whole source for this post, following the development of eden, or contributing yourself, the project can be found here.

1. I absolutely love the naming scheme in the optics packages.

2. This is not its real type, but it’s true at least conceptually.

3. Except that local would break our invariant. As an exercise to the reader, see if you can prove it.

4. My attempt at naming things with as consistent a metaphor as the lens people appears like it might have been taken too far.