Is there a way to "lift" a class instance in Haskell easily?
I've been frequently needing to create, e.g., Num instances for some classes that are just "lifting" the Num structure through the type constructor like this:
data SomeType a = SomeCons a
instance (Num a)=>Num SomeCons a where
(SomeCons x) + (SomeCons y) = SomeCons (x+y)
negate (SomeCons x) = SomeCons (negate x)
-- similarly for other functions.
Is there a way to avoid this boilerplate and "lift" this Num structure automatically? I usually have to do this with Show and other classes also when I was trying to learn existencials and the compiler wouldn't let me use deriving(Show).
The generalized newtype deriving extension is what you want here:
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
module Main where
newtype SomeType a = SomeCons a deriving (Num, Show, Eq)
main = do
let a = SomeCons 2
b = SomeCons 3
print $ a + b
Output:
*Main> main
SomeCons 5
GHC implements what you want : Extensions to the deriving mecanism.
These modifications are often shown for future standard language extension (As seen on haskell' wiki)
To Enable this extension, you must use the following pragma
{-# GeneralizedNewtypeDeriving #-}
and then use a deriving on your newtype declaration, as usual
data SomeType a = SomeCons a deriving (Num)
GeneralizedNewtypeDeriving
Related
I am using data-reify and graphviz to transform an eDSL into a nice graphical representation, for introspection purposes.
As simple, contrived example, consider:
{-# LANGUAGE GADTs #-}
data Expr a where
Constant :: a -> Expr a
Map :: (other -> a) -> Expr a -> Expr a
Apply :: Expr (other -> a) -> Expr a -> Expr a
instance Functor Expr where
fmap fun val = Map fun val
instance Applicative Expr where
fun_expr <*> data_expr = Apply fun_expr data_expr
pure val = Constant val
-- And then some functions to optimize an Expr AST, evaluate Exprs, etc.
To make introspection nicer, I would like to print the values which are stored inside certain AST nodes of the DSL datatype.
However, in general any a might be stored in Constant, even those that do not implement Show. This is not necessarily a problem since we can constrain the instance of Expr like so:
instance Show a => Show (Expr a) where
...
This is not what I want however: I would still like to be able to print Expr even if a is not Show-able, by printing some placeholder value (such as just its type and a message that it is unprintable) instead.
So we want to do one thing if we have an a implementing Show, and another if a particular a does not.
Furthermore, the DSL also has the constructors Map and Apply which are even more problematic. The constructor is existential in other, and thus we cannot assume anything about other, a or (other -> a). Adding constraints to the type of other to the Map resp. Apply constructors would break the implementation of Functor resp. Applicative which forwards to them.
But here also I'd like to print for the functions:
a unique reference. This is always possible (even though it is not pretty as it requires unsafePerformIO) using System.Mem.StableName.
Its type, if possible (one technique is to use show (typeOf fun), but it requires that fun is Typeable).
Again we reach the issue where we want to do one thing if we have an f implementing Typeable and another if f does not.
How to do this?
Extra disclaimer: The goal here is not to create 'correct' Show instances for types that do not support it. There is no aspiration to be able to Read them later, or that print a != print b implies a != b.
The goal is to print any datastructure in a 'nice for human introspection' way.
The part I am stuck at, is that I want to use one implementation if extra constraints are holding for a resp. (other -> a), but a 'default' one if these do not exist.
Maybe type classes with FlexibleInstances, or maybe type families are needed here? I have not been able to figure it out (and maybe I am on the wrong track all together).
Not all problems have solutions. Not all constraint systems have a satisfying assignment.
So... relax the constraints. Store the data you need to make a sensible introspective function in your data structure, and use functions with type signatures like show, fmap, pure, and (<*>), but not exactly equal to them. If you need IO, use IO in your type signature. In short: free yourself from the expectation that your exceptional needs fit into the standard library.
To deal with things where you may either have an instance or not, store data saying whether you have an instance or not:
data InstanceOrNot c where
Instance :: c => InstanceOrNot c
Not :: InstanceOrNot c
(Perhaps a Constraint-kinded Either-alike, rather than Maybe-alike, would be more appropriate. I suspect as you start coding this you will discover what's needed.) Demand that clients that call notFmap and friends supply these as appropriate.
In the comments, I propose parameterizing your type by the constraints you demand, and giving a Functor instance for the no-constraints version. Here's a short example showing how that might look:
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleInstances #-}
import Data.Kind
type family All cs a :: Constraint where
All '[] a = ()
All (c:cs) a = (c a, All cs a)
data Lol cs a where
Leaf :: a -> Lol cs a
Fmap :: All cs b => (a -> b) -> Lol cs a -> Lol cs b
instance Functor (Lol '[]) where
fmap f (Leaf a) = Leaf (f a)
fmap f (Fmap g garg) = Fmap (f . g) garg
Great timing! Well-typed recently released a library which allows you to recover runtime information. They specifically have an example of showing arbitrary values. It's on github at https://github.com/well-typed/recover-rtti.
It turns out that this is a problem which has been recognized by multiple people in the past, known as the 'Constrained Monad Problem'. There is an elegant solution, explained in detail in the paper The Constrained-Monad Problem by Neil Sculthorpe and Jan Bracker and George Giorgidze and Andy Gill.
A brief summary of the technique: Monads (and other typeclasses) have a 'normal form'. We can 'lift' primitives (which are constrained any way we wish) into this 'normal form' construction, itself an existential datatype, and then use any of the operations available for the typeclass we have lifted into. These operations themselves are not constrained, and thus we can use all of Haskell's normal typeclass functions.
Finally, to turn this back into the concrete type (which again has all the constraints we are interested in) we 'lower' it, which is an operation that takes for each of the typeclass' operations a function which it will apply at the appropriate time.
This way, constraints from the outside (which are part of the functions supplied to the lowering) and constraints from the inside (which are part of the primitives we lifted) are able to be matched, and finally we end up with one big happy constrained datatype for which we have been able to use any of the normal Functor/Monoid/Monad/etc. operations.
Interestingly, while the intermediate operations are not constrained, to my knowledge it is impossible to write something which 'breaks' them as this would break the categorical laws that the typeclass under consideration should adhere to.
This is available in the constrained-normal Hackage package to use in your own code.
The example I struggled with, could be implemented as follows:
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE UndecidableInstances #-}
module Example where
import Data.Dynamic
import Data.Kind
import Data.Typeable
import Control.Monad.ConstrainedNormal
-- | Required to have a simple constraint which we can use as argument to `Expr` / `Expr'`.
-- | This is definitely the part of the example with the roughest edges: I have yet to figure out
-- | how to make Haskell happy with constraints
class (Show a, Typeable a) => Introspectable a where {}
instance (Show a, Typeable a) => Introspectable a where {}
data Expr' (c :: * -> Constraint) a where
C :: a -> Expr' c a
-- M :: (a -> b) -> Expr' a -> Expr' b --^ NOTE: This one is actually never used as ConstrainedNormal will use the 'free' implementation based on A + C.
A :: c a => Expr' c (a -> b) -> Expr' c a -> Expr' c b
instance Introspectable a => Show (Expr' Introspectable a) where
show e = case e of
C x -> "(C " ++ show x ++ ")"
-- M f x = "(M " ++ show val ++ ")"
A fx x -> "(A " ++ show (typeOf fx) ++ " " ++ show x ++ ")"
-- | In user-facing code you'd not want to expose the guts of this construction
-- So let's introduce a 'wrapper type' which is what a user would normally interact with.
type Expr c a = NAF c (Expr' c) a
liftExpr :: c a => Expr' c a -> Expr c a
liftExpr expr = liftNAF expr
lowerExpr :: c a => Expr c a -> Expr' c a
lowerExpr lifted_expr = lowerNAF C A lifted_expr
constant :: Introspectable a => a -> Expr c a
constant val = pure val -- liftExpr (C val)
You could now for instance write
ghci> val = constant 10 :: Expr Introspectable Int
(C 10)
ghci> (+2) <$> val
(C 12)
ghci> (+) <$> constant 10 <*> constant 32 :: Expr Introspectable Int
And by using Data.Constraint.Trivial (part of the trivial-constrained library, although it is also possible to write your own 'empty constrained') one could instead write e.g.
ghci> val = constant 10 :: Expr Unconstrained Int
which will work just as before, but now val cannot be printed.
The one thing I have not yet figured out, is how to properly work with subsets of constraints (i.e. if I have a function that only requires Show, make it work with something that is Introspectable). Currently everything has to work with the 'big' set of constraints.
Another minor drawback is of course that you'll have to annotate the constraint type (e.g. if you do not want constraints, write Unconstrained manually), as GHC will otherwise complain that c0 is not known.
We've reached the goal of having a type which can be optionally be constrained to be printable, with all machinery that does not need printing to work also on all instances of the family of types including those that are not printable, and the types can be used as Monoids, Functors, Applicatives, etc just as you like.
I think it is a beautiful approach, and want to commend Neil Sculthorpe et al. for their work on the paper and the constrained-normal library that makes this possible. It's very cool!
I have the following GADT:
{-# LANGUAGE GADTs #-}
data LogProtocol a where
Message :: String -> LogProtocol String
StartRun :: forall rc. (Show rc, Eq rc, Titled rc, ToJSON rc, FromJSON rc)
=> rc -> LogProtocol rc
... and many more...
toJSON is straight forward and not shown.
fromJSON implementation is based on:
This SO Question and
This Blog Post - pattern 2
and is as follows:
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE TemplateHaskell #-}
-- tag type is used in to/ from JSON to reduce the use of magic strings
data LPTag = MessageT |
StartRunT |
... and many more...
deriving (Show, Eq, Enum)
tagList :: Enum a => [a]
tagList = enumFrom $ toEnum 0
$(deriveJSON defaultOptions ''LPTag)
-- a wrapper to hide the a type param in the GADT
data Some (t :: k -> *) where
Some :: t x -> Some t
instance FromJSON (Some LogProtocol) where
parseJSON :: Value -> Parser (Some LogProtocol)
parseJSON v#(Object o) =
let
tag :: Maybe LPTag
tag = do
t <- (HML.lookup "type" o)
parseMaybe parseJSON t
failMessage :: [Char]
failMessage = toS $ "Could not parse LogProtocol no type field or type field value is not a member of specified in: "
<> (show(tagList :: [LPTag]))
<> show v
in
maybe
(fail failMessage )
(
\case
MessageT -> Some <$> (Message <$> o .: "txt")
StartRunT -> Some <$> (StartRun <$> o .: "runConfig")
)
tag
parseJSON wrng = typeMismatch "LogProtocol" wrng
The case for '''Message''' is fine. The problem I am having are errors such as:
* No instance for (Titled x2) arising from a use of `StartRun'
* In the first argument of `(<$>)', namely `StartRun'
In the second argument of `(<$>)', namely
`(StartRun <$> o .: "runConfig")'
In the expression: Some <$> (StartRun <$> o .: "runConfig")
Anywhere I have my own type class constraints (such as Titled)
in the data constructor the compiler says "No".
Is there a way to resolve this?
Existential types are an antipattern, especially if you need to do deserialization. StartRun should contain a concrete type instead. Deserialization requires a concrete type anyway, hence you might as well specialize StartRun to it.
How can i represent a list which include 1 String and another list with maximum of 3 Strings.
Like this one:
osztaly = [("András", ["mákos", "meggyes", "almás"]), ("Joli", ["túrós"]), ("Anna", ["almás", "almás"]), ("Tamás", []), ("Mari", ["almás", "meggyes"]), ("Vera", [])]
If you just need size 3:
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveTraversable #-}
data ListUpTo3 a
= Zero
| One a
| Two a a
| Three a a a
deriving (Functor, Foldable, Traversable)
The Functor, Foldable, and Traversable instances recover many (but not all) of the convenient functions available for the builtin lists.
If you may need other sizes than max-3, you can generalize this, but it takes significantly more type-level programming, which adds significant programmer effort both for the implementer of the type and for the user of the type.
Personally, I probably would not try to capture this constraint at the type level. Then the max-length-3 bit is not compiler checked; but it is also much simpler to implement and use. You can read more about this idea elsewhere on the net under the keywords "smart constructor".
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
-- N.B. we do not export the value constructor, only the type constructor
module UpTo3 (ListUpTo3, fromList, toList) where
newtype ListUpTo3 a = ListUpTo3 [a] deriving (Functor, Foldable, Traversable)
fromList :: [a] -> Maybe (ListUpTo3 a)
fromList xs = if null (drop 3 xs) then Just (ListUpTo3 xs) else Nothing
toList :: ListUpTo3 a -> [a]
toList (ListUpTo3 xs) = xs
I'm attempting to define an abstract syntax type using ekmett's libraries bound and free. I have something working, which I can strip down to the following minimal example:
{-# LANGUAGE DeriveFunctor #-}
import Bound
import Control.Monad.Free
type Id = String
data TermF f α =
AppF α α
| BindF Id (Scope () f α)
deriving Functor
newtype Term' α = T {unT :: Free (TermF Term) α}
type Term = Free (TermF Term')
Those last two lines are, uh, not what I was hoping for. They make it kind of a PITA to actually exploit the open recursion for annotations (or whatever).
Is there a better way of using these two libraries together, and/or should I just give up on trying to make Term a free monad?
Make it simple
You can simplify the last two lines into.
newtype Term α = T {unT :: Free (TermF Term) α}
This should help you know to consistently use T and unT everywhere instead of only at every other level.
Make it complicated
Both Free and TermF have the kind (*->*)->(*->*), which is the kind of a transformer. You are looking for the fixed point of the composition of Free and TermF. We can write the composition of transformers in general.
{-# LANGUAGE PolyKinds #-}
newtype ComposeT g h f a = ComposeT { unComposeT :: g (h f) a}
deriving Functor
We can also write the fixed point of transformers in general.
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}
newtype FixT t a = FixT { unFixT :: t (FixT t) a }
deriving instance Functor (t (FixT t)) => Functor (FixT t)
Then you could write
type Term = FixT (ComposeT Free TermF)
Then use FixT . ComposeT everywhere you would have just used T and unComposeT . unFixT everywhere you would have used unT.
I'm writing FFI to pdflib. Pdflib C API has lots of functions that return and/or take various handles (document, page, image, font) as plain Integer (not pointer).
In order to ensure i do not accidentally pass the wrong param to a function i create a bunch of newtypes in the form of:
newtype PdiDoc = PdiDoc Int
newtype PdiPage = PdiPage Int
newtype PdfImage = PdfImage Int
newtype PdfFont = PdfFont Int
Now i need to provide a marshaller for those types.
image2c (PdfImage i) = fromIntegral i
font2c (PdfFont f) = fromIntegral f
pdipage2c (PdiPage i) = fromIntegral i
As you see the marshallers are exactly the same, just for different types.
So my question is, is there some kind of type magic, SYB vodoo trick that i can use to have just one function to marshall all those types, or do i have to write same functions again and again for different newtypes ?
EDIT: I accepted Don's answer, because it solved my problem.
I switched on
GeneralizedNewtypeDeriving
added
deriving (Eq, Ord, Num, Enum, Real, Integral)
to each of my newtypes, and now i can use standard fromIntegral to marshall all of them.
Nathan Howell's answer is also correct one, i upvoted it. But unfortunately his solution would mean giving up on FFI preprocessors like c2hs i am using.
GHC's FFI extensions allow using newtypes that wrap FFI primitives. You could change the imported function signatures to use the newtypes and (hopefully) avoid having to unwrap them manually.
{-# LANGUAGE ForeignFunctionInterface #-}
module Main where
newtype Foo = Foo Int
foreign import ccall someCall :: Foo -> IO Foo
main :: IO ()
main = do
Foo x <- someCall (Foo 1)
print x
Alternatively, the new GHC Generics functionality (available since 7.2.1) allows generic unpacking and repacking of newtypes:
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE ForeignFunctionInterface #-}
{-# LANGUAGE TypeFamilies #-}
module Main where
import GHC.Generics
-- use a regular newtype
newtype Foo1 = Foo1 Int deriving (Generic, Show)
-- or with record syntax
newtype Foo2 = Foo2{foo2 :: Int} deriving (Generic, Show)
unpack :: (Generic a, Rep a ~ D1 dc (C1 cc (S1 sc (K1 R kc)))) => a -> kc
unpack = unK1 . unM1 . unM1 . unM1 . from
pack :: (Generic a, Rep a ~ D1 dc (C1 cc (S1 sc (K1 R kc)))) => kc -> a
pack = to . M1 . M1 . M1 . K1
-- the C import uses Ints
foreign import ccall "someCall" c'someCall :: Int -> IO Int
-- and the typed wrapper packs/unpacks to FFI primitives
someCall :: Foo1 -> IO Foo2
someCall = fmap pack . c'someCall . unpack
main :: IO ()
main = do
Foo2 x <- someCall (Foo1 1)
print x
You can derive 'Num' for your types using GeneralizedNewtypeDeriving, this helps you a bit with literals and operators.
For the marshalling, I'd use a FFI preprocess, such as hsc2hs, which can automate the wrapping and unwrapping of newtypes.
An example from RWH: