## Picnic: put containers into a backpack

This blog post walks the reader through the Backpack implementation of the uniform interface for containers (Maps and Sets). We will go through the reasons for choosing Backpack, a comparison with a typeclass-based approach, and a basic tutorial for Backpack. You can find the proposed solution in the following repository:

I also gave a talk based on this blog post, so you can watch it as well:

## Motivation

The Haskell ecosystem contains multiple libraries that implement Map-like data structures. Among them there are structures like balanced binary-search trees, Patricia trees, hash array-mapped trees, including lazy and strict versions, and many others. Even though existing implementations contain functions with the same name and structurally the same type, they don’t share a common interface because such an interface doesn’t exist. Which means that each time you want to use a type with a Map-like or Set-like interface, you have to choose a concrete data type explicitly. This straightforward approach has the advantage of having predictable and explicitly specified performance and memory characteristics for each data type. However, it reduces code reusability and composability, in particular:

1. It’s not easy to switch from one data type to another: we need to change package dependencies, imports, data type name and function names.
2. We often want to write functions that can work for any Map or Set (consider benchmarks). Or like in the following example:
{-# LANGUAGE ScopedTypeVariables #-}

import Data.Foldable (foldl')
import Data.List.NonEmpty (NonEmpty (..), (<|))
import Data.Map (Map)
import qualified Data.Map as M

groupBy :: forall k f a . (Foldable f, Ord k)
=> (a -> k) -> f a -> Map k (NonEmpty a)
groupBy f = foldl' mapGroup M.empty
where
mapGroup :: Map k (NonEmpty a) -> a -> Map k (NonEmpty a)
mapGroup m a =
let val :: Maybe (NonEmpty a) -> NonEmpty a
val Nothing   = a :| []
val (Just xs) = a <| xs
in M.alter (Just . val) (f a) m

And here is an example of using this function:

ghci> groupBy even [1..10]
fromList [ (False,  9 :| [7,5,3,1])
, (True,  10 :| [8,6,4,2])
]

ghci> groupBy (mod 3) [1..10]
fromList [ (0,  9 :| [6,3])
, (1, 10 :| [7,4,1])
, (2,  8 :| [5,2])
]

It would be great if we could reuse this groupBy function with any Map-like data structure. Moreover, for most popular data types like Map, HashMap, or IntMap, we can’t really write a more efficient version. It would be more convenient to have all functions like groupBy implemented once and have the ability to choose a specialized implementation based on the needs of the program.

To explore what people would think of such an interface we made a poll recently. And it looks like people are apprehensive but interested about having a unified interface. From the feedback we received in the comments, Backpack looks like the most suitable solution for this problem at the moment. So we accepted the challenge and decided to try using Backpack. This blog post contains the detailed description of our results.

## Solution with typeclasses

Backpack is a relatively new technology. However, people have been making attempts to implement a common interface for Maps long before that. One of the most famous examples is the mono-traversable package. We tried to create an alternative solution in relude. To get an idea of how a typeclass-based solution might look like, you can take a look at this extract from relude:

class StaticMap t where
type Key t :: Type
type Val t :: Type

size   :: t -> Int
lookup :: Key t -> t -> Maybe (Val t)
member :: Key t -> t -> Bool

class StaticMap t => DynamicMap t where
insert     :: Key t -> Val t -> t -> t
insertWith :: (Val t -> Val t -> Val t) -> Key t -> Val t -> t -> t
delete     :: Key t -> t -> t
alter      :: (Maybe (Val t) -> Maybe (Val t)) -> Key t -> t -> t

The nice thing about the StaticMap typeclass is that it allows to generalize Map and Set with a single typeclass. Set a can be considered as a special case of Map a () or Map a a where each value is equal to the corresponding key.

NOTE: The difficulties in unifying Set and Map arise with functions like insert, where the number of arguments is different. You can read this StackOverflow question regarding possible solutions to this problem. Still, it looks like there’s no completely satisfactory approach.

Aside from the difficulties mentioned above, there are still several issues with the typeclass-based solutions:

1. The types of the generalized functions are less approachable, in particular due to the use of type families.
2. Performance is not predictable and often worse because type class specialization is not guaranteed.

Having a typeclass can potentially decrease performance because of the way typeclasses are implemented in Haskell. For something like access to the database the overhead of a type class is not noticeable, but for operations with pure maps it’s a huge disadvantage to have non-optimized functions. In addition to not having a performance overhead, Backpack also contains a lot of other features (read motivation behind Backpack to see the whole list).

Below we look at how Backpack can be used to implement an interface for Map-like data structures without the disadvantages of type classes.

## Backpack

The general idea behind using Backpack to solve this problem is simple. First, you write the types of the desired methods — signatures. And then you implement these signatures for the different data types. But there are different challenges in using this approach for Map-like data types:

1. Data types are different across libraries (like Map and HashMap).
2. Every library has its own constraints for the keys (Map requires Ord constraint and HashMap requires Eq and Hashable constraints).
3. Types might have different kinds (consider Map and IntMap).
4. Some maps don’t have efficient modification operations since they are based on arrays (Map from primitive-containers package).
5. Different libraries implement the same functions with different constraints.

But don’t worry, we are going to describe how we overcame these issues.

### Map from containers

First, let’s put all signatures into a separate package that contains only the signature file. The Cabal file for this package looks like this:

cabal-version:       2.0
name:                containers-sig
version:             0.0.0
build-type:          Simple

library
hs-source-dirs:      src
signatures:          Map
build-depends:       base
default-language:    Haskell2010

Note that there’s no exposed-modules field in the containers-sig.cabal file. Instead, there’s a signatures field. Signatures are files with extension .hsig. Such files contain only an abstract description of an interface expressed through the type signatures (name signatures comes from the idea that modules can have signatures just like functions can have type signatures). Here’s is how the signature for Maps might look like:

signature Map
( Map
, Key
, empty
, alter
) where

data Map k v
class Key k

instance (Show k, Show v) => Show (Map k v)

empty :: Map k v
alter :: Key k => (Maybe v -> Maybe v) -> k -> Map k v -> Map k v

Unlike ordinary Haskell modules, a signature starts with the signature keyword instead of module. We declare the Map data type without a definition. The type is parametrized by two type variables: k for keys and v for values. Implementations of operations such as lookup or insert might need to perform various operations on keys (compare them, take their hashes, etc), so we also define a constraint on keys — Key. Signatures can also contain required instances for data types. And then we can put the names of functions with their types.

NOTE: The example above contains only one possible version of the signature for Map. In our case, we went with minimal required set of functions for our examples.

Now we can implement a groupBy function in terms of a Map interface rather than a particular implementation. This function can be in the same package with the signature or in another package.

For a Haskell module there is no difference between signature files and other Haskell modules, you can import signatures just like you would import an ordinary Haskell module. Let us now put all functions that are implemented for the general interface into the containers-contrib package. The Cabal file for this package has the following content:

cabal-version:       2.0
name:                containers-contrib
version:             0.0.0
build-type:          Simple

library
hs-source-dirs:      src
exposed-modules:     Map.Contrib.Group
build-depends:       base
, containers-sig
default-language:    Haskell2010

And here is the implementation of groupBy that uses only the containers-sig package:

{-# LANGUAGE ScopedTypeVariables #-}

module Map.Contrib.Group
( groupBy
) where

import Data.Foldable (foldl')
import Data.List.NonEmpty (NonEmpty (..), (<|))

import Map (Key, Map)
import qualified Map as M

groupBy :: forall k f a . (Foldable f, Key k)
=> (a -> k) -> f a -> Map k (NonEmpty a)
groupBy f = foldl' mapGroup M.empty
where
mapGroup :: Map k (NonEmpty a) -> a -> Map k (NonEmpty a)
mapGroup m a =
let val :: Maybe (NonEmpty a) -> NonEmpty a
val Nothing   = a :| []
val (Just xs) = a <| xs
in M.alter (Just . val) (f a) m

NOTE: You can see that the implementation is almost the same!

diff --git a/Map.hs b/containers-contrib/src/Map/Contrib/Group.hs
index 7b5e4e4..a47dea6 100644
--- a/Map.hs
+++ b/containers-contrib/src/Map/Contrib/Group.hs
@@ -1,4 +1,4 @@
-groupBy :: forall k f a . (Foldable f, Ord k)
+groupBy :: forall k f a . (Foldable f, Key k)
=> (a -> k) -> f a -> Map k (NonEmpty a)
groupBy f = foldl' mapGroup M.empty
where

It is still very simple Haskell: the type signatures are readable, no complicated features are used, no scary error messages, no performance overhead. For comparison, look at how groupBy is implemented for DynamicMap in relude:

groupBy :: forall f t a . (Foldable f, DynamicMap t, Val t ~ NonEmpty a, Monoid t)
=> (a -> Key t) -> f a -> t
groupBy f = foldl’ mapGroup mempty
where
mapGroup :: t -> a -> t
mapGroup m a =
let val :: Maybe (NonEmpty a) -> NonEmpty a
val Nothing   = x :| []
val (Just xs) = a <| xs
in alter (Just . val) (f x) m

The implementation is the same, but types are not as straightforward.

However, from package management side there’s a huge difference between an ordinary package and a package that depends on some signature. You can’t use the groupBy function and see the result of its evaluation without a real implementation for signatures (though you can implement another function that works for any signature based on groupBy). So you might think of the containers-contrib package as a kind of function on the package level. Backpack basically allows to convert usual packages into functions.

So containers-contrib is a function that takes a component like a library or an executable with an implementation of containers-sig and returns an ordinary package.

Now, let’s proceed to writing down the real definitions behind our signatures. We are going to put the implementation of signatures into a separate package called containers-ordered-strict. We don’t need to depend on containers-sig package to do so. But we are aware of our signatures, so we are going to produce a containers-sig-compatible module. To implement this signature, we need to export all types and classes with the same names and kinds, and all functions with the same names and types from the module with the implementation. Our signature is very similar to Map from the containers package, so let’s implement it first:

{-# LANGUAGE ConstraintKinds #-}

module Map.Ord
( Map
, Key
, empty
, alter
) where

import qualified Data.Map.Strict as M

type Map = M.Map
type Key = Ord

empty :: Map k v
empty = M.empty

alter :: Key k => (Maybe v -> Maybe v) -> k -> Map k v -> Map k v
alter = M.alter

It’s necessary to eta-reduce type-aliases because of the way Backpack works. There are some difficulties due to this limitation, but this will be covered later.

There’s also one important thing in the cabal file for our containers-ordered-strict package. Let’s have a closer look at it:

cabal-version:       2.0
name:                containers-ordered-strict
version:             0.0.0
build-type:          Simple

library
hs-source-dirs:      src

exposed-modules:     Map.Ord
reexported-modules:  Map.Ord as Map

build-depends:       base, containers
default-language:    Haskell2010

Having reexported-modules field is a vital part of our interface. Backpack matches the name of the signature module with the name of the module with the implementation. There’s an alternative way to achieve the same result, but it requires creating even more packages.

Now we can finally use our example from the containers-contrib package. Let’s implement the example in the containers-example package. First, we need to specify in the container-example.cabal file that we want to use the containers-contrib package with our containers-ordered-strict package as an implementation of the Map signature. This can be done in the following way:

cabal-version:       2.0
name:                containers-example
version:             0.0.0
build-type:          Simple

executable map-exe
hs-source-dirs:      app
main-is:             Main.hs
build-depends:       base
, containers-ordered-strict
, containers-contrib

default-language:    Haskell2010

That’s all! Backpack will substitute the implementation of the Map signature from the containers-ordered-strict package. This is because we used reexported-modules field to give the Map.Ord module the same name as the signature, and there are no other modules named Map in the dependencies.

Our final example looks like this:

module Main where

import Map.Contrib.Group (groupBy)

main :: IO ()
main = do
putStrLn "=== Map ==="
print $groupBy (mod 2) ([1..10] :: [Int]) After compiling and running, it works like a charm! $ cabal new-exec map-exe
=== Map ===
fromList [(0,10 :| [8,6,4,2]),(1,9 :| [7,5,3,1])]

### HashMap from unordered-containers

We now have one implementation of the containers-sig package. But that’s not enough. The key point is to have a generalized interface for different implementations. It doesn’t make much sense to have an interface with only one implementation, so let’s create our interface for HashMap from the unordered-containers package. Similarly to the containers-ordered-strict package, we are creating the containers-unordered-strict package.

NOTE: At this point, you might notice that Backpack requires to create many packages. And that’s true. We could put the implementation inside containers-ordered-strict under a different module name, but in our case we don’t want to have extra dependencies if the user is only interested in a single implementation. Also, it wouldn’t work well with reexported-modules approach since we can’t reexport two different modules under same name.

The Cabal file for containers-ordered-strict is almost the same. And the implementation of the signature could look like this:

{-# LANGUAGE ConstraintKinds #-}

module Map.Hash
( Map
, Key
, empty
, alter
) where

import Data.Hashable (Hashable)
import qualified Data.HashMap.Strict as M

type Map = M.HashMap
type Key a = (Eq a, Hashable a)

empty :: Map k v
empty = M.empty

alter :: Key k => (Maybe v -> Maybe v) -> k -> Map k v -> Map k v
alter = M.alter

However, this doesn’t compile with the following error:

   • Type constructor ‘Key’ has conflicting definitions in the module
and its hsig file
Main module: type Key a =
(ghc-prim-0.5.2.0:GHC.Classes.Eq a,
hashable-1.2.7.0:Data.Hashable.Class.Hashable a)
:: Constraint
Hsig file:  class Key k
Illegal parameterized type synonym in implementation of abstract data.
(Try eta reducing your type synonym so that it is nullary.)
• while checking that containers-unordered-strict-0.0.0:Map.Hash
implements signature Map in
containers-contrib-0.0.0[Map=containers-unordered-strict-0.0.0:Map.Hash]

So, does it mean that we can’t use our type alias? Not really. To overcome this problem, we will use the following trick:

{-# LANGUAGE FlexibleInstances    #-}
{-# LANGUAGE MonoLocalBinds       #-}
{-# LANGUAGE UndecidableInstances #-}

class (Eq k, Hashable k) => Key k
instance (Eq k, Hashable k) => Key k

Since we can’t use type alias for Key, we need to create our own type class with (Eq k, Hashable k) constraint. And implement this type class for every type that has specified constraints.

And now if we want to use our HashMap instead of Map in our example, we only need to replace these line in cabal file

    , containers-ordered-strict

with the following line:

    , containers-unordered-strict

That’s all! It’s extremely easy to switch implementations when using Backpack.

### Use several implementations inside a single package

Since we now have two implementations of our Map.hsig interface, we might want to use them both in a single package. Unfortunately, we can’t just add containers-unordered-strict package to dependencies in addition to containers-ordered-strict and enjoy. Since both packages have a reexported module with the same name Map we will see a compilation error about conflicting definitions. To solve this problem, Cabal has the mixins field inside stanza. Our containers-example.cabal file will now look like this:

cabal-version:       2.0
name:                containers-example
version:             0.0.0
build-type:          Simple

executable map-exe
hs-source-dirs:      app
main-is:             Main.hs
build-depends:       base
, containers-ordered-strict
, containers-contrib

mixins:              containers-contrib (Map.Contrib.Group as Map.Contrib.Group.Ord)
requires (Map as Map.Ord)
, containers-contrib (Map.Contrib.Group as Map.Contrib.Group.Hash)
requires (Map as Map.Hash)

default-language:    Haskell2010

This syntax allows to specify what module should be used as an implementation for a specific signature and under which name. The as part is essential because in case of multiple implementations we do need to have modules with different names.

And our example will now look like this:

module Main where

import qualified Map.Contrib.Group.Hash as HM (groupBy)
import qualified Map.Contrib.Group.Ord as M (groupBy)

main :: IO ()
main = do
putStrLn "### Map ###"
print $M.groupBy (mod 2) ([1..10] :: [Int]) putStrLn "### HashMap ###" print$ HM.groupBy (mod 2) ([1..10] :: [Int])

You can see that Backpack has the ability to use multiple implementations of a single interface. But they should be accessible under different namespaces.

### IntMap from containers

Now, this data type is more difficult. First, keys don’t have constraint like Ord, they only have the specific monomorphic type Int. Second, IntMap data type has kind Type while Map from signature has kind Type -> Type. But these problems are also solvable. To fix the issue with constraint, our Key constraint can be just type equality to Int. This can be achieved by partially applying type equality operator (~) to the Int type. Regarding different kinds: we can introduce our custom newtype with phantom type parameter. So the final solution looks like this:

{-# LANGUAGE DerivingStrategies         #-}
{-# LANGUAGE FlexibleInstances          #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE TypeFamilies               #-}

module Map.Int
( Map
, Key
, empty
, alter
) where

import qualified Data.IntMap.Strict as M

newtype Map k v = IM { unIM :: M.IntMap v }
deriving newtype (Show)

type Key = (~) Int

empty :: Map k v
empty = IM M.empty

alter :: Key k => (Maybe v -> Maybe v) -> k -> Map k v -> Map k v
alter f k = IM . M.alter f k . unIM

This solution is not perfect. And it’s still an open question how to make it better. Possible improvements are:

1. Figure out how to remove the Key constraint from functions like toList (such functions can know that k type variable is Int only when the constraint is in scope).
2. Use coerce to implement all functions and give more guarantees on performance.

But at least this solution doesn’t require advanced type-level features like -XTypeFamilies (despite the fact that this extension is enabled — it’s needed only for type equalities). It’s still plain Haskell. And we need to solve these problems only inside the Map.Int module, consumers of the signature interface don’t need to be aware of any complicated tricks. You can still write polymorphic functions without worrying about how particular instances are implemented internally.

### Map from primitive-containers

As I mentioned at the beginning of this blog post, some Map-like types are optimized for lookups. Thus they don’t support efficient modification operations. And that’s why it’s necessary to somehow separate read-only maps from modifiable maps. When you use typeclasses, you can easily have two different typeclasses with different names. With signatures, it’s also easy to achieve the desired result. We only need to move our updating operations into a separate package. To do so, we need to create a signature with exact same name but in another package. So now we have two packages with the same signatures:

• containers-sig-readonly
• containers-sig

Signatures are externally extensible, which means that you don’t need to open an issue to the main repository that contains the root of all signatures to extend a signature. You can just create a .hsig file in your library, add couple extra functions you require there, and you can reuse other functions from the existing signature if you specify the package with signature in the dependencies. That’s all. No need to specify a superclass constraint for your custom type class. The signature merging algorithm will do this work for you. In simple words, if you have two signatures with the same name, they can be merged into a single signature if data types and classes have equal kinds and if the functions with same names have the same types.

Both containers-sig-readonly and containers-sig packages should contain the Map.hsig file with data Map k v and class Key k. That’s the only boilerplate required. When both packages are used, Map data type and Key class will be merged with the corresponding types from other signatures.

So if, let’s say, the authors of containers-backpack package forgot to add some vital function to the interface, you could implement your own signature and implementation, and still enjoy the rest of the ecosystem without any problems!

## Conclusion

As the result of this Backpack journey, the containers-backpack repository contains the following packages:

• containers-sig-readonly: signatures for read-only maps
• containers-sig: signatures for maps that can be modified
• containers-ordered-strict: implementation of signatures for the Map.Strict data type from the containers package
• containers-int-strict: implementation of signatures for the IntMap.Strict type from the containers package
• containers-unordered-strict: implementation of signatures for the HashMap.Strict from the unordered-containers package
• containers-primitive: implementation of signatures for the Map.Lifted.Lifted from the primitive-containers package
• containers-contrib-readonly: general functions for maps implemented using the containers-sig-readonly package
• containers-contrib: general functions for maps implemented using the containers-sig-readonly and containers-sig packages
• containers-example: package that mixes signatures and different implementations

Whoa, that’s a lot of packages! But life should become more relaxed once support for multiple public libraries in cabal is implemented:

Backpack is a really great and exciting way to develop Haskell libraries despite the number of packages it requires. This approach is extremely new and unexplored. And I encourage everyone to try it!

For now, these are the opportunities I see with Backpack:

• Functions that work with a String/Text/ByteString-unified interface (the initial and most popular use case).
• unpacked-containers: make polymorphic containers more efficient.
• Use Int8/Int16/Int32/Int64/Word8/Word16/Word32/Word64 as keys in the IntMap data type without massive code duplication and performance overhead.
• Unified interfaces for data structures like Maps and Graphs. This should also reduce the amount of boilerplate required for tests and benchmarks.
• Write code with the help of lens signatures that can later be replaced with either microlens or lens or something else to not have both packages in the dependencies.

I might be wrong in some cases, but Backpack is still a very useful tool that you can put in the backpack of your Haskell skills.