I want to have an overloaded function in Haskell.
{-# LANGUAGE FlexibleInstances #-}
class Foo a where
foo :: a
instance Foo (String -> Int) where
foo = length
instance Foo String where
foo = "world"
However such overloading deals very poorly with type ambiguities. print $ foo "hello" would result in an error, while print $ length "hello" works fine. However, provided that my list of instances is fixed, there shouldn't be a technical reason why Haskell can't realize that the only instance of foo :: String -> a is foo :: String -> Int. Can I have Haskell make this realization?
It is easy to do in this particular case. Simply:
instance a ~ Int => Foo (String -> a) where foo = length
In your case GHCI knows, that foo :: String -> ??
We are going to change signature to String -> Int:
print (foo "hello" :: Int)
Related
I have an enumeration type, e.g.
data MyType = A | B
And I want to be able to pass values of this type implicitly to my functions. I can do this using the ImplicitParams GHC extension like this:
type HasMyType = (?myType :: MyType)
myFun :: HasMyType => String
myFun = case ?myType of
A -> "Foo"
B -> "Bar"
But I've heard many times that it's better to use the Haskell package reflection for this task. Unfortunately, the reflection documentation doesn't explain how to write a similar code using the library. And it's not that straightforward to figure it out.
So, my question is, whether it's possible to use the reflection library to implement a similar code and to satisfy the following requirements?
Values of MyType should be passed implicitly.
If the HasMyType constraint is not specified, the default value of MyType should be taken.
It should be possible to override the value passed via the HasMyType constraint in a single place, e.g. at the beginning of the application.
Does something like this is possible? Or what would be the closest approximation of this using the reflection library?
This answers two ways of implementing question 1. using reflection.
Using Reifies:
type HasMyType :: forall k. k -> Constraint
type HasMyType name = Reifies name MyType
myFun :: HasMyType name => Proxy name -> String
myFun name = case reflect name of
A -> "Foo"
B -> "Bar"
-- reify :: MyType -> (forall name. HasMyType name => Proxy name -> res) -> res
>> reify A myFun
"Foo"
>> reify B myFun
"Bar"
>> reify A \name -> myFun name
"Foo"
>> reify B \name -> myFun name
"Bar"
Haskell can't abstract over type variables yet \#name -> .. so it uses \(Proxy :: Proxy name) -> ...
The Proxy can be removed from myFun where name is supplied with visible type applications, but reify still generates a Proxy whose name must be "extracted"
{-# Language ScopedTypeVariables #-}
{-# Language TypeApplications #-} ..
myFun :: forall name. HasMyType name => String
myFun = case reflect #name Proxy of
A -> "Foo"
B -> "Bar"
>> reify A \(_ :: _ name) -> myFun #name
"Foo"
>> reify B \(_ :: _ name) -> myFun #name
"Bar"
A simpler option (Given) doesn't rely on type-level "names" to distinguish between different dictionaries, therefore it is more dangerous with the following warning:
You should only give a single value for each type. If multiple instances are in scope, then the behavior is implementation defined.
type HasMyType :: Constraint
type HasMyType = Given MyType
myFun :: HasMyType => String
myFun = case given of
A -> "Foo"
B -> "Bar"
-- give :: MyType -> (HasMyType => res) -> res
>> give A myFun
"Foo"
>> give B myFun
"Bar"
I've got some code like this:
{-# LANGUAGE AllowAmbiguousTypes #-}
module Foo where
import Data.Proxy
class Foo x y
class Bar x y
class Baz x y
where
baz :: Proxy x -> Proxy y -> ()
instance (Foo a v, Bar b v) => Baz a b
where
baz _ _ = ()
instance Foo String String
instance Bar Int String
Now I actually want to use that Baz instance, so I write:
test :: Proxy String -> Proxy Int -> ()
test = baz
But of course there is an ambiguous "existential" v type parameter that I have not yet fixed to String (and there's no fundeps), so I get:
[typecheck] [E] /tmp/foo/src/Main.hs:20:8: error:
• Ambiguous type variable ‘v1’ arising from a use of ‘baz’
prevents the constraint ‘(Foo [Char] v1)’ from being solved.
Probable fix: use a type annotation to specify what ‘k1’,
‘v1’ should be.
These potential instance exist:
one instance involving out-of-scope types
(use -fprint-potential-instances to see them all)
• In the expression: baz
In an equation for ‘test’: test = baz
But how can I actually fix that type variable? I can't see a way to fix it using visible type application, because for example the following doesn't work:
test2 :: Proxy String -> Proxy Int -> ()
test2 = baz #String #Int #String -- is there some variation of this that would work?
I also can't see a way to use an explicit type annotation to fix that type parameter. Have I written an instance that is impossible to actually use?
It is indeed impossible to use that instance. When you call baz, you can supply a and b, but not v. v would have to be determined by some combination of superclass and instance constraints, and it is not.
You should be able to patch this up various places. Try either
instance s ~ String => Foo String s
or
instance s ~ String => Bar Int s
for example.
I'd like to write a program that prints out some metadata of a Haskell type. Although I know this isn't valid code, the idea is something like:
data Person = Person { name :: String, age :: Int }
metadata :: Type -> String
metadata t = ???
metadata Person -- returns "Person (name,age)"
The important restriction being I don't have an instance of Person, just the type.
I've started looking into Generics & Typeable/Data, but without an instance I'm not sure they'll do what I need. Can anyone point me in the right direction?
Reflection in Haskell works using the Typeable class, which is defined in Data.Typeable and includes the typeOf* method to get a run-time representation of a value's type.
ghci> :m +Data.Typeable
ghci> :t typeOf 'a'
typeOf 'a' :: TypeRep
ghci> typeOf 'a' -- We could use any value of type Char and get the same result
Char -- the `Show` instance of `TypeRep` just returns the name of the type
If you want Typeable to work for your own types, you can have the compiler generate an instance for you with the DeriveDataTypeable extension.
{-# LANGUAGE DeriveDataTypeable #-}
import Data.Typeable
data Person = Person { name :: String, age :: Int } deriving Typeable
You can also write your own instance, but really, no one has the time for that. Apparently you can't - see the comments
You can now use typeOf to grab a run-time representation of your type. We can query information about the type constructor (abbreviated to TyCon) and its type arguments:
-- (undefined :: Person) stands for "some value of type Person".
-- If you have a real Person you can use that too.
-- typeOf does not use the value, only the type
-- (which is known at compile-time; typeOf is dispatched using the normal instance selection rules)
ghci> typeOf (undefined :: Person)
Person
ghci> tyConName $ typeRepTyCon $ typeOf (undefined :: Person)
"Person"
ghci> tyConModule $ typeRepTyCon $ typeOf (undefined :: Person)
"Main"
Data.Typeable also provides a type-safe cast operation which allows you to branch on a value's runtime type, somewhat like C#'s as operator.
f :: Typeable a => a -> String
f x = case (cast x :: Maybe Int) of
Just i -> "I can treat i as an int in this branch " ++ show (i * i)
Nothing -> case (cast x :: Maybe Bool) of
Just b -> "I can treat b as a bool in this branch " ++ if b then "yes" else "no"
Nothing -> "x was of some type other than Int or Bool"
ghci> f True
"I can treat b as a bool in this branch yes"
ghci> f (3 :: Int)
"I can treat i as an int in this branch 9"
Incidentally, a nicer way to write f is to use a GADT enumerating the set of types you expect your function to be called with. This allows us to lose the Maybe (f can never fail!), does a better job of documenting our assumptions, and gives compile-time feedback when we need to change the set of admissible argument types for f. (You can write a class to make Admissible implicit if you like.)
data Admissible a where
AdInt :: Admissible Int
AdBool :: Admissible Bool
f :: Admissible a -> a -> String
f AdInt i = "I can treat i as an int in this branch " ++ show (i * i)
f AdBool b = "I can treat b as a bool in this branch " ++ if b then "yes" else "no"
In reality I probably wouldn't do either of these - I'd just stick f in a class and define instances for Int and Bool.
If you want run-time information about the right-hand side of a type definition, you need to use the entertainingly-named Data.Data, which defines a subclass of Typeable called Data.** GHC can derive Data for you too, with the same extension:
{-# LANGUAGE DeriveDataTypeable #-}
import Data.Typeable
import Data.Data
data Person = Person { name :: String, age :: Int } deriving (Typeable, Data)
Now we can grab a run-time representation of the values of a type, not just the type itself:
ghci> dataTypeOf (undefined :: Person)
DataType {tycon = "Main.Person", datarep = AlgRep [Person]}
ghci> dataTypeConstrs $ dataTypeOf (undefined :: Person)
[Person] -- Person only defines one constructor, called Person
ghci> constrFields $ head $ dataTypeConstrs $ dataTypeOf (undefined :: Person)
["name","age"]
Data.Data is the API for generic programming; if you ever hear people talking about "Scrap Your Boilerplate", this (along with Data.Generics, which builds on Data.Data) is what they mean. For example, you can write a function which converts record types to JSON using reflection on the type's fields.
toJSON :: Data a => a -> String
-- Implementation omitted because it is boring.
-- But you only have to write the boring code once,
-- and it'll be able to serialise any instance of `Data`.
-- It's a good exercise to try to write this function yourself!
* In recent versions of GHC, this API has changed somewhat. Consult the docs.
** Yes, the fully-qualified name of that class is Data.Data.Data.
I'm trying to make a variadic function with a monadic return type, whose parameters also require the monadic context. (I'm not sure how to describe that second point: e.g. printf can return IO () but it's different in that its parameters are treated the same whether it ends up being IO () or String.)
Basically, I've got a data constructor that takes, say, two Char parameters. I want to provide two pointer style ID Char arguments instead, which can be automagically decoded from an enclosing State monad via a type class instance. So, instead of doing get >>= \s -> foo1adic (Constructor (idGet s id1) (idGet s id2)), I want to do fooVariadic Constructor id1 id2.
What follows is what I've got so far, Literate Haskell style in case somebody wants to copy it and mess with it.
First, the basic environment:
> {-# LANGUAGE FlexibleContexts #-}
> {-# LANGUAGE FlexibleInstances #-}
> {-# LANGUAGE MultiParamTypeClasses #-}
> import Control.Monad.Trans.State
> data Foo = Foo0
> | Foo1 Char
> | Foo2 Bool Char
> | Foo3 Char Bool Char
> deriving Show
> type Env = (String,[Bool])
> newtype ID a = ID {unID :: Int}
> deriving Show
> class InEnv a where envGet :: Env -> ID a -> a
> instance InEnv Char where envGet (s,_) i = s !! unID i
> instance InEnv Bool where envGet (_,b) i = b !! unID i
Some test data for convenience:
> cid :: ID Char
> cid = ID 1
> bid :: ID Bool
> bid = ID 2
> env :: Env
> env = ("xy", map (==1) [0,0,1])
I've got this non-monadic version, which simply takes the environment as the first parameter. This works fine but it's not quite what I'm after. Examples:
$ mkFoo env Foo0 :: Foo
Foo0
$ mkFoo env Foo3 cid bid cid :: Foo
Foo3 'y' True 'y'
(I could use functional dependencies or type families to get rid of the need for the :: Foo type annotations. For now I'm not fussed about it, since this isn't what I'm interested in anyway.)
> mkFoo :: VarC a b => Env -> a -> b
> mkFoo = variadic
>
> class VarC r1 r2 where
> variadic :: Env -> r1 -> r2
>
> -- Take the partially applied constructor, turn it into one that takes an ID
> -- by using the given state.
> instance (InEnv a, VarC r1 r2) => VarC (a -> r1) (ID a -> r2) where
> variadic e f = \aid -> variadic e (f (envGet e aid))
>
> instance VarC Foo Foo where
> variadic _ = id
Now, I want a variadic function that runs in the following monad.
> type MyState = State Env
And basically, I have no idea how I should proceed. I've tried expressing the type class in different ways (variadicM :: r1 -> r2 and variadicM :: r1 -> MyState r2) but I haven't succeeded in writing the instances. I've also tried adapting the non-monadic solution above so that I somehow "end up" with an Env -> Foo which I could then easily turn into a MyState Foo, but no luck there either.
What follows is my best attempt thus far.
> mkFooM :: VarMC r1 r2 => r1 -> r2
> mkFooM = variadicM
>
> class VarMC r1 r2 where
> variadicM :: r1 -> r2
>
> -- I don't like this instance because it requires doing a "get" at each
> -- stage. I'd like to do it only once, at the start of the whole computation
> -- chain (ideally in mkFooM), but I don't know how to tie it all together.
> instance (InEnv a, VarMC r1 r2) => VarMC (a -> r1) (ID a -> MyState r2) where
> variadicM f = \aid -> get >>= \e -> return$ variadicM (f (envGet e aid))
>
> instance VarMC Foo Foo where
> variadicM = id
>
> instance VarMC Foo (MyState Foo) where
> variadicM = return
It works for Foo0 and Foo1, but not beyond that:
$ flip evalState env (variadicM Foo1 cid :: MyState Foo)
Foo1 'y'
$ flip evalState env (variadicM Foo2 cid bid :: MyState Foo)
No instance for (VarMC (Bool -> Char -> Foo)
(ID Bool -> ID Char -> MyState Foo))
(Here I would like to get rid of the need for the annotation, but the fact that this formulation needs two instances for Foo makes that problematic.)
I understand the complaint: I only have an instance that goes from Bool ->
Char -> Foo to ID Bool -> MyState (ID Char -> Foo). But I can't make the
instance it wants because I need MyState in there somewhere so that I can
turn the ID Bool into a Bool.
I don't know if I'm completely off track or what. I know that I could solve my basic issue (I don't want to pollute my code with the idGet s equivalents all over the place) in different ways, such as creating liftA/liftM-style functions for different numbers of ID parameters, with types like (a -> b -> ... -> z -> ret) -> ID a -> ID b -> ... -> ID z -> MyState ret, but I've spent too much time thinking about this. :-) I want to know what this variadic solution should look like.
WARNING
Preferably don't use variadic functions for this type of work. You only have a finite number of constructors, so smart constructors don't seem to be a big deal. The ~10-20 lines you would need are a lot simpler and more maintainable than a variadic solution. Also an applicative solution is much less work.
WARNING
The monad/applicative in combination with variadic functions is the problem. The 'problem' is the argument addition step used for the variadic class. The basic class would look like
class Variadic f where
func :: f
-- possibly with extra stuff
where you make it variadic by having instances of the form
instance Variadic BaseType where ...
instance Variadic f => Variadic (arg -> f) where ...
Which would break when you would start to use monads. Adding the monad in the class definition would prevent argument expansion (you would get :: M (arg -> f), for some monad M). Adding it to the base case would prevent using the monad in the expansion, as it's not possible (as far as I know) to add the monadic constraint to the expansion instance. For a hint to a complex solution see the P.S..
The solution direction of using a function which results in (Env -> Foo) is more promising. The following code still requires a :: Foo type constraint and uses a simplified version of the Env/ID for brevity.
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses, TypeFamilies #-}
module Test where
data Env = Env
data ID a = ID
data Foo
= Foo0
| Foo1 Char
| Foo2 Char Bool
| Foo3 Char Bool Char
deriving (Eq, Ord, Show)
class InEnv a where
resolve :: Env -> ID a -> a
instance InEnv Char where
resolve _ _ = 'a'
instance InEnv Bool where
resolve _ _ = True
The Type families extension is used to make the matching stricter/better. Now the variadic function class.
class MApp f r where
app :: Env -> f -> r
instance MApp Foo Foo where
app _ = id
instance (MApp r' r, InEnv a, a ~ b) => MApp (a -> r') (ID b -> r) where
app env f i = app env . f $ resolve env i
-- using a ~ b makes this instance to match more easily and
-- then forces a and b to be the same. This prevents ambiguous
-- ID instances when not specifying there type. When using type
-- signatures on all the ID's you can use
-- (MApp r' r, InEnv a) => MApp (a -> r') (ID a -> r)
-- as constraint.
The environment Env is explicitly passed, in essence the Reader monad is unpacked preventing the problems between monads and variadic functions (for the State monad the resolve function should return a new environment). Testing with app Env Foo1 ID :: Foo results in the expected Foo1 'a'.
P.S.
You can get monadic variadic functions to work (to some extent) but it requires bending your functions (and mind) in some very strange ways. The way I've got such things to work is to 'fold' all the variadic arguments into a heterogeneous list. The unwrapping can then be done monadic-ally. Though I've done some things like that, I strongly discourage you from using such things in actual (used) code as it quickly gets incomprehensible and unmaintainable (not to speak of the type errors you would get).
Given an existential data type, for example:
data Foo = forall a . (Typeable a, Binary a) => Foo a
I'd like to write instance Binary Foo. I can write the serialisation (serialise the TypeRep then serialise the value), but I can't figure out how to write the deserialisation. The basic problem is that given a TypeRep you need to map back to the type dictionary for that type - and I don't know if that can be done.
This question has been asked before on the haskell mailing list http://www.haskell.org/pipermail/haskell/2006-September/018522.html, but no answers were given.
You need some way that each Binary instance can register itself (just as in your witness version). You can do this by bundling each instance declaration with an exported foreign symbol, where the symbol name is derived from the TypeRep. Then when you want to deserialize you get the name from the TypeRep and look up that symbol dynamically (with dlsym() or something similar). The value exported by the foreign export can, e.g., be the deserializer function.
It's crazy ugly, but it works.
This can be solved in GHC 7.10 and onwards using the Static Pointers Language extension:
{-# LANGUAGE StaticPointers #-}
{-# LANGUAGE InstanceSigs #-}
data Foo = forall a . (StaticFoo a, Binary a, Show a) => Foo a
class StaticFoo a where
staticFoo :: a -> StaticPtr (Get Foo)
instance StaticFoo String where
staticFoo _ = static (Foo <$> (get :: Get String))
instance Binary Foo where
put (Foo x) = do
put $ staticKey $ staticFoo x
put x
get = do
ptr <- get
case unsafePerformIO (unsafeLookupStaticPtr ptr) of
Just value -> deRefStaticPtr value :: Get Foo
Nothing -> error "Binary Foo: unknown static pointer"
A full description of the solution can be found on this blog post, and a complete snippet here.
If you could do that, you would also be able to implement:
isValidRead :: TypeRep -> String -> Bool
This would be a function that changes its behavior due to someone defining a new type! Not very pure-ish.. I think (and hope) that one can't implement this in Haskell..
I have an answer that slightly works in some situations (not enough for my purposes), but may be the best that can be done. You can add a witness function to witness any types that you have, and then the deserialisation can lookup in the witness table. The rough idea is (untested):
witnesses :: IORef [Foo]
witnesses = unsafePerformIO $ newIORef []
witness :: (Typeable a, Binary a) => a -> IO ()
witness x = modifyIORef (Foo x :)
instance Binary Foo where
put (Foo x) = put (typeOf x) >> put x
get = do
ty <- get
wits <- unsafePerformIO $ readIORef witnesses
case [Foo x | Foo x <- wits, typeOf x == ty] of
Foo x:_ -> fmap Foo $ get `asTypeOf` return x
[] -> error $ "Could not find a witness for the type: " ++ show ty
The idea is that as you go through, you call witness on values of every type that you may plausibly encounter when deserialising. When you deserialise you search this list. The obvious problem is that if you fail to call witness before deserialisation you get a crash.