I'm trying to run the code from:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.39.8039&rep=rep1&type=pdf
using ghci 7.6.3
{-# LANGUAGE LiberalTypeSynonyms, TypeSynonymInstances #-}
type C m a = (a -> Action m) -> Action m
data Action m = Atom (m (Action m)) | Fork (Action m) (Action m) | Stop
This original form:
instance (Monad m) => Monad (C m) where
f >>= k = \c -> f (\a -> k a c)
return x = \c -> c x
gives this error:
Type synonym `C' should have 2 arguments, but has been given 1
In the instance declaration for `Monad (C m)'
Trying with the additional argument:
instance (Monad m) => Monad (C m b) where
f >>= k = \c -> f (\a -> k a c)
return x = \c -> c x
shows this error:
Kind mis-match
The first argument of `Monad' should have kind `* -> *',
but `C m b' has kind `*'
In the instance declaration for `Monad (C m b)'
How to correct this definition? Thanks
Partially applied type synonyms can't be type class instances, and the only way to avoid that in this case is to make this a data or newtype declaration.
You will have to change the definition of C to make this work to e.g.
newtype C m a = C ((a -> Action m) -> Action m)
I'm trying to understand why one version of this code compiles, and one version does not.
{-# LANGUAGE RankNTypes, FlexibleContexts #-}
module Foo where
import Data.Vector.Generic.Mutable as M
import Data.Vector.Generic as V
import Control.Monad.ST
import Control.Monad.Primitive
data DimFun v m r =
DimFun {dim::Int, func :: v (PrimState m) r -> m ()}
runFun1 :: (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun1 (DimFun dim t) x | V.length x == dim = runST $ do
y <- thaw x
t y
unsafeFreeze y
runFun2 :: (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun2 t x = runST $ do
y <- thaw x
evalFun t y
unsafeFreeze y
evalFun :: (PrimMonad m, MVector v r) => DimFun v m r -> v (PrimState m) r -> m ()
evalFun (DimFun dim f) y | dim == M.length y = f y
runFun2 compiles fine (GHC-7.8.2), but runFun1 results in errors:
Could not deduce (PrimMonad m0) arising from a pattern
from the context (Vector v r, MVector (Mutable v) r)
bound by the type signature for
tfb :: (Vector v r, MVector (Mutable v) r) =>
(forall (m :: * -> *). PrimMonad m => TensorFunc m r) -> v r -> v r
at Testing/Foo.hs:(26,8)-(28,15)
The type variable ‘m0’ is ambiguous
Note: there are several potential instances:
instance PrimMonad IO -- Defined in ‘Control.Monad.Primitive’
instance PrimMonad (ST s) -- Defined in ‘Control.Monad.Primitive’
In the pattern: TensorFunc _ f
In an equation for ‘tfb’:
tfb (TensorFunc _ f) x
= runST
$ do { y <- thaw x;
f y;
unsafeFreeze y }
Couldn't match type ‘m0’ with ‘ST s’
because type variable ‘s’ would escape its scope
This (rigid, skolem) type variable is bound by
a type expected by the context: ST s (v r)
at Testing/Foo.hs:(29,26)-(32,18)
Expected type: ST s ()
Actual type: m0 ()
Relevant bindings include
y :: Mutable v s r (bound at Testing/Foo.hs:30:3)
f :: forall (v :: * -> * -> *).
MVector v r =>
v (PrimState m0) r -> m0 ()
(bound at Testing/Foo.hs:29:19)
In a stmt of a 'do' block: f y
In the second argument of ‘($)’, namely
‘do { y <- thaw x;
f y;
unsafeFreeze y }’
Could not deduce (s ~ PrimState m0)
from the context (Vector v r, MVector (Mutable v) r)
bound by the type signature for
tfb :: (Vector v r, MVector (Mutable v) r) =>
(forall (m :: * -> *). PrimMonad m => TensorFunc m r) -> v r -> v r
at Testing/Foo.hs:(26,8)-(28,15)
‘s’ is a rigid type variable bound by
a type expected by the context: ST s (v r) at Testing/Foo.hs:29:26
Expected type: Mutable v (PrimState m0) r
Actual type: Mutable v s r
Relevant bindings include
y :: Mutable v s r (bound at Testing/Foo.hs:30:3)
f :: forall (v :: * -> * -> *).
MVector v r =>
v (PrimState m0) r -> m0 ()
(bound at Testing/Foo.hs:29:19)
In the first argument of ‘f’, namely ‘y’
In a stmt of a 'do' block: f y
I'm pretty sure the rank-2 type is to blame, possibly caused by a monomorphism restriction. However, as suggested in a previous question of mine, I enabled -XNoMonomorphismRestriction, but got the same error.
What is the difference between these seemingly identical code snippets?
I think that having a rough mental model of the type-level plumbing involved here is essential, so I'm going go talk about "implicit things" in a bit more detail, and scrutinize your problem only after that. Readers only interested in the direct solution to the question may skip to the "Pattern matching on polymorhpic values" subsection and the end.
1. Implicit function arguments
Type arguments
GHC compiles Haskell to a small intermediate language called Core, which is essentially a rank-n polymorphic typed lambda calculus called System F (plus some extensions). Below I am going use Haskell alongside a notation somewhat resembling Core; I hope it's not overly confusing.
In Core, polymorphic functions are functions which take types as additional arguments, and arguments further down the line can refer to those types or have those types:
-- in Haskell
const :: forall (a :: *) (b :: *). a -> b -> a
const x y = x
-- in pseudo-Core
const' :: (a :: *) -> (b :: *) -> a -> b -> a
const' a b x y = x
This means that we must also supply type arguments to these functions whenever we want to use them. In Haskell type inference usually figures out the type arguments and supplies them automatically, but if we look at the Core output (for example, see this introduction for how to do that), type arguments and applications are visible everywhere. Building a mental model of this makes figuring out higher-rank code a whole lot easier:
-- Haskell
poly :: (forall a. a -> a) -> b -> (Int, b)
poly f x = (f 0, f x)
-- pseudo-Core
poly' :: (b :: *) -> ((a :: *) -> a -> a) -> b -> (Int, b)
poly' b f x = (f Int 0, f b x)
And it makes clear why some things don't typecheck:
wrong :: (a -> a) -> (Int, Bool)
wrong f = (f 0, f True)
wrong' :: (a :: *) -> (a -> a) -> (Int, Bool)
wrong' a f = (f ?, f ?) -- f takes an "a", not Int or Bool.
Class constraint arguments
-- Haskell
show :: forall a. Show a => a -> String
show x = show x
-- pseudo-Core
show' :: (a :: *) -> Show a -> a -> String
show' a (ShowDict showa) x = showa x
What is ShowDict and Show a here? ShowDict is just a Haskell record containing a show instance, and GHC generates such records for each instance of a class. Show a is just the type of this instance record:
-- We translate classes to a record type:
class Show a where show :: a -> string
data Show a = ShowDict (show :: a -> String)
-- And translate instances to concrete records of the class type:
instance Show () where show () = "()"
showUnit :: Show ()
showUnit = ShowDict (\() -> "()")
For example, whenever we want to apply show, the compiler has to search the scope in order to find a suitable type argument and an instance dictionary for that type. Note that while instances are always top level, quite often in polymorphic functions the instances are passed in as arguments:
data Foo = Foo
-- instance Show Foo where show _ = "Foo"
showFoo :: Show Foo
showFoo = ShowDict (\_ -> "Foo")
-- The compiler fills in an instance from top level
fooStr :: String
fooStr = show' Foo showFoo Foo
polyShow :: (Show a, Show b) => a -> b -> String
polyShow a b = show a ++ show b
-- Here we get the instances as arguments (also, note how (++) also takes an extra
-- type argument, since (++) :: forall a. [a] -> [a] -> [a])
polyShow' :: (a :: *) -> (b :: *) -> Show a -> Show b -> a -> b -> String
polyShow' a b (ShowDict showa) (ShowDict showb) a b -> (++) Char (showa a) (showb b)
Pattern matching on polymorphic values
In Haskell, pattern matching on functions doesn't make sense. Polymorphic values can be also viewed as functions, but we can pattern match on them, just like in OP's erroneous runfun1 example. However, all the implicit arguments must be inferable in the scope, or else the mere act of pattern matching is a type error:
import Data.Monoid
-- it's a type error even if we don't use "a" or "n".
-- foo :: (forall a. Monoid a => (a, Int)) -> Int
-- foo (a, n) = 0
foo :: ((a :: *) -> Monoid a -> (a, Int)) -> Int
foo f = ? -- What are we going to apply f to?
In other words, by pattern matching on a polymorphic value, we assert that all implicit arguments have been already applied. In the case of foo here, although there isn't a syntax for type application in Haskell, we can sprinkle around type annotations:
{-# LANGUAGE ScopedTypeVariables, RankNTypes #-}
foo :: (forall a. Monoid a => (a, Int)) -> Int
foo x = case (x :: (String, Int)) of (_, n) -> n
-- or alternatively
foo ((_ :: String), n) = n
Again, pseudo-Core makes the situation clearer:
foo :: ((a :: *) -> Monoid a -> (a, Int)) -> Int
foo f = case f String monoidString of (_ , n) -> n
Here monoidString is some available Monoid instance of String.
2. Implicit data fields
Implicit data fields usually correspond to the notion of "existential types" in Haskell. In a sense, they are dual to implicit function arguments with respect to term obligations:
When we construct functions, the implicit arguments are available in the function body.
When we apply functions, we have extra obligations to fulfill.
When we construct data with implicit fields, we must supply those extra fields.
When we pattern match on data, the implicit fields also come into scope.
Standard example:
{-# LANGUAGE GADTs #-}
data Showy where
Showy :: forall a. Show a => a -> Showy
-- pseudo-Core
data Showy where
Showy :: (a :: *) -> Show a -> a -> Showy
-- when constructing "Showy", "Show a" must be also available:
someShowy :: Showy
someShowy = Showy (300 :: Int)
-- in pseudo-Core
someShowy' = Showy Int showInt 300
-- When pattern matching on "Showy", we get an instance in scope too
showShowy :: Showy -> String
showShowy (Showy x) = show x
showShowy' :: Showy -> String
showShowy' (Showy a showa x) = showa x
3. Taking a look at OP's example
We have the function
runFun1 :: (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun1 dfun#(DimFun dim t) x | V.length x == dim = runST $ do
y <- thaw x
t y
unsafeFreeze y
Remember that pattern matching on polymorphic values asserts that all implicit arguments are available in the scope. Except that here, at the point of pattern matching there is no m at all in scope, let alone a PrimMonad instance for it.
With GHC 7.8.x it's is good practice to use type holes liberally:
runFun1 :: (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun1 (DimFun dim t) x | V.length x == dim = _
Now GHC will duly display the type of the hole, and also the types of the variables in the context. We can see that t has type Mutable v (PrimState m0) r -> m0 (), and we also see that m0 is not listed as bound anywhere. Indeed, it is a notorious "ambiguous" type variable conjured up by GHC as a placeholder.
So, why don't we try manually supplying the arguments, just as in the prior example with the Monoid instance? We know that we will use t inside an ST action, so we can try fixing m as ST s and GHC automatically applies the PrimMonad instance for us:
runFun1 :: forall v r. (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun1 (DimFun dim (t :: Mutable v s r -> ST s ())) x
| V.length x == dim = runST $ do
y <- thaw x
t y
unsafeFreeze y
... except it doesn't work and we get the error "Couldn't match type ‘s’ with ‘s1’ because type variable ‘s1’ would escape its scope".
It turns out - comes as no surprise - that we've forgotten about yet another implicit argument. Recall the type of runST:
runST :: (forall s. ST s a) -> a
We can imagine that runST takes a function of type ((s :: PrimState ST) -> ST s a), and then our code looks like this:
runST $ \s -> do
y <- thaw x -- y :: Mutable v s r
t y -- error: "t" takes a "Mutable v s r" with a different "s".
unsafeFreeze y
The s in t's argument type is silently introduced at the outermost scope:
runFun1 :: forall v s r. ...
And thus the two s-es are distinct.
A possible solution is to pattern match on the DimFun argument inside the ST action. There, the correct s is in scope, and GHC can supply ST s as m:
runFun1 :: forall v r. (Vector v r, MVector (Mutable v) r) =>
(forall m . PrimMonad m => DimFun (Mutable v) m r) -> v r -> v r
runFun1 dimfun x = runST $ do
y <- thaw x
case dimfun of
DimFun dim t | dim == M.length y -> t y
unsafeFreeze y
With some parameters made explicit:
runST $ \s -> do
y <- thaw x
case dimfun (ST s) primMonadST of
DimFun dim t | dim == M.length y -> t y
unsafeFreeze y
As an exercise, let's convert all of the function to pseudo-Core (but let's not desugar the do syntax, because that would be way too ugly):
-- the full types of the functions involved, for reference
thaw :: forall m v a. (PrimMonad m, V.Vector v a) => v a -> m (V.Mutable v (PrimState m) a)
runST :: forall a. (forall s. ST s a) -> a
unsafeFreeze :: forall m v a. (PrimMonad m, Vector v a) => Mutable v (PrimState m) a -> v a
M.length :: forall v s a. MVector v s a -> Int
(==) :: forall a. Eq a => a -> a -> Bool
runFun1 ::
(v :: * -> *) -> (r :: *)
-> Vector v r -> MVector (Mutable v) r
-> ((m :: (* -> *)) -> PrimMonad m -> DimFun (Mutable v) m r)
-> v r -> v r
runFun1 v r vecInstance mvecInstance dimfun x = runST r $ \s -> do
y <- thaw (ST s) v r primMonadST vecInstance x
case dimFun (ST s) primMonadST of
DimFun dim t | (==) Int eqInt dim (M.length v s r y) -> t y
unsafeFreeze (ST s) v r primMonadST vecInstance y
That was a mouthful.
Now we are well-equipped to explain why runFun2 worked:
runFun2 :: (Vector v r, MVector (Mutable v) r) =>
(forall m . (PrimMonad m) => DimFun (Mutable v) m r) -> v r -> v r
runFun2 t x = runST $ do
y <- thaw x
evalFun t y
unsafeFreeze y
evalFun :: (PrimMonad m, MVector v r) => DimFun v m r -> v (PrimState m) r -> m ()
evalFun (DimFun dim f) y | dim == M.length y = f y
evalFun is just a polymorphic function that gets called in the right place (we ultimately pattern match on t in the right place), where the correct ST s is available as the m argument.
As a type system gets more sophisticated, pattern matching becomes a progressively more serious affair, with far-reaching consequences and non-trivial requirements. At the end of the spectrum you find full-dependent languages and proof assistants such as Agda, Idris or Coq, where pattern matching on a piece of data can mean accepting an arbitrary logical proposition as true in a certain branch of your program.
Though #AndrasKovacs gave a great answer, I think it is worth pointing out how to avoid this nastiness altogether. This answer to a related question by me shows how the "correct" definition for DimFun makes all of the rank-2 stuff go away.
By defining DimFun as
data DimFun v r =
DimFun {dim::Int, func :: forall s . (PrimMonad s) => v (PrimState s) r -> s ()}
runFun1 becomes:
runFun1 :: (Vector v r)
=> DimFun (Mutable v) r -> v r -> v r
runFun1 (DimFun dim t) x | dim == V.length x = runST $ do
y <- thaw x
t y
unsafeFreeze y
and compiles without issue.
Pattern-match on a constrained value is not allowed, I think. In particular, you could use a pattern-match, but only for a GADT constructor that fixed the type(s) in the constraint and choose a specific instance. Otherwise, I get the ambiguous type variable error.
That is, I don't think that GHC can unify the type of a value matching the pattern (DimFun dim t) with the type (forall m . (PrimMonad m) => DimFun (Mutable v) m r).
Note that the pattern match in evalFun looks similar, but it is allowed to put constraints on m since the quantification is scoped over the whole evalFun; in constrast, runFun1 as a smaller scope for the quantification of m.
HTH
{-# LANGUAGE Haskell2010 #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
class PoC m where
type Wrapper m :: * -> *
wrap :: l -> Wrapper m l
I'm working with haskell-src-exts, and I want to upgrade my AST to have freshly generatable labels. Since I want to do it in an extensible fashion, I created an interface like the code above. However, code to upgrade the AST doesn't work. I have the following:
upgrade :: forall f m l. (PoC m, Functor f) => f l -> f (Wrapper m l)
upgrade x = fmap (wrap :: l -> Wrapper m l) x
But with or without the use of ScopedTypeVariables, I get the same error:
/tmp/PoC.hs:10:19:
Could not deduce (Wrapper m ~ Wrapper m0)
from the context (PoC m, Functor f)
bound by the type signature for
upgrade :: (PoC m, Functor f) => f l -> f (Wrapper m l)
at /tmp/PoC.hs:9:12-69
NB: `Wrapper' is a type function, and may not be injective
The type variable `m0' is ambiguous
Possible fix: add a type signature that fixes these type variable(s)
Expected type: l -> Wrapper m0 l
Actual type: l -> Wrapper m l
In the first argument of `fmap', namely
`(wrap :: l -> Wrapper m l)'
In the expression: fmap (wrap :: l -> Wrapper m l) x
In an equation for `upgrade':
upgrade x = fmap (wrap :: l -> Wrapper m l) x
But I don't understand where GHC binds this m0. Is "may not be injective" the core of the problem here?
Non-injectivity is the problem, indeed. Injectivity would allow GHC to know that if f a ~ f b then a ~ b but since you can have two PoC m instances with the same choice of Wrapper m type it's hard to know what m was after you've solved for what Wrapper m is.
You should be able to fix it by adding an input term to wrap which contains the m type parameter. This can be a proxy argument which is never evaluated
data Proxy a = Proxy
class PoC m where
type Wrapper m :: * -> *
wrap :: proxy m -> l -> Wrapper m l
instance PoC () where
type Wrapper () = Maybe
wrap _ = return
aUnit :: Proxy ()
aUnit = Proxy
upgrade :: (PoC m, Functor f) => proxy m -> f l -> f (Wrapper m l)
upgrade aProxy x = fmap (wrap aProxy) x
When compiling this program in GHC:
import Control.Monad
f x = let
g y = let
h z = liftM not x
in h 0
in g 0
I receive an error:
test.hs:5:21:
Could not deduce (m ~ m1)
from the context (Monad m)
bound by the inferred type of f :: Monad m => m Bool -> m Bool
at test.hs:(3,1)-(7,8)
or from (m Bool ~ m1 Bool, Monad m1)
bound by the inferred type of
h :: (m Bool ~ m1 Bool, Monad m1) => t1 -> m1 Bool
at test.hs:5:5-21
`m' is a rigid type variable bound by
the inferred type of f :: Monad m => m Bool -> m Bool
at test.hs:3:1
`m1' is a rigid type variable bound by
the inferred type of
h :: (m Bool ~ m1 Bool, Monad m1) => t1 -> m1 Bool
at test.hs:5:5
Expected type: m1 Bool
Actual type: m Bool
In the second argument of `liftM', namely `x'
In the expression: liftM not x
In an equation for `h': h z = liftM not x
Why? Also, providing an explicit type signature for f (f :: Monad m => m Bool -> m Bool) makes the error disappear. But this is exactly the same type as the type that Haskell infers for f automatically, according to the error message!
This is pretty straightforward, actually. The inferred types of let-bound variables are implicitly generalised to type schemes, so there’s a quantifier in your way. The generalised type of h is:
h :: forall a m. (Monad m) => a -> m Bool
And the generalised type of f is:
f :: forall m. (Monad m) => m Bool -> m Bool
They’re not the same m. You would get essentially the same error if you wrote this:
f :: (Monad m) => m Bool -> m Bool
f x = let
g y = let
h :: (Monad m) => a -> m Bool
h z = liftM not x
in h 0
in g 0
And you could fix it by enabling the “scoped type variables” extension:
{-# LANGUAGE ScopedTypeVariables #-}
f :: forall m. (Monad m) => m Bool -> m Bool
f x = let
g y = let
h :: a -> m Bool
h z = liftM not x
in h 0
in g 0
Or by disabling let-generalisation with the “monomorphic local bindings” extension, MonoLocalBinds.
I have a large number of in place vector functions of the type
f :: (M.MVector v r, PrimMonad m) =>
v (PrimState m) r -> v (PrimState m) r -> m ()
These functions mostly work in-place, so it is convenient to have their argument be a mutable vector so that I can compose, iterate, etc. However, at the top level, I only want to work with immutable "Haskell"/pure vectors.
Here is an example of the problem:
{-# LANGUAGE TypeFamilies,
ScopedTypeVariables,
MultiParamTypeClasses,
FlexibleInstances #-}
import Data.Vector.Generic as V hiding (eq)
import Data.Vector.Generic.Mutable as M
import Control.Monad.ST
import Control.Monad.Primitive
f :: (M.MVector v r, PrimMonad m) =>
v (PrimState m) r -> v (PrimState m) r -> m ()
f vIn vOut = do val <- M.read vIn 0
M.write vOut 0 val
applyFunc :: (M.MVector v r, PrimMonad m, V.Vector v' r, v ~ Mutable v') =>
(v (PrimState m) r -> v (PrimState m) r -> m ()) -> v' r -> v' r
applyFunc g x = runST $ do
y <- V.thaw x
g y y -- LINE 1
V.unsafeFreeze y
topLevelFun :: (V.Vector v r) => r -> v r
topLevelFun a =
let x = V.replicate 10 a
in applyFunc f x -- LINE 2
The code as written results in an error on LINE 1:
Could not deduce (m ~ ST s)
Expected type: ST s ()
Actual type: m ()
in the return type of g, LINE 1
Commenting out LINE 1 results in the error on LINE 2:
Ambiguous type variable `m0' in the constraint:
(PrimMonad m0) arising from a use of `applyFun'
I've tried a variety of explicit typing (using ScopedTypeVariables, explicit foralls, etc) but haven't found a way to fix the first error. For the LINE 1 error, it seems that m should simply be inferred to be ST s since I'm in a runST.
For the LINE 2 error (with LINE 1 commented out), the only thing I've come up with that works is
class Fake m v where
kindSig :: m a -> v b c
instance Fake m v
topLevelFun :: forall m v v' r . (V.Vector v' r, M.MVector v r, PrimMonad m, Fake m v, v ~ Mutable v') => r -> v' r
topLevelFun a =
let x = V.replicate 10 a
in applyFunc (f::Transform m v r) x -- LINE 2
which is obviously unsatisfactory: I have to create a fake class, with an even more pointless method whose only job is to demonstrate the kinds of the class arguments. Then I create a generic instance for everything so that I can have m in scope in topLevelFun, so that I can add a constraint and cast f. There has GOT to be a better way.
I could be doing a wide variety of things wrong here, so any suggestions would be helpful.
Does the following type for applyFunc work for you?
applyFunc :: (Vector v a) =>
(forall s. Mutable v s a -> Mutable v s a -> ST s ())
-> v a -> v a
That should compile with out problem so long as you have the Rank2Types extension, which you need because you work with a function that has to work on all ST monads. The reason for this is the type of runST is (forall s. ST s a) -> a, so the body of the code after runST needs to work for all s, hence g needs to work for all s.
(You could instead take a function that work with all PrimMonads but there are strictly fewer of those).
GHC can not infer higher rank types. There are very good reasons to not infer RankNTypes (it is undecidable), and although Rank2 is in theory inferable, the GHC people decided for the rule "infer if and only if the principle type is a Hindley-Milner type" which for people like me is very easy to reason about, and makes the compiler writers job not so hard.
In the comments you ask about taking a tuple. Tuples with polymorphic types require ImpredicativeTypes and can be done like
applyFuncInt :: (Vector v a) =>
((forall s. Mutable v s a -> Mutable v s a -> ST s ()),Int)
-> v a -> v a
applyFuncInt (g,_) x = runST $ do
y <- V.thaw x
g y y
V.unsafeFreeze y
although, usually it would be better to simply pass the number as a separate argument.