This library Has transformers

What?

A very slim library for first-order effects based on monad transformers (and nearly nothing else).

What exactly?

Given a transformer stack t1 (t2 (t3 (... m))) a, you can automatically lift any function thing :: tN m a into the stack with a single function, liftH.

What features does it have?

• Final encoding: There is a type class Has t m that says that the transformer t is in the stack m.
• Extensibility: Standard transformers are supported out of the box. You can add any further transformers to your stack.
• No runtime overhead: There is no runtime overhead related to handling effects. Your code is as fast as if you had written it just with a lot of manual lifts. (No benchmarks yet though.)

What features does it not have?

• Higher-order effects: For example, you cannot encode in the Has typeclass:
  • catchE: Exception handling
  • local: Modify a reader computation
• Separation of effect signatures and effect carriers. For example, you cannot have one signature of writer effects, and then later decide whether you want to interpret them as strict WriterT, lazy WriterT, CPS-style WriterT, an IO-based log, and so on. You have to choose one transformer that represents your effect.

Why?

Imagine you have a rather complex transformer stack, say ReaderT r (ExceptT e (AccumT a (StateT s m))). To write programs in it, you would have to do yoga exercises like lift $ lift $ lift $ put s all over your business logic code. And at some point you maybe want to add logging to your stack, thus insert a WriterT w, and then discover that your ExceptT e is sitting in the wrong place after all. You change your stack, and all your business logic is broken. Even those modules that didn't even need to know anything about logging and error handling.

Wouldn't it be nice to save yourself writing all these repetitive lifts, avoid spelling out the complete stack in all your code, separate concerns, invert dependencies, have clean architecture, and be able to change your monad stack without breaking existing code?

Then simply use the Has typeclass, and replace all your lift orgies with its one function, liftH.

But isn't this a solved problem, you ask? Read on.

Why not mtl, fused-effects, freer-simple, operational, polysemy, eff, rio, ...?

Because has-transformers has some advantages over each of these libraries. It also has some disadvantages over each. The usual advantage is that has-transformers is fast and simple, and the disadvantage is that it doesn't have higher order effects.

There is a big design space here, and maybe there is no ideal library for every use case. While some corners of the space have been explored thoroughly, there is this neat little corner that hasn't received as much attention as maybe deserved.

mtl

Historically, mtl solves the same problem like has-transformers, but declares a type class manually for each transformer: MonadReader for ReaderT, MonadState for StateT, and so on. Which means that one has to implement MonadReader for every transformer you want to use. And if you want to add your custom transformer FooT, not only do you have to implement MonadReader etc. for all the classes you need, you also have to invent your own MonadFoo, and implement instanes for all transformers for it. This is well-known, and called the "quadratic instance problem". If you or someone else has written a good blog post or article about this topic, let me know, I'll link to it. The gist is that mtl is practically not extensible.

has-transformers doesn't have this problem. You don't have to invent your own MonadFoo, because you get Has FooT for free, together with all relevant instances.

As a downside, has-transformers doesn't have higher-order effects, so you cannot lift operations like catchE through it. You can of course still use them, at the cost of either using mtl or some other higher-order library, or explicitly declaring the monad stack at the calling site.

fused-effects

If you wish, you can think of has-transformers as a miniature version of fused-effects, or of fused-effects as the fully-featured, well-researched version of has-transformers. In particular, both are "fused" in that type classes are used to insert effects, and a transformer stack chosen at compile time to interpret them. This is great for performance.

fused-effects has two big features in comparison:

• Higher order effects: You can declare and handle e.g. exceptions, MonadPlus, backtracking, and so on, within the framework.
• Separation of signatures and effects: You can define one type operator representing only your effect interface, and decide in a different place what transformer stack (or other kind of monad) you use to interpret the effect.

But has-transformers also has some advantages which may appeal to you:

• No separation of signatures and effects: You don't need to define a signature separately.
• No complicated type class: You don't need to implement the impressive Algebra type class for your transformer.
• Fewer language extensions: fused-effects needs a lot of language extensions, most of them modern but benign, but also the slightly vexing UndecidableInstances when defining your own effect carrier.

freer-simple, freer-effects, freer, operational, polysemy, eff, ...

I expect has-transformers to be more performant, because there is no runtime overhead associated to effect handling. (Although the overhead is expected to be small in eff when/if delimited continuations are merged in GHC.) How big this overhead is, I can't judge, but it's probably smaller than you'll care about in production. Also see the fused-effects benchmarks and a polysemy performance discussion.

On the other hand, all these libraries support higher-order effects. (operational is not really extensible out of the box. (But extensibility could be added with sum types, which is another story for another day.) ) And they also separate effect signatures from interpreters.

RIO

The RIO monad also offers first-order extensible effects via a ReaderT that holds all handlers. The big disadvantage of RIO is that it is tied to IO, so you cannot e.g. do algebraic reasoning, guarantee determinism or absence of side effects, IO-free mocking, and so on.

(Note that this is not about of rio-the-library, but RIO-the-monad), which of course is the heartpiece of the aforementioned library.)

Is it compatible with all these? Or do I have to choose?

Yes, has-transformers is to some extent compatible with all these other effect libraries! No, you don't have to choose one and discard all the others!

• Any transformer stack can also be adressed with fused-effects, or to some extent with mtl.
• The bottom monad of your stack can be Eff from freer-simple & co, or RIO, or any other Monad or MonadIO.
• Effect signatures can be added to your stack with a free monad like ProgramT.

Can you please give us a feature matrix?

Library	Extensible	Higher order effects	"Fusion" / no runtime interpretation	Arbitrary base monads
has-transformers	✅	❌	✅	✅
mtl	❌	✅	✅	✅
fused-effects	✅	✅	✅	✅
polysemy, freer-simple, ...	✅	✅	❌	✅
rio	✅	❌	✅	❌

Let me know if other features & libraries are important to you.

What are these higher order effects you keep talking about?

A good example is mtl's MonadError class. It has two methods:

• throwError :: e -> m a
• catchError :: m a -> (e -> m a) -> m a

A transformer stack m containing ExceptT e (which is based on the Either e monad) can use throwError to insert a (properly lifted) Left e value into the stack (an "exception"), and catchError to handle any such exception.

Such a stack satisfies Has (ExceptT e) m, and you can use liftH to define throw :: HasExcept e m => e -> m (), but nothing like catchError.

The reason is that the type signature of catchError is higher order in the monad m: It appears on the left-hand side of the final ->. In other words, catchError does not only return something of type m a, it also expects inputs related to the type m. But if you look at the type signature of liftH, you will notice that m only appears on the right hand side of the ->, so it is not possible to implement a function like catchError with liftH.

This excludes many advanced operations on effects that you might be interested in, e.g. continuation passing, error handling, logic backtracking, and others. If you need these, you either have to make the transformer stack explicit (which somewhat defeats the purpose of an effect library), or use another library to address these effects.

So what's your recommendation on effect systems?

My opinionated, limited-point-of-view recommendation, without knowing your use case, is that you should use transformers and give has-transformers a try if you have a small project that doesn't do anything too fancyful with effects, and when you hit stuff like complex error handling, backtracking, and so on, upgrade to fused-effects if you don't get a headache with the types, or migrate to polysemy (or maybe freer-simple) otherwise.

How?

The central insight is that a transformer t is not only an effect handler, but at the same time an effect signature.

For example, StateT s m a is always inhabited by put and get no matter the base monad m, and these form a complete signature for this transformer.

So we simply need to lift the effects of a transformer into arbitrary stacks. This is done with the Has typeclass. Has t m says that m is composed of transformers and a base monad, and that t is one of these transformers, i.e. t is in the monad stack m.

How do I separate effect signatures and handlers?

First of all, note that you don't always have to, and that can be a simplification: Your transformer t also serves as an effect signature. If you still want to separate them, and interpret them, you can still use a free monad such as FreeT or ProgramT to make your effect signature into a monad transformer, and then use this transformer in your stack. Of course, this will incur a runtime penalty when interpreting the effect. An example is found in StateSig.

Relatedly, if you want to re-interpret one transformer (say, lazy StateT) as another with the same API (say, strict StateT), you can do a similar procedure.

Can I use two ReaderT, two StateT, etc., in the same stack?

Yes. See the TwoReaders example. You might have to add some type signatures here and there to help GHC figure it out.

Does this work with any transformer?

Most transformers. ContT (and other continuation based transformers like LogicT) don't work, but any transformer that is strictly positive in its monad works (i.e., ReaderT, WriterT, StateT, ExceptT, AccumT, and so on).

The issue with ContT & co. is that their interface is inherently higher order. Consider, for example, callCC :: MonadCont m => ((a -> m b) -> m a) -> m a, or msplit :: MonadLogic m => m a -> m (Maybe (a, m a)), which each define the minimal interface for their respective mtl-style class. They need m on the left hand side of the final arrow, and thus cannot be encoded in the form of liftH.

(Why) Hasn't this been done before?

I'm not sure, to be honest. It seems such a simple idea that I guess someone must have had it before. If you know who and where, please let me know, and I'll link here.