I am working with Data.Typeable and in particular I want to be able to generate correct types of a particular kind (say *). The problem that I'm running into is that TypeRep allows us to do the following (working with the version in GHC 7.8):
let maybeType = typeRep (Proxy :: Proxy Maybe)
let maybeCon = fst (splitTyConApp maybeType)
let badType = mkTyConApp maybeCon [maybeType]
Here badType is in a sense the representation of the type Maybe Maybe, which is not a valid type of any Kind:
> :k Maybe (Maybe)
<interactive>:1:8:
Expecting one more argument to ‘Maybe’
The first argument of ‘Maybe’ should have kind ‘*’,
but ‘Maybe’ has kind ‘* -> *’
In a type in a GHCi command: Maybe (Maybe)
I'm not looking for enforcing this at type level, but I would like to be able to write a program that is smart enough to avoid constructing such types at runtime. I can do this with data-level terms with TypeRep. Ideally, I would have something like
data KindRep = Star | KFun KindRep KindRep
and have a function kindOf with kindOf Int = Star (probably really kindOf (Proxy :: Proxy Int) = Star) and kindOf Maybe = KFun Star Star, so that I could "kind-check" my TypeRep value.
I think I can do this manually with a polykinded typeclass like Typeable, but I'd prefer to not have to write my own instances for everything. I'd also prefer to not revert to GHC 7.6 and use the fact that there are separate type classes for Typeable types of different kinds. I am open to methods that get this information from GHC.
We can get the kind of a type, but we need to throw a whole host of language extensions at GHC to do so, including the (in this case) exceeding questionable UndecidableInstances and AllowAmbiguousTypes.
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE AllowAmbiguousTypes #-}
import Data.Proxy
Using your definition for a KindRep
data KindRep = Star | KFun KindRep KindRep
we define the class of Kindable things whose kind can be determined
class Kindable x where
kindOf :: p x -> KindRep
The first instance for this is easy, everything of kind * is Kindable:
instance Kindable (a :: *) where
kindOf _ = Star
Getting the kind of higher-kinded types is hard. We will try to say that if we can find the kind of its argument and the kind of the result of applying it to an argument, we can figure out its kind. Unfortunately, since it doesn't have an argument, we don't know what type its argument will be; this is why we need AllowAmbiguousTypes.
instance (Kindable a, Kindable (f a)) => Kindable f where
kindOf _ = KFun (kindOf (Proxy :: Proxy a)) (kindOf (Proxy :: Proxy (f a)))
Combined, these definitions allow us to write things like
kindOf (Proxy :: Proxy Int) = Star
kindOf (Proxy :: Proxy Maybe) = KFun Star Star
kindOf (Proxy :: Proxy (,)) = KFun Star (KFun Star Star)
kindOf (Proxy :: Proxy StateT) = KFun Star (KFun (KFun Star Star) (KFun Star Star))
Just don't try to determine the kind of a polykinded type like Proxy
kindOf (Proxy :: Proxy Proxy)
which fortunately results in a compiler error in only a finite amount of time.
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!
Question
I want to case on a type variable that is restricted to finitely many possibilities due to a kind constraint. And I want to know statically that casing will always discover one of these finitely many possibilities. I can't figure out how to write this case without an unreachable catch-all.
As a concrete example, suppose I have a data kind
data{-kind-} Temp = Hot | Cold
Then my goal is write a function like caseTemp below that determines the Temp a given Temp-kinded type. Something like
data CaseTemp (t :: Temp) where
IsHot :: CaseTemp 'Hot
IsCold :: CaseTemp 'Cold
caseTemp :: forall (t :: Temp). CaseTemp t
caseTemp = ???
I'm OK with having some extra constraints on caseTemp, like the Typeable t in my failed attempt below. Or even with an entirely different approach.
Failed Solution Attempt
Here is my best attempt, but it includes a branch that I think should be unreachable, and that would allow caseTemp to break silently if I added another constructor to Temp (tested in GHC 8.0.2):
{-# OPTIONS_GHC -Wall #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE StandaloneDeriving #-}
module SOQuestion where
import Data.Typeable ( (:~:)(..), Typeable, eqT )
data{-kind-} Temp = Hot | Cold
data CaseTemp (t :: Temp) where
IsHot :: CaseTemp 'Hot
IsCold :: CaseTemp 'Cold
deriving instance Show (CaseTemp t)
caseTemp :: forall (t :: Temp). Typeable t => CaseTemp t
caseTemp =
case eqT :: Maybe (t :~: 'Hot) of
Just Refl -> IsHot
Nothing -> case eqT :: Maybe (t :~: 'Cold) of
-- (GHC says this "pattern match is redundant" ???
-- Sounds like a bug!)
Just Refl -> IsCold
-- MY QUESTION: is there a way to eliminate the
-- unreachable branch here?
Nothing -> error "Unreachable!"
The problem with this attempt is that GHC believes the Nothing -> error "Unreachable!" branch is reachable.
Updates
User #Alec mentions that Any :: Temp is a fundamental reason that it's impossible to do what I want, since e.g.
import GHC.Prim ( Any )
[...]
badCase :: CaseTemp Any
badCase = undefined :: CaseTemp Any
is accepted by GHC. However, Any is not Typeable, so it's not clear to me that putting constraints on caseTemp couldn't work around this.
There isn't a direct way, because when eqT returns Nothing it doesn't come with a disequality proof.
How about using a type class?
class IsTemp (b :: Temp) where
caseTemp :: CaseTemp b
Suppose I have a simple data type in Haskell for storing a value:
data V a = V a
I want to make V an instance of Show, regardless of a's type. If a is an instance of Show, then show (V a) should return show a otherwise an error message should be returned. Or in Pseudo-Haskell:
instance Show (V a) where
show (V a) = if a instanceof Show
then show a
else "Some Error."
How could this behaviour be implemented in Haskell?
As I said in a comment, the runtime objects allocated in memory don't have type tags in a Haskell program. There is therefore no universal instanceof operation like in, say, Java.
It's also important to consider the implications of the following. In Haskell, to a first approximation (i.e., ignoring some fancy stuff that beginners shouldn't tackle too soon), all runtime function calls are monomorphic. I.e., the compiler knows, directly or indirectly, the monomorphic (non-generic) type of every function call in an executable program. Even though your V type's show function has a generic type:
-- Specialized to `V a`
show :: V a -> String -- generic; has variable `a`
...you can't actually write a program that calls the function at runtime without, directly or indirectly, telling the compiler exactly what type a will be in every single call. So for example:
-- Here you tell it directly that `a := Int`
example1 = show (V (1 :: Int))
-- Here you're not saying which type `a` is, but this just "puts off"
-- the decision—for `example2` to be called, *something* in the call
-- graph will have to pick a monomorphic type for `a`.
example2 :: a -> String
example2 x = show (V x) ++ example1
Seen in this light, hopefully you can spot the problem with what you're asking:
instance Show (V a) where
show (V a) = if a instanceof Show
then show a
else "Some Error."
Basically, since the type for the a parameter will be known at compilation time for any actual call to your show function, there's no point to testing for this type at runtime—you can test for it at compilation time! Once you grasp this, you're led to Will Sewell's suggestion:
-- No call to `show (V x)` will compile unless `x` is of a `Show` type.
instance Show a => Show (V a) where ...
EDIT: A more constructive answer perhaps might be this: your V type needs to be a tagged union of multiple cases. This does require using the GADTs extension:
{-# LANGUAGE GADTs #-}
-- This definition requires `GADTs`. It has two constructors:
data V a where
-- The `Showable` constructor can only be used with `Show` types.
Showable :: Show a => a -> V a
-- The `Unshowable` constructor can be used with any type.
Unshowable :: a -> V a
instance Show (V a) where
show (Showable a) = show a
show (Unshowable a) = "Some Error."
But this isn't a runtime check of whether a type is a Show instance—your code is responsible for knowing at compilation time where the Showable constructor is to be used.
You can with this library: https://github.com/mikeizbicki/ifcxt. Being able to call show on a value that may or may not have a Show instance is one of the first examples it gives. This is how you could adapt that for V a:
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances #-}
import IfCxt
import Data.Typeable
mkIfCxtInstances ''Show
data V a = V a
instance forall a. IfCxt (Show a) => Show (V a) where
show (V a) = ifCxt (Proxy::Proxy (Show a))
(show a)
"<<unshowable>>"
This is the essence of this library:
class IfCxt cxt where
ifCxt :: proxy cxt -> (cxt => a) -> a -> a
instance {-# OVERLAPPABLE #-} IfCxt cxt where ifCxt _ t f = f
I don't fully understand it, but this is how I think it works:
It doesn't violate the "open world" assumption any more than
instance {-# OVERLAPPABLE #-} Show a where
show _ = "<<unshowable>>"
does. The approach is actually pretty similar to that: adding a default case to fall back on for all types that do not have an instance in scope. However, it adds some indirection to not make a mess of the existing instances (and to allow different functions to specify different defaults). IfCxt works as a a "meta-class", a class on constraints, that indicates whether those instances exist, with a default case that indicates "false.":
instance {-# OVERLAPPABLE #-} IfCxt cxt where ifCxt _ t f = f
It uses TemplateHaskell to generate a long list of instances for that class:
instance {-# OVERLAPS #-} IfCxt (Show Int) where ifCxt _ t f = t
instance {-# OVERLAPS #-} IfCxt (Show Char) where ifCxt _ t f = t
which also implies that any instances that were not in scope when mkIfCxtInstances was called will be considered non-existing.
The proxy cxt argument is used to pass a Constraint to the function, the (cxt => a) argument (I had no idea RankNTypes allowed that) is an argument that can use the constraint cxt, but as long as that argument is unused, the constraint doesn't need to be solved. This is similar to:
f :: (Show (a -> a) => a) -> a -> a
f _ x = x
The proxy argument supplies the constraint, then the IfCxt constraint is solved to either the t or f argument, if it's t then there is some IfCxt instance where this constraint is supplied which means it can be solved directly, if it's f then the constraint is never demanded so it gets dropped.
This solution is imperfect (as new modules can define new Show instances which won't work unless it also calls mkIfCxtInstances), but being able to do that would violate the open world assumption.
Even if you could do this, it would be a bad design. I would recommend adding a Show constraint to a:
instance Show a => Show (V a) where ...
If you want to store members in a container data type that are not an instance of Show, then you should create a new data type fore them.
I couldn't find an answer to my question among several ambiguous type variable error questions.
Basically I want to take type information to the value level. The last line in this example fails.
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE TypeOperators #-}
module Test where
data Typ = TInteger | TString deriving Show
data Empty = Empty
data a ## b = Cons a b
class Typical a b | a -> b where
typical :: a -> b
instance Typical Empty [Typ] where
typical _ = []
instance Typical Integer Typ where
typical _ = TInteger
instance Typical String Typ where
typical _ = TString
instance (Typical a Typ, Typical b [Typ]) => Typical (a ## b) [Typ] where
typical _ = typical (undefined :: a) : typical (undefined :: b)
Here is the first error message:
Test.hs:27:17:
Could not deduce (Typical a0 Typ) arising from a use of `typical'
from the context (Typical a Typ, Typical b [Typ])
bound by the instance declaration at Test.hs:26:10-67
The type variable `a0' is ambiguous
Possible fix: add a type signature that fixes these type variable(s)
Note: there are several potential instances:
instance Typical String Typ -- Defined at Test.hs:23:10
instance Typical Integer Typ -- Defined at Test.hs:20:10
Possible fix: add an instance declaration for (Typical a0 Typ)
In the first argument of `(:)', namely `typical (undefined :: a)'
In the expression:
typical (undefined :: a) : typical (undefined :: b)
In an equation for `typical':
typical _ = typical (undefined :: a) : typical (undefined :: b)
I just don't get it.
What is a0 here? Could it be that the a from my last line is not identified with that from the 2nd last line?
Where should I put a type signature and why?
Please enlighten me!
Ok, I have a solution, but I don't know if this is the cleanest workaround.
Adding {-# LANGUAGE ScopedTypeVariables #-} makes the code compile. This makes it possible to identify a0 with a from the error message (corresponding to the as from the last two lines of the code).
Please comment!
I want to write a function with this type signature:
getTypeRep :: Typeable a => t a -> TypeRep
where the TypeRep will be the type representation for a, not for t a. That is, the compiler should automatically return the correct type representation at any call sites [to getTypeRep], which will have concrete types for a.
To add some context, I want to create a "Dynamic type" data type, with the twist that it will remember the top-level type, but not its parameter. For example, I want to turn MyClass a into Dynamic MyClass, and the above function will be used to create instances of Dynamic MyClass that store a representation of the type parameter a.
Well, how about using scoped type variables to select the inner component:
{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE ScopedTypeVariables #-}
import Data.Dynamic
import Data.Typeable
getTypeRep :: forall t a . Typeable a => t a -> TypeRep
getTypeRep _ = typeOf (undefined :: a)
Works for me:
*Main> getTypeRep (Just ())
()
*Main> getTypeRep (Just 7)
Integer
*Main> getTypeRep ([True])
Bool
Interesting design.
On a tangential note to Don's solution, notice that code rarely require ScopedTypeVariables. It just makes the solution cleaner (but less portable). The solution without scoped types is:
{-# LANGUAGE ExplicitForAll #-}
import Data.Typeable
helper :: t a -> a
helper _ = undefined
getTypeRep :: forall t a. Typeable a => t a -> TypeRep
getTypeRep = typeOf . helper
This function (now) exists in Data.Typeable typeRep