[Haskell-cafe] Annotated ASTs, and the tension between Bound, Free, and Cofree...

[Merijn Verstraaten]

Hi,

So I'm playing around with using bound to define a simple AST using the bound library to deal with substitution/abstraction.

Being a lazy haskeller I figured that ASTs map nicely onto Free and that I could get all the necessary Applicative, Monad, etc. instances for free by using something like:

newtype Expr a = Expr { unExpr :: Free (ExprF Expr) a }
deriving (Functor,Applicative,Monad,Foldable,Traversable)

data ExprF f a
= App (f a) (f a)
| Lam Type (Scope () f a)
| TmTrue
| TmFalse
| If (f a) (f a) (f a)
deriving (Eq,Ord,Show,Read,Functor,Foldable,Traversable)

Now, for an AST to be useful, it has to be annotated with things like source location, type info, etc. So I started looking into how to accomplish this in a way where it's easy to add/modify annotations on any node of the AST.

My initial idea was to use FreeT with ((,) a) as a base monad for annotations, but I quickly realised this fails, because "((,) a)" is only a Monad if 'a' is a Monoid and there's no sensible Monoid for type information/source locations.

Then I looked around more and realised that this actually sounds a lot like Cofree. But here's where I run into problems. Bound expects the type of variables to be in the functor position of my Expr type, whereas Cofree expects the type of *annotations* to be in the functor position.

So I can't figure out an elegant way to both use bound to deal with substitution for me *and* use Cofree to deal with annotations, since there's no way to make the types line up sanely.

So my question boils down too: Has anyone done all the hard work for me already? i.e. how can I have an annotated AST with substitution *and* an easy way to modify the annotations, without writing a ton of boiler plate to deal with substitution and/or annotations?

Cheers,
Merijn

[Alan & Kim Zimmerman]

Have you looked at this? https://hackage.haskell.org/package/Annotations

Alan

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[Tom Ellis]

On Wed, Jul 29, 2015 at 05:43:23PM +0200, Merijn Verstraaten wrote:
> newtype Expr a = Expr { unExpr :: Free (ExprF Expr) a }
> deriving (Functor,Applicative,Monad,Foldable,Traversable)
>
> data ExprF f a
> = App (f a) (f a)
> | Lam Type (Scope () f a)
> | TmTrue
> | TmFalse
> | If (f a) (f a) (f a)
> deriving (Eq,Ord,Show,Read,Functor,Foldable,Traversable)
>
> Now, for an AST to be useful, it has to be annotated with things like
> source location, type info, etc. So I started looking into how to
> accomplish this in a way where it's easy to add/modify annotations on any
> node of the AST.

If you want *some* subterms to be annotated, can you just add another
constructor to ExprF?

| Annotation annotationType (f a)

Or if you want *every* subterm annotated then how about

newtype Expr f a = Expr { unExpr :: Free (ExprF (Compose f Expr)) a }

[Tom Ellis]

On Wed, Jul 29, 2015 at 05:43:23PM +0200, Merijn Verstraaten wrote:

> Being a lazy haskeller I figured that ASTs map nicely onto Free and that I
> could get all the necessary Applicative, Monad, etc. instances for free
> by using something like:
>
> newtype Expr a = Expr { unExpr :: Free (ExprF Expr) a }
> deriving (Functor,Applicative,Monad,Foldable,Traversable)
>
> data ExprF f a
> = App (f a) (f a)
> | Lam Type (Scope () f a)
> | TmTrue
> | TmFalse
> | If (f a) (f a) (f a)
> deriving (Eq,Ord,Show,Read,Functor,Foldable,Traversable)

By the way, when I was playing around with bound and free I guessed that it
would be more appropriate to define a "higher order" free thing which is
called Mu here:

Was bound but now I'm free: http://lpaste.net/136836

I'd be grateful if you'd take a look and see if you think it has any benefit
over just using Free.

Tom

[mikael....@gmail.com]

Tom Ellis <tom-lists-has...@jaguarpaw.co.uk> writes:

> Or if you want *every* subterm annotated then how about
>
> newtype Expr f a = Expr { unExpr :: Free (ExprF (Compose f Expr)) a }

Merijn, if you get something like this working, I'd be interested to see
some of your code, since I too tripped over a similar problem when
looking for a nice way to represent annotated ASTs with bound. Having a
good solution seems like it would be widely useful.

-- Mikael Brockman