Applicative, bidirectional serialization combinators

A neat GADT/Applicative trick
Posted in: haskell.


If you are only interested in the neat Haskell trick, skip this section. It has been a while since I updated my personal blog here. There has been a lot going on in my life in the past few months, including exams, a breakup with my girlfriend and moving to Tokyo for an internship at Tsuru Capital.

It has been really great so far, the work is interesting, so are the people, and we have a nice view from the office.

View from the Tsuru Capital office
View from the Tsuru Capital office


This blogpost is written in literate Haskell (source here), so you can drop it in a file, load it in GHCi and play around with it, should you feel like doing this.

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeSynonymInstances #-}
import Control.Applicative
import Control.Monad
import Data.Aeson

A lot of serialization libraries use a technique employing two typeclasses (or one typeclass with two methods) in order to convert data from and to some format. An example is the excellent aeson library:

data Food = Food
{ foodName :: String
, foodCost :: Int
} deriving (Show)
instance ToJSON Food where
toJSON (Food name cost) = object
[ "name" .= name
, "cost" .= cost
instance FromJSON Food where
parseJSON (Object obj) = Food
<$> obj .: "name"
<*> obj .: "cost"
parseJSON _ = mzero

Some other libraries using this technique are cassava, postgresql-simple, and binary.

While working on some new internal SQLite bindings and utilities at Tsuru, I discovered another technique which is more concise, but keeps the nice Applicative interface. The code in this blogpost disregards performance and only supports the most basic of features in order to be easier to understand.

Primitive types

We start out by defining a typeclass for primitive serializable types, such as Int and String. We disregard performance, as said before, and we are also going to ignore proper error checking: we just serialize these primitive types to Strings.

class Field a where
fieldType :: a -> String -- Should work with 'undefined'
fieldRead :: String -> a
fieldShow :: a -> String
instance Field String where
fieldType = const "TEXT"
fieldRead = id -- We need proper escaping here
fieldShow = id
instance Field Int where
fieldType = const "INTEGER"
fieldRead = read
fieldShow = show

These fields are sufficient to store some Food, so what else do we need? We need “instantiations” of these fields which actually represent a part of a record. This can be modeled as:

data FieldInfo t a = FieldInfo
{ fieldName :: String
, fieldExtract :: t -> a

Let’s give an example, we would map the cost of food as:

costFieldInfo :: FieldInfo Food Int
costFieldInfo = FieldInfo "cost" foodCost

This costFieldInfo is not used in the code below, it is just an example.


In the case of an SQLite database, such a FieldInfo actually represent a column in our table. We will be building our table using Applicative, without actually evaluating anything yet. This seems related to free monads – determining the exact category-theoretical relation is left as an excercise for the mathematical-minded reader.

We just have constructors for each method of the applicative interface, plus an SQLite primitive to add a column to our table.

This requires the great GADTs extension, it is not possible to do this with Haskell 98 datatypes – the wiki page has more information.

data Table t f where
-- Applicative interface:
-- <$>, pure and <*>
Map :: (a -> b) -> Table t a -> Table t b
Pure :: a -> Table t a
App :: Table t (a -> b) -> Table t a -> Table t b
-- Primitives
Column :: Field a => FieldInfo t a -> Table t a

This makes the Functor and Applicative instances trivial to implement.

instance Functor (Table t) where
fmap = Map
instance Applicative (Table t) where
pure = Pure
(<*>) = App

This GADT allows us to model actual tables:

foodTable :: Table Food Food
foodTable = Food
<$> Column (FieldInfo "name" foodName)
<*> Column (FieldInfo "cost" foodCost)

Let’s make some nicer syntax and write foodTable again:

column :: Field a => String -> (t -> a) -> Table t a
column name extract = Column (FieldInfo name extract)
foodTable' :: Table Food Food
foodTable' = Food
<$> column "name" foodName
<*> column "cost" foodCost

Lookin’ good!

The real work

While procrastrinating by creating GADT wrappers is fun, at one point we should write some actual implementation.

These implementations work by evaluating the trees we created with the different constructors for the GADT.

Our first method crawls the table tree and returns the name and type of each column:

metaRecord :: Table t t -> [(String, String)]
metaRecord = go
go :: forall t a. Table t a -> [(String, String)]
go (Map _ t) = go t
go (Pure _ ) = []
go (App t1 t2) = go t1 ++ go t2
go (Column fi) = [(fieldName fi, fieldType (undefined :: a))]

The second method is only slightly more complicated: instead of returning the type of each column, it calls our custom extract function for that column to get its value. We can then call fieldShow on that to do the final serialization, and what we get is the serialized name and value of each column.

toRecord :: forall t. Table t t -> t -> [(String, String)]
toRecord tab x = go tab
go :: forall a. Table t a -> [(String, String)]
go (Map _ t) = go t
go (Pure _ ) = []
go (App t1 t2) = go t1 ++ go t2
go (Column fi) =
[(fieldName fi, fieldShow $ fieldExtract fi x)]

The deserialization method is the hardest. It works by actually evaluating the tree we built. Because of our GADT use, we can do this in a type-safe way.

fromRecord :: forall t. Table t t -> [(String, String)] -> t
fromRecord tab record = go tab
go :: forall a. Table t a -> a
go (Map f t) = f (go t)
go (Pure x) = x
go (App ft t) = (go ft) (go t)
go (Column fi) = case lookup (fieldName fi) record of
Nothing -> error $ "Missing field: " ++ fieldName fi
Just str -> fieldRead str


We add a small utility function to pretty-print our records:

printRecord :: [(String, String)] -> IO ()
printRecord = putStrLn . unlines . map (\(x, y) -> x ++ " = " ++ y)

And a typeclass so we do not have to create an xxxTable function for each datatype:

class HasTable t where
table :: Table t t


Now let’s implement food serialization for real: we only need to implement a single typeclass with a single method!

instance HasTable Food where
table = Food
<$> column "name" foodName
<*> column "cost" foodCost

Some concrete deliciousness:

ramen :: Food
ramen = Food "ラーメン" 800

And a trivial demo:

main :: IO ()
main = do
putStrLn "Meta record (used in CREATE TABLE... etc.):"
printRecord $ metaRecord (table :: Table Food Food)
putStrLn "Serialized ramen:"
printRecord (toRecord table ramen)
putStrLn "Deserialized sashimi:"
print (fromRecord table [("name", "刺身"), ("cost", "1200")] :: Food)


I think this is a nice use case of GADTs, and although it has a performance impact, it looks like it is worth it (for now). If it turns out that we can nicely generalize this code, we will probably release it on Hackage. But feel free to steal the idea, and comments are also welcome, of course!

Exercise for the reader: can you make Table a Monad? Why (not)?