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5th Applicatives are too restrictive, breaking Applicatives and introducing Functional BuildersThis post aims to document a practical design implementation we came up with when designing some APIs in Scala. Of course the concept is not Scala specific and applies to other functional languages. If you don’t want to go into the full introduction, this post talks about how Applicatives are too restrictive and breaking them into two independent components can be interesting for Contravariant and Invariant Functors. Jump to implementation attached. We are taking JSON serialization/deserialization as a motivating example.
Implementing Writing JSON we have its dual:
Implementing Writes provides a way to write JSON for a type We have also a type that represents both, being able to read and write a JSON for an
Reads happens to be a monad, which is interesting but we are not going to talk about this much more. What we are interested in is having a simple way of combining JSON serializers, meaning if we have
it could be very interesting to have a This is actually quite easy to achieve with Applicative Functors. To simplify, Applicative Functors are Functors (having the map or fmap function implemented) together with the Applicative part which adds the power we need to achieve the combination we want to do. Explaining Applicative Functors is out of scope and there is a lot of material on the web explaining these.
This composition simply means that if we have two readers of two different types, they could read from the same JSON and provide two values which I can pack into another type (User here). Now that we solved our problem of combining the Reads with Applicative Functors, wouldn’t it be even more interesting if we could combine similarly the Writes? Having:
then we could have a Almost. If we have two writers (capable of writing two different JsValue from two different types, Int and String here) then we end up with two Let’s do a new type that only writes
Now it makes sense to have one writer out of our two writes above ( writeAge, writeName) by simply merging the resulting objects. So logically it makes sense, except that we can’t use our Applicative based builder since an OWrites is not a Functor at all! Actually our OWrite is, naturally, the dual of a Functor, a CoFunctor (or Contravariant). Put simply, this means that to change the
So or status here, we know how to transform the type of OWrites, we know how to merge two OWrites but all of that doesn’t help us to use the builder which based on an Applicative Functor. What if we split our problem into two components. Let’s introduce a new type that we call FunctionalCanBuild:
Meaning for a given container M, we can some how compose two instances into one with the tuple of the type parameters. So for Reads it will be:
and for the OWrites it will make:
But that gets us only half way through what we want to achieve. What we want is actually a Reads and OWrites of User and not tuple of Int, String. For the So it seems that separating the problem into two sub problems is working for us. But what about format? Format is not a Functor and a Contra, it is actually Invariant. This means that it need functions in both directions, Like the
Now we can implement FunctionalCanBuild[OFormat] :
and once we have the This led us to an API that is capable of building compositions for Functors ( Bottom Line: By breaking ps: FunctionalCanBuild[M[_]] may look like a monoid but it is not exactly one. ps2: This is a work I did together with @mandubian and other Zenexity guys ps3: The Format,Reads and Writes approach is copied and adapted from @debasishg on sjson ps4: This work is integrated into Play’s included JSON library ps5: A potentially more readable version as a gist |