What's a better way of managing large Haskell records? - haskell

Replacing fields names with letters, I have cases like this:
data Foo = Foo { a :: Maybe ...
, b :: [...]
, c :: Maybe ...
, ... for a lot more fields ...
} deriving (Show, Eq, Ord)
instance Writer Foo where
write x = maybeWrite a ++
listWrite b ++
maybeWrite c ++
... for a lot more fields ...
parser = permute (Foo
<$?> (Nothing, Just `liftM` aParser)
<|?> ([], bParser)
<|?> (Nothing, Just `liftM` cParser)
... for a lot more fields ...
-- this is particularly hideous
foldl1 merge [foo1, foo2, ...]
merge (Foo a b c ...seriously a lot more...)
(Foo a' b' c' ...) =
Foo (max a a') (b ++ b') (max c c') ...
What techniques would allow me to better manage this growth?
In a perfect world a, b, and c would all be the same type so I could keep them in a list, but they can be many different types. I'm particularly interested in any way to fold the records without needing the massive patterns.
I'm using this large record to hold the different types resulting from permutation parsing the vCard format.
Update
I've implemented both the generics and the foldl approaches suggested below. They both work, and they both reduce three large field lists to one.

Datatype-generic programming techniques can be used to transform all the fields of a record in some "uniform" sort of way.
Perhaps all the fields in the record implement some typeclass that we want to use (the typical example is Show). Or perhaps we have another record of "similar" shape that contains functions, and we want to apply each function to the corresponding field of the original record.
For these kinds of uses, the generics-sop library is a good option. It expands the default Generics functionality of GHC with extra type-level machinery that provides analogues of functions like sequence or ap, but which work over all the fields of a record.
Using generics-sop, I tried to create a slightly less verbose version of your merge funtion. Some preliminary imports:
{-# language TypeOperators #-}
{-# language DeriveGeneric #-}
{-# language TypeFamilies #-}
{-# language DataKinds #-}
import Control.Applicative (liftA2)
import qualified GHC.Generics as GHC
import Generics.SOP
A helper function that lifts a binary operation to a form useable by the functions of generics-sop:
fn_2' :: (a -> a -> a) -> (I -.-> (I -.-> I)) a -- I is simply an Identity functor
fn_2' = fn_2 . liftA2
A general merge function that takes a vector of operators and works on any single-constructor record that derives Generic:
merge :: (Generic a, Code a ~ '[ xs ]) => NP (I -.-> (I -.-> I)) xs -> a -> a -> a
merge funcs reg1 reg2 =
case (from reg1, from reg2) of
(SOP (Z np1), SOP (Z np2)) ->
let npResult = funcs `hap` np1 `hap` np2
in to (SOP (Z npResult))
Code is a type family that returns a type-level list of lists describing the structure of a datatype. The outer list is for constructors, the inner lists contain the types of the fields for each constructor.
The Code a ~ '[ xs ] part of the constraint says "the datatype can only have one constructor" by requiring the outer list to have exactly one element.
The (SOP (Z _) pattern matches extract the (heterogeneus) vector of field values from the record's generic representation. SOP stands for "sum-of-products".
A concrete example:
data Person = Person
{
name :: String
, age :: Int
} deriving (Show,GHC.Generic)
instance Generic Person -- this Generic is from generics-sop
mergePerson :: Person -> Person -> Person
mergePerson = merge (fn_2' (++) :* fn_2' (+) :* Nil)
The Nil and :* constructors are used to build the vector of operators (the type is called NP, from n-ary product). If the vector doesn't match the number of fields in the record, the program won't compile.
Update. Given that the types in your record are highly uniform, an alternative way of creating the vector of operations is to define instances of an auxiliary typeclass for each field type, and then use the hcpure function:
class Mergeable a where
mergeFunc :: a -> a -> a
instance Mergeable String where
mergeFunc = (++)
instance Mergeable Int where
mergeFunc = (+)
mergePerson :: Person -> Person -> Person
mergePerson = merge (hcpure (Proxy :: Proxy Mergeable) (fn_2' mergeFunc))
The hcliftA2 function (that combines hcpure, fn_2 and hap) could be used to simplify things further.

Some suggestions:
(1) You can use the RecordWildCards extension to automatically
unpack a record into variables. Doesn't help if you need to unpack
two records of the same type, but it's a useful to keep in mind.
Oliver Charles has a nice blog post on it: (link)
(2) It appears your example application is performing a fold over the records.
Have a look at Gabriel Gonzalez's foldl package. There is also a blog post: (link)
Here is a example of how you might use it with a record like:
data Foo = Foo { _a :: Int, _b :: String }
The following code computes the maximum of the _a fields and the
concatenation of the _b_ fields.
import qualified Control.Foldl as L
import Data.Profunctor
data Foo = Foo { _a :: Int, _b :: String }
deriving (Show)
fold_a :: L.Fold Foo Int
fold_a = lmap _a (L.Fold max 0 id)
fold_b :: L.Fold Foo String
fold_b = lmap _b (L.Fold (++) "" id)
fold_foos :: L.Fold Foo Foo
fold_foos = Foo <$> fold_a <*> fold_b
theFoos = [ Foo 1 "a", Foo 3 "b", Foo 2 "c" ]
test = L.fold fold_foos theFoos
Note the use of the Profunctor function lmap to extract out
the fields we want to fold over. The expression:
L.Fold max 0 id
is a fold over a list of Ints (or any Num instance), and therefore:
lmap _a (L.Fold max 0 id)
is the same fold but over a list of Foo records where we use _a
to produce the Ints.

Related

Set specific properties for data in Haskell

Let us say I want to make a ADT as follows in Haskell:
data Properties = Property String [String]
deriving (Show,Eq)
I want to know if it is possible to give the second list a bounded and enumerated property? Basically the first element of the list will be the minBound and the last element will be the maxBound. I am trying,
data Properties a = Property String [a]
deriving (Show, Eq)
instance Bounded (Properties a) where
minBound a = head a
maxBound a = (head . reverse) a
But not having much luck.
Well no, you can't do quite what you're asking, but maybe you'll find inspiration in this other neat trick.
{-# language ScopedTypeVariables, FlexibleContexts, UndecidableInstances #-}
import Data.Reflection -- from the reflection package
import qualified Data.List.NonEmpty as NE
import Data.List.NonEmpty (NonEmpty (..))
import Data.Proxy
-- Just the plain string part
newtype Pstring p = P String deriving Eq
-- Those properties you're interested in. It will
-- only be possible to produce bounds if there's at
-- least one property, so NonEmpty makes more sense
-- than [].
type Props = NonEmpty String
-- This is just to make a Show instance that does
-- what you seem to want easier to write. It's not really
-- necessary.
data Properties = Property String [String] deriving Show
Now we get to the key part, where we use reflection to produce class instances that can depend on run-time values. Roughly speaking, you can think of
Reifies x t => ...
as being a class-level version of
\(x :: t) -> ...
Because it operates at the class level, you can use it to parametrize instances. Since Reifies x t binds a type variable x, rather than a term variable, you need to use reflect to actually get the value back. If you happen to have a value on hand whose type ends in p, then you can just apply reflect to that value. Otherwise, you can always magic up a Proxy :: Proxy p to do the job.
-- If some Props are "in the air" tied to the type p,
-- then we can show them along with the string.
instance Reifies p Props => Show (Pstring p) where
showsPrec k p#(P str) =
showsPrec k $ Property str (NE.toList $ reflect p)
-- If some Props are "in the air" tied to the type p,
-- then we can give Pstring p a Bounded instance.
instance Reifies p Props => Bounded (Pstring p) where
minBound = P $ NE.head (reflect (Proxy :: Proxy p))
maxBound = P $ NE.last (reflect (Proxy :: Proxy p))
Now we need to have a way to actually bind types that can be passed to the type-level lambdas. This is done using the reify function. So let's throw some Props into the air and then let the butterfly nets get them back.
main :: IO ()
main = reify ("Hi" :| ["how", "are", "you"]) $
\(_ :: Proxy p) -> do
print (minBound :: Pstring p)
print (maxBound :: Pstring p)
./dfeuer#squirrel:~/src> ./WeirdBounded
Property "Hi" ["Hi","how","are","you"]
Property "you" ["Hi","how","are","you"]
You can think of reify x $ \(p :: Proxy p) -> ... as binding a type p to the value x; you can then pass the type p where you like by constraining things to have types involving p.
If you're just doing a couple of things, all this machinery is way more than necessary. Where it gets nice is when you're performing lots of operations with values that have phantom types carrying extra information. In many cases, you can avoid most of the explicit applications of reflect and the explicit proxy handling, because type inference just takes care of it all for you. For a good example of this technique in action, see the hyperloglog package. Configuration information for the HyperLogLog data structure is carried in a type parameter; this guarantees, at compile time, that only similarly configured structures are merged with each other.

Test if a value matches a constructor

Say I have a data type like so:
data NumCol = Empty |
Single Int |
Pair Int Int |
Lots [Int]
Now I wish to filter out the elements matching a given constructor from a [NumCol]. I can write it for, say, Pair:
get_pairs :: [NumCol] -> [NumCol]
get_pairs = filter is_pair
where is_pair (Pair _ _) = True
is_pair _ = False
This works, but it's not generic. I have to write a separate function for is_single, is_lots, etc.
I wish instead I could write:
get_pairs = filter (== Pair)
But this only works for type constructors that take no arguments (i.e. Empty).
So the question is, how can I write a function that takes a value and a constructor, and returns whether the value matches the constructor?
At least get_pairs itself can be defined relatively simply by using a list comprehension to filter instead:
get_pairs xs = [x | x#Pair {} <- xs]
For a more general solution of matching constructors, you can use prisms from the lens package:
{-# LANGUAGE TemplateHaskell #-}
import Control.Lens
import Control.Lens.Extras (is)
data NumCol = Empty |
Single Int |
Pair Int Int |
Lots [Int]
-- Uses Template Haskell to create the Prisms _Empty, _Single, _Pair and _Lots
-- corresponding to your constructors
makePrisms ''NumCol
get_pairs :: [NumCol] -> [NumCol]
get_pairs = filter (is _Pair)
Tags of tagged unions ought to be first-class values, and with a wee bit of effort, they are.
Jiggery-pokery alert:
{-# LANGUAGE GADTs, DataKinds, KindSignatures,
TypeFamilies, PolyKinds, FlexibleInstances,
PatternSynonyms
#-}
Step one: define type-level versions of the tags.
data TagType = EmptyTag | SingleTag | PairTag | LotsTag
Step two: define value-level witnesses for the representability of the type-level tags. Richard Eisenberg's Singletons library will do this for you. I mean something like this:
data Tag :: TagType -> * where
EmptyT :: Tag EmptyTag
SingleT :: Tag SingleTag
PairT :: Tag PairTag
LotsT :: Tag LotsTag
And now we can say what stuff we expect to find associated with a given tag.
type family Stuff (t :: TagType) :: * where
Stuff EmptyTag = ()
Stuff SingleTag = Int
Stuff PairTag = (Int, Int)
Stuff LotsTag = [Int]
So we can refactor the type you first thought of
data NumCol :: * where
(:&) :: Tag t -> Stuff t -> NumCol
and use PatternSynonyms to recover the behaviour you had in mind:
pattern Empty = EmptyT :& ()
pattern Single i = SingleT :& i
pattern Pair i j = PairT :& (i, j)
pattern Lots is = LotsT :& is
So what's happened is that each constructor for NumCol has turned into a tag indexed by the kind of tag it's for. That is, constructor tags now live separately from the rest of the data, synchronized by a common index which ensures that the stuff associated with a tag matches the tag itself.
But we can talk about tags alone.
data Ex :: (k -> *) -> * where -- wish I could say newtype here
Witness :: p x -> Ex p
Now, Ex Tag, is the type of "runtime tags with a type level counterpart". It has an Eq instance
instance Eq (Ex Tag) where
Witness EmptyT == Witness EmptyT = True
Witness SingleT == Witness SingleT = True
Witness PairT == Witness PairT = True
Witness LotsT == Witness LotsT = True
_ == _ = False
Moreover, we can easily extract the tag of a NumCol.
numColTag :: NumCol -> Ex Tag
numColTag (n :& _) = Witness n
And that allows us to match your specification.
filter ((Witness PairT ==) . numColTag) :: [NumCol] -> [NumCol]
Which raises the question of whether your specification is actually what you need. The point is that detecting a tag entitles you an expectation of that tag's stuff. The output type [NumCol] doesn't do justice to the fact that you know you have just the pairs.
How might you tighten the type of your function and still deliver it?
One approach is to use DataTypeable and the Data.Data module. This approach relies on two autogenerated typeclass instances that carry metadata about the type for you: Typeable and Data. You can derive them with {-# LANGUAGE DeriveDataTypeable #-}:
data NumCol = Empty |
Single Int |
Pair Int Int |
Lots [Int] deriving (Typeable, Data)
Now we have a toConstr function which, given a value, gives us a representation of its constructor:
toConstr :: Data a => a -> Constr
This makes it easy to compare two terms just by their constructors. The only remaining problem is that we need a value to compare against when we define our predicate! We can always just create a dummy value with undefined, but that's a bit ugly:
is_pair x = toConstr x == toConstr (Pair undefined undefined)
So the final thing we'll do is define a handy little class that automates this. The basic idea is to call toConstr on non-function values and recurse on any functions by first passing in undefined.
class Constrable a where
constr :: a -> Constr
instance Data a => Constrable a where
constr = toConstr
instance Constrable a => Constrable (b -> a) where
constr f = constr (f undefined)
This relies on FlexibleInstance, OverlappingInstances and UndecidableInstances, so it might be a bit evil, but, using the (in)famous eyeball theorem, it should be fine. Unless you add more instances or try to use it with something that isn't a constructor. Then it might blow up. Violently. No promises.
Finally, with the evil neatly contained, we can write an "equal by constructor" operator:
(=|=) :: (Data a, Constrable b) => a -> b -> Bool
e =|= c = toConstr e == constr c
(The =|= operator is a bit of a mnemonic, because constructors are syntactically defined with a |.)
Now you can write almost exactly what you wanted!
filter (=|= Pair)
Also, maybe you'd want to turn off the monomorphism restriction. In fact, here's the list of extensions I enabled that you can just use:
{-# LANGUAGE DeriveDataTypeable, FlexibleInstances, NoMonomorphismRestriction, OverlappingInstances, UndecidableInstances #-}
Yeah, it's a lot. But that's what I'm willing to sacrifice for the cause. Of not writing extra undefineds.
Honestly, if you don't mind relying on lens (but boy is that dependency a doozy), you should just go with the prism approach. The only thing to recommend mine is that you get to use the amusingly named Data.Data.Data class.

Why constraints on data are a bad thing?

I know this question has been asked and answered lots of times but I still don't really understand why putting constraints on a data type is a bad thing.
For example, let's take Data.Map k a. All of the useful functions involving a Map need an Ord k constraint. So there is an implicit constraint on the definition of Data.Map. Why is it better to keep it implicit instead of letting the compiler and programmers know that Data.Map needs an orderable key.
Also, specifying a final type in a type declaration is something common, and one can see it as a way of "super" constraining a data type.
For example, I can write
data User = User { name :: String }
and that's acceptable. However is that not a constrained version of
data User' s = User' { name :: s }
After all 99% of the functions I'll write for the User type don't need a String and the few which will would probably only need s to be IsString and Show.
So, why is the lax version of User considered bad:
data (IsString s, Show s, ...) => User'' { name :: s }
while both User and User' are considered good?
I'm asking this, because lots of the time, I feel I'm unnecessarily narrowing my data (or even function) definitions, just to not have to propagate constraints.
Update
As far as I understand, data type constraints only apply to the constructor and don't propagate. So my question is then, why do data type constraints not work as expected (and propagate)? It's an extension anyway, so why not have a new extension doing data properly, if it was considered useful by the community?
TL;DR:
Use GADTs to provide implicit data contexts.
Don't use any kind of data constraint if you could do with Functor instances etc.
Map's too old to change to a GADT anyway.
Scroll to the bottom if you want to see the User implementation with GADTs
Let's use a case study of a Bag where all we care about is how many times something is in it. (Like an unordered sequence. We nearly always need an Eq constraint to do anything useful with it.
I'll use the inefficient list implementation so as not to muddy the waters over the Data.Map issue.
GADTs - the solution to the data constraint "problem"
The easy way to do what you're after is to use a GADT:
Notice below how the Eq constraint not only forces you to use types with an Eq instance when making GADTBags, it provides that instance implicitly wherever the GADTBag constructor appears. That's why count doesn't need an Eq context, whereas countV2 does - it doesn't use the constructor:
{-# LANGUAGE GADTs #-}
data GADTBag a where
GADTBag :: Eq a => [a] -> GADTBag a
unGADTBag (GADTBag xs) = xs
instance Show a => Show (GADTBag a) where
showsPrec i (GADTBag xs) = showParen (i>9) (("GADTBag " ++ show xs) ++)
count :: a -> GADTBag a -> Int -- no Eq here
count a (GADTBag xs) = length.filter (==a) $ xs -- but == here
countV2 a = length.filter (==a).unGADTBag
size :: GADTBag a -> Int
size (GADTBag xs) = length xs
ghci> count 'l' (GADTBag "Hello")
2
ghci> :t countV2
countV2 :: Eq a => a -> GADTBag a -> Int
Now we didn't need the Eq constraint when we found the total size of the bag, but it didn't clutter up our definition anyway. (We could have used size = length . unGADTBag just as well.)
Now lets make a functor:
instance Functor GADTBag where
fmap f (GADTBag xs) = GADTBag (map f xs)
oops!
DataConstraints_so.lhs:49:30:
Could not deduce (Eq b) arising from a use of `GADTBag'
from the context (Eq a)
That's unfixable (with the standard Functor class) because I can't restrict the type of fmap, but need to for the new list.
Data Constraint version
Can we do as you asked? Well, yes, except that you have to keep repeating the Eq constraint wherever you use the constructor:
{-# LANGUAGE DatatypeContexts #-}
data Eq a => EqBag a = EqBag {unEqBag :: [a]}
deriving Show
count' a (EqBag xs) = length.filter (==a) $ xs
size' (EqBag xs) = length xs -- Note: doesn't use (==) at all
Let's go to ghci to find out some less pretty things:
ghci> :so DataConstraints
DataConstraints_so.lhs:1:19: Warning:
-XDatatypeContexts is deprecated: It was widely considered a misfeature,
and has been removed from the Haskell language.
[1 of 1] Compiling Main ( DataConstraints_so.lhs, interpreted )
Ok, modules loaded: Main.
ghci> :t count
count :: a -> GADTBag a -> Int
ghci> :t count'
count' :: Eq a => a -> EqBag a -> Int
ghci> :t size
size :: GADTBag a -> Int
ghci> :t size'
size' :: Eq a => EqBag a -> Int
ghci>
So our EqBag count' function requires an Eq constraint, which I think is perfectly reasonable, but our size' function also requires one, which is less pretty. This is because the type of the EqBag constructor is EqBag :: Eq a => [a] -> EqBag a, and this constraint must be added every time.
We can't make a functor here either:
instance Functor EqBag where
fmap f (EqBag xs) = EqBag (map f xs)
for exactly the same reason as with the GADTBag
Constraintless bags
data ListBag a = ListBag {unListBag :: [a]}
deriving Show
count'' a = length . filter (==a) . unListBag
size'' = length . unListBag
instance Functor ListBag where
fmap f (ListBag xs) = ListBag (map f xs)
Now the types of count'' and show'' are exactly as we expect, and we can use standard constructor classes like Functor:
ghci> :t count''
count'' :: Eq a => a -> ListBag a -> Int
ghci> :t size''
size'' :: ListBag a -> Int
ghci> fmap (Data.Char.ord) (ListBag "hello")
ListBag {unListBag = [104,101,108,108,111]}
ghci>
Comparison and conclusions
The GADTs version automagically propogates the Eq constraint everywhere the constructor is used. The type checker can rely on there being an Eq instance, because you can't use the constructor for a non-Eq type.
The DatatypeContexts version forces the programmer to manually propogate the Eq constraint, which is fine by me if you want it, but is deprecated because it doesn't give you anything more than the GADT one does and was seen by many as pointless and annoying.
The unconstrained version is good because it doesn't prevent you from making Functor, Monad etc instances. The constraints are written exactly when they're needed, no more or less. Data.Map uses the unconstrained version partly because unconstrained is generally seen as most flexible, but also partly because it predates GADTs by some margin, and there needs to be a compelling reason to potentially break existing code.
What about your excellent User example?
I think that's a great example of a one-purpose data type that benefits from a constraint on the type, and I'd advise you to use a GADT to implement it.
(That said, sometimes I have a one-purpose data type and end up making it unconstrainedly polymorphic just because I love to use Functor (and Applicative), and would rather use fmap than mapBag because I feel it's clearer.)
{-# LANGUAGE GADTs #-}
import Data.String
data User s where
User :: (IsString s, Show s) => s -> User s
name :: User s -> s
name (User s) = s
instance Show (User s) where -- cool, no Show context
showsPrec i (User s) = showParen (i>9) (("User " ++ show s) ++)
instance (IsString s, Show s) => IsString (User s) where
fromString = User . fromString
Notice since fromString does construct a value of type User a, we need the context explicitly. After all, we composed with the constructor User :: (IsString s, Show s) => s -> User s. The User constructor removes the need for an explicit context when we pattern match (destruct), becuase it already enforced the constraint when we used it as a constructor.
We didn't need the Show context in the Show instance because we used (User s) on the left hand side in a pattern match.
Constraints
The problem is that constraints are not a property of the data type, but of the algorithm/function that operates on them. Different functions might need different and unique constraints.
A Box example
As an example, let's assume we want to create a container called Box which contains only 2 values.
data Box a = Box a a
We want it to:
be showable
allow the sorting of the two elements via sort
Does it make sense to apply the constraint of both Ord and Show on the data type? No, because the data type in itself could be only shown or only sorted and therefore the constraints are related to its use, not it's definition.
instance (Show a) => Show (Box a) where
show (Box a b) = concat ["'", show a, ", ", show b, "'"]
instance (Ord a) => Ord (Box a) where
compare (Box a b) (Box c d) =
let ca = compare a c
cb = compare b d
in if ca /= EQ then ca else cb
The Data.Map case
Data.Map's Ord constraints on the type is really needed only when we have > 1 elements in the container. Otherwise the container is usable even without an Ord key. For example, this algorithm:
transf :: Map NonOrd Int -> Map NonOrd Int
transf x =
if Map.null x
then Map.singleton NonOrdA 1
else x
Live demo
works just fine without the Ord constraint and always produce a non empty map.
Using DataTypeContexts reduces the number of programs you can write. If most of those illegal programs are nonsense, you might say it's worth the runtime cost associated with ghc passing in a type class dictionary that isn't used. For example, if we had
data Ord k => MapDTC k a
then #jefffrey's transf is rejected. But we should probably have transf _ = return (NonOrdA, 1) instead.
In some sense the context is documentation that says "every Map must have ordered keys". If you look at all of the functions in Data.Map you'll get a similar conclusion "every useful Map has ordered keys". While you can create maps with unordered keys using
mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a
singleton :: k2 a -> Map k2 a
But the moment you try to do anything useful with them, you'll wind up with No instance for Ord k2 somewhat later.

How do I implement this function without using mixed lists?

Let's say I have a function that takes a list of function-list pairs, and maps the function in each pair onto the list in the pair, for example:
myFunction [("SOME"++,["DAY","ONE"]), (show,[1,2])] == [["SOMEDAY", "SOMEONE"],["1","2"]]
Is there a way of implementing myFunction so that the code I provided above will work as is without any modifications?
My problem is I can't figure out how to implement myFunction because the types of each sub-list could be different (in my example I have a list of strings ["DAY", ONE"], and a list of numbers: [1,2]). I know that each function in the list will convert its list into a list of strings (so the final list will have type [[Char]]), but I don't know how to express this in Haskell.
You can do it with existential types
{-# LANGUAGE ExistentialQuantification #-}
data T = forall a b. Show b => (:?:) (a -> b) [a]
table =
[ ("SOME"++) :?: ["DAY","ONE"]
, (show) :?: [1,2]
, (+1) :?: [2.9, pi]
]
And run it as:
apply :: T -> String
apply (f :?: xs) = show $ map f xs
main = print $ map apply table
You want to use existential quantification to define a type that can hold any value as long as it is a member of the Show typeclass. For example:
{-# LANGUAGE ExistentialQuantification #-}
data S = forall a. Show a => S a
instance Show S where
show (S s) = show s
f :: [S] -> [String]
f xs = map show xs
And now in ghci:
*Main> f [S 1, S True, S 'c']
["1","True","'c'"]
You won't be able to run the code in your question without modification, because it contains a heterogeneous list, which the Haskell type system forbids. Instead you can wrap heterogeneous types up as a variant type (if you know in advance all the types that will be required) or as an existentially quantified type (if you don't know what types will be required, but you do know a property that they must satisfy).

Sort by constructor ignoring (part of) value

Suppose I have
data Foo = A String Int | B Int
I want to take an xs :: [Foo] and sort it such that all the As are at the beginning, sorted by their strings, but with the ints in the order they appeared in the list, and then have all the Bs at the end, in the same order they appeared.
In particular, I want to create a new list containg the first A of each string and the first B.
I did this by defining a function taking Foos to (Int, String)s and using sortBy and groupBy.
Is there a cleaner way to do this? Preferably one that generalizes to at least 10 constructors.
Typeable, maybe? Something else that's nicer?
EDIT: This is used for processing a list of Foos that is used elsewhere. There is already an Ord instance which is the normal ordering.
You can use
sortBy (comparing foo)
where foo is a function that extracts the interesting parts into something comparable (e.g. Ints).
In the example, since you want the As sorted by their Strings, a mapping to Int with the desired properties would be too complicated, so we use a compound target type.
foo (A s _) = (0,s)
foo (B _) = (1,"")
would be a possible helper. This is more or less equivalent to Tikhon Jelvis' suggestion, but it leaves space for the natural Ord instance.
To make it easier to build comparison function for ADTs with large number of constructors, you can map values to their constructor index with SYB:
{-# LANGUAGE DeriveDataTypeable #-}
import Data.Generics
data Foo = A String Int | B Int deriving (Show, Eq, Typeable, Data)
cIndex :: Data a => a -> Int
cIndex = constrIndex . toConstr
Example:
*Main Data.Generics> cIndex $ A "foo" 42
1
*Main Data.Generics> cIndex $ B 0
2
Edit:After re-reading your question, I think the best option is to make Foo an instance of Ord. I do not think there is any way to do this automatically that will act the way you want (just using deriving will create different behavior).
Once Foo is an instance of Ord, you can just use sort from Data.List.
In your exact example, you can do something like this:
data Foo = A String Int | B Int deriving (Eq)
instance Ord Foo where
(A _ _) <= (B _) = True
(A s _) <= (A s' _) = s <= s'
(B _) <= (B _) = True
When something is an instance of Ord, it means the data type has some ordering. Once we know how to order something, we can use a bunch of existing functions (like sort) on it and it will behave how you want. Anything in Ord has to be part of Eq, which is what the deriving (Eq) bit does automatically.
You can also derive Ord. However, the behavior will not be exactly what you want--it will order by all of the fields if it has to (e.g. it will put As with the same string in order by their integers).
Further edit: I was thinking about it some more and realized my solution is probably semantically wrong.
An Ord instance is a statement about your whole data type. For example, I'm saying that Bs are always equal with each other when the derived Eq instance says otherwise.
If the data your representing always behaves like this (that is, Bs are all equal and As with the same string are all equal) then an Ord instance makes sense. Otherwise, you should not actually do this.
However, you can do something almost exactly like this: write your own special compare function (Foo -> Foo -> Ordering) that encapsulates exactly what you want to do then use sortBy. This properly codifies that your particular sorting is special rather than the natural ordering of the data type.
You could use some template haskell to fill in the missing transitive cases. The mkTransitiveLt creates the transitive closure of the given cases (if you order them least to greatest). This gives you a working less-than, which can be turned into a function that returns an Ordering.
{-# LANGUAGE TemplateHaskell #-}
import MkTransitiveLt
import Data.List (sortBy)
data Foo = A String Int | B Int | C | D | E deriving(Show)
cmp a b = $(mkTransitiveLt [|
case (a, b) of
(A _ _, B _) -> True
(B _, C) -> True
(C, D) -> True
(D, E) -> True
(A s _, A s' _) -> s < s'
otherwise -> False|])
lt2Ord f a b =
case (f a b, f b a) of
(True, _) -> LT
(_, True) -> GT
otherwise -> EQ
main = print $ sortBy (lt2Ord cmp) [A "Z" 1, A "A" 1, B 1, A "A" 0, C]
Generates:
[A "A" 1,A "A" 0,A "Z" 1,B 1,C]
mkTransitiveLt must be defined in a separate module:
module MkTransitiveLt (mkTransitiveLt)
where
import Language.Haskell.TH
mkTransitiveLt :: ExpQ -> ExpQ
mkTransitiveLt eq = do
CaseE e ms <- eq
return . CaseE e . reverse . foldl go [] $ ms
where
go ms m#(Match (TupP [a, b]) body decls) = (m:ms) ++
[Match (TupP [x, b]) body decls | Match (TupP [x, y]) _ _ <- ms, y == a]
go ms m = m:ms

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