Related
(I'm totally rewriting this question to give it a better focus; you can see the history of changes if you want to see the original.)
Let's say I have two modules:
One module defines the function inverseAndSqrt. What this function actually does is not important; what is important is that it returns none, one, or both of two things in a way that the client can distinguish which one is which;
module Module1 (inverseAndSqrt) where
type TwoOpts a = (Maybe a, Maybe a)
inverseAndSqrt :: Int -> TwoOpts Float
inverseAndSqrt x = (if x /= 0 then Just (1.0/(fromIntegral x)) else Nothing,
if x >= 0 then Just (sqrt $ fromIntegral x) else Nothing)
another module defines other functions depending on inverseAndSqrt and on its type
module Module2 where
import Module1
fun :: (Maybe Float, Maybe Float) -> Float
fun (Just x, Just y) = x + y
fun (Just x, Nothing) = x
fun (Nothing, Just y) = y
exportedFun :: Int -> Float
exportedFun = fun . inverseAndSqrt
What I want to understand from the perspective of design principle is: how should I interface Module1 with other modules (e.g. Module2) in a way that makes it well encapsulated, reusable, etc?
The problems I see are
I could one day decide that I don't want to use a pair to return the two results anymore; I could decide to use a 2 elements list; or another type which is isomorphic (I think this is the right adjective, isn't it?) to a pair; if I do this, all client code will break
Exporting the TwoOpts type synonym doesn't solve anything, as Module1 could still change its implementation thus breaking client code.
Module1 is also forcing the type of the two optionals to be the same, but I'm not sure this is really relevant to this question...
How should I design Module1 (and thus edit Module2 as well) such that the two are not tightly coupled?
One thing I can think of is that maybe I should define a typeclass expressing what "a box with two optional things in it" is, and then Module1 and Module2 would use that as a common interface. But should that be in both module? In either of them? Or in none of them, in a third module? Or maybe such a class/concept is not needed?
I'm not a computer scientist so I'm sure that this question highlights some misunderstanding of mine due to lack of experience and theoretical background. Any help filling the gaps is welcome.
Possible modifications I'd like to support
Related to what chepner suggested in a comment to his answer, at some point I might want to extend the support from 2-tuple things to both 2- and 3-tuple things, having different accessor names for them, suche as get1of2/get2of2 (let's say these are the name we use when we first design Module1) vs get1of3/get2of3/get3of3.
At some point I would also be able to complement this 2-tuple-like type with something else, for instance an optional containing Just the sum¹ of the two main contents only if they are both Justs, or a Nothing if at least one of the two main contents is a Nothing. I guess in this case the internal representation of this class would be something like ((Maybe a, Maybe a), Maybe b) (¹ The sum is really a stupid example, so I've used b here instead of a to be more general than the sum would require).
To me, Haskell design is all type-centric. The design rule for functions is just "use the most general and accurate types that do the job", and the whole problem of design in Haskell is about coming up with the best types for the job.
We would like there to be no "junk" in the types, so that they have exactly one representation for each value you want to denote. E.g. String is a bad representation for numbers, because "0", "0.0", "-0" all mean the same thing, and also because "The Prisoner" is not a number -- it is a valid representation that does not have a valid denotation. If, say for performance reasons, the same denotation can be represented multiple ways, the type's API should make that difference invisible to the user.
So in your case, (Maybe a, Maybe a) is perfect -- it means exactly what you need it to mean. Using something more complicated is unnecessary, and will just complicate matters for the user. At some point whatever you expose will have to be convertible to a Maybe a for the first thing and a Maybe a for the second thing, and there is no extra information than that, so the tuple is perfect. Whether you use a type synonym or not is a matter of style -- I prefer not use synonyms at all and only give types names when I have a more formal abstraction in mind.
Connotation is important. For example, if I had a function for finding the roots of a quadratic polynomial, I probably wouldn't use TwoOpts, even though there are at most two of them. The fact that my return values are all "the same kind of thing" in an intuitive sense makes me prefer a list (or if I'm feeling particularly picky, a Set or Bag), even if the list has at most two elements. I just have it match my best understanding of the domain at the time, so I won't change it unless my understanding of the domain has changed in a significant way, in which case the opportunity to review all its uses is exactly what I want. If you are writing your functions to be as polymorphic as possible, then often you won't need to change anything but the specific moments the meaning is used, the exact moment domain knowledge is required (such as understanding the relationship between TwoOpts and Set). You don't need to "redo the plumbing" if it's made of a sufficiently flexible, polymorphic material.
Supposing you didn't have a clean isomorphism to a standard type like (Maybe a, Maybe a), and you wanted to formalize TwoOpts. The way here is to build an API out of its constructors, combinators, and eliminators. For example:
data TwoOpts a -- abstract, not exposed
-- constructors
none :: TwoOpts a
justLeft :: a -> TwoOpts a
justRight :: a -> TwoOpts a
both :: a -> a -> TwoOpts a
-- combinators
-- Semigroup and Monoid at least
swap :: TwoOpts a -> TwoOpts a
-- eliminators
getLeft :: TwoOpts a -> Maybe a
getRight :: TwoOpts a -> Maybe a
In this case the eliminators give exactly your representation (Maybe a, Maybe a) as their final coalgebra.
-- same as the tuple in a newtype, just more conventional
data TwoOpts a = TwoOpts (Maybe a) (Maybe a)
Or if you wanted to focus on the constructors side you could use an initial algebra
data TwoOpts a
= None
| JustLeft a
| JustRight a
| Both a a
You are at liberty to change this representation as long as it still implements the combinatory API above. If you have reason to use different representations of the same API, make the API into a typeclass (typeclass design is a whole other story).
In Einstein's famous words, "make it as simple as possible, but no simpler".
Don't define a simple type alias; this exposes the details of how you implement TwoOpts.
Instead, define a new type, but don't export the data constructor, but rather functions for accessing the two components. Then you are free to change the implementation of the type all you like without changing the interface, because the user can't pattern-match on a value of type TwoOpts a.
module Module1 (TwoOpts, inverseAndSqrt, getFirstOpt, getSecondOpt) where
data TwoOpts a = TwoOpts (Maybe a) (Maybe a)
getFirstOpt, getSecondOpt :: TwoOpts a -> Maybe a
getFirstOpt (TwoOpts a _) = a
getSecondOpt (TwoOpts _ b) = b
inverseAndSqrt :: Int -> TwoOpts Float
inverseAndSqrt x = TwoOpts (safeInverse x) (safeSqrt x)
where safeInverse 0 = Nothing
safeInverse x = Just (1.0 / fromIntegral x)
safeSqrt x | x >= 0 = Just $ sqrt $ fromIntegral x
| otherwise = Nothing
and
module Module2 where
import Module1
fun :: TwoOpts Float -> Float
fun a = case (getFirstOpts a, getSecondOpt a) of
(Just x, Just y) -> x + y
(Just x, Nothing) -> x
(Nothing, Just y) -> y
exportedFun :: Int -> Float
exportedFun = fun . inverseAndSqrt
Later, when you realize that you've reimplemented the type product, you can change your definitions without affecting any user code.
newtype TwoOpts a = TwoOpts { getOpts :: (Maybe a, Maybe a) }
getFirstOpt, getSecondOpt :: TwoOpts a -> Maybe a
getFirstOpt = fst . getOpts
getSecondOpt = snd . getOpts
I'm covering polymorphism and I'm trying to see the practical uses of such a feature.
My basic understanding of Rank 2 is:
type MyType = ∀ a. a -> a
subFunction :: a -> a
subFunction el = el
mainFunction :: MyType -> Int
mainFunction func = func 3
I understand that this is allowing the user to use a polymorphic function (subFunction) inside mainFunction and strictly specify it's output (Int). This seems very similar to GADT's:
data Example a where
ExampleInt :: Int -> Example Int
ExampleBool :: Bool -> Example Bool
1) Given the above, is my understanding of Rank 2 polymorphism correct?
2) What are the general situations where Rank 2 polymorphism can be used, as opposed to GADT's, for example?
If you pass a polymorphic function as and argument to a Rank2-polymorphic function, you're essentially passing not just one function but a whole family of functions – for all possible types that fulfill the constraints.
Typically, those forall quantifiers come with a class constraint. For example, I might wish to do number arithmetic with two different types simultaneously (for comparing precision or whatever).
data FloatCompare = FloatCompare {
singlePrecision :: Float
, doublePrecision :: Double
}
Now I might want to modify those numbers through some maths operation. Something like
modifyFloat :: (Num -> Num) -> FloatCompare -> FloatCompare
But Num is not a type, only a type class. I could of course pass a function that would modify any particular number type, but I couldn't use that to modify both a Float and a Double value, at least not without some ugly (and possibly lossy) converting back and forth.
Solution: Rank-2 polymorphism!
modifyFloat :: (∀ n . Num n => n -> n) -> FloatCompare -> FloatCompare
mofidyFloat f (FloatCompare single double)
= FloatCompare (f single) (f double)
The best single example of how this is useful in practice are probably lenses. A lens is a “smart accessor function” to a field in some larger data structure. It allows you to access fields, update them, gather results... while at the same time composing in a very simple way. How it works: Rank2-polymorphism; every lens is polymorphic, with the different instantiations corresponding to the “getter” / “setter” aspects, respectively.
The go-to example of an application of rank-2 types is runST as Benjamin Hodgson mentioned in the comments. This is a rather good example and there are a variety of examples using the same trick. For example, branding to maintain abstract data type invariants across multiple types, avoiding confusion of differentials in ad, a region-based version of ST.
But I'd actually like to talk about how Haskell programmers are implicitly using rank-2 types all the time. Every type class whose methods have universally quantified types desugars to a dictionary with a field with a rank-2 type. In practice, this is virtually always a higher-kinded type class* like Functor or Monad. I'll use a simplified version of Alternative as an example. The class declaration is:
class Alternative f where
empty :: f a
(<|>) :: f a -> f a -> f a
The dictionary representing this class would be:
data AlternativeDict f = AlternativeDict {
empty :: forall a. f a,
(<|>) :: forall a. f a -> f a -> f a }
Sometimes such an encoding is nice as it allows one to use different "instances" for the same type, perhaps only locally. For example, Maybe has two obvious instances of Alternative depending on whether Just a <|> Just b is Just a or Just b. Languages without type classes, such as Scala, do indeed use this encoding.
To connect to leftaroundabout's reference to lenses, you can view the hierarchy there as a hierarchy of type classes and the lens combinators as simply tools for explicitly building the relevant type class dictionaries. Of course, the reason it isn't actually a hierarchy of type classes is that we usually will have multiple "instances" for the same type. E.g. _head and _head . _tail are both "instances" of Traversal' s a.
* A higher-kinded type class doesn't necessarily lead to this, and it can happen for a type class of kind *. For example:
-- Higher-kinded but doesn't require universal quantification.
class Sum c where
sum :: c Int -> Int
-- Not higher-kinded but does require universal quantification.
class Length l where
length :: [a] -> l
If you are using modules in Haskell, you are already using Rank-2 types. Theoretically speaking, modules are records with rank-2 type properties.
For example, the Foo module below in Haskell ...
module Foo(id) where
id :: forall a. a -> a
id x = x
import qualified Foo
main = do
putStrLn (Foo.id "hello")
return ()
... can actually be thought as a record as follows:
type FooType = FooType {
id :: forall a. a -> a
}
Foo :: FooType
Foo = Foo {
id = \x -> x
}
P/S (unrelated this question): from a language design perspective, if you are going to support module system, then you might as well support higher-rank types (i.e. allow arbitrary quantification of type variables on any level) to reduce duplication of efforts (i.e. type checking a module should be almost the same as type checking a record with higher rank types).
I have heard Haskell described as having structural typing. Records are an exception to that though as I understand. For example foo cannot be called with something of type HRec2 even though HRec and HRec2 are only nominally different in their fields.
data HRec = HRec { x :: Int, y :: Bool }
data HRec2 = HRec2 { p :: Int, q :: Bool }
foo :: HRec -> Bool
Is there some explanation for rejecting extending structural typing to everything including records?
Are there statically typed languages with structural typing even for records? Is there maybe some debate on this I can read about for all statically typed languages in general?
Haskell has structured types, but not structural typing, and that's not likely to change.*
The refusal to permit nominally different but structurally similar types as interchangeable arguments is called type safety. It's a good thing. Haskell even has a newtype declaration to provide types which are only nominally different, to allow you to enforce more type safety. Type safety is an easy way to catch bugs early rather than permit them at runtime.
In addition to amindfv's good answer which includes ad hoc polymorphism via typeclasses (effectively a programmer-declared feature equivalence), there's parametric polymorphism where you allow absolutely any type, so [a] allows any type in your list and BTree a allows any type in your binary tree.
This gives three answers to "are these types interchangeable?".
No; the programmer didn't say so.
Equivalent for a specific purpose because the programmer said so.
Don't care - I can do the same thing to this collection of data because it doesn't use any property of the data itself.
There's no 4: compiler overrules programmer because they happened to use a couple of Ints and a String like in that other function.
*I said Haskell is unlikely to change to structural typing. There is some discussion to introduce some form of extensible records, but no plans to make (Int,(Int,Int)) count as the same as (Int, Int, Int) or Triple {one::Int, two::Int, three::Int} the same as Triple2 {one2::Int, two2::Int, three2::Int}.
Haskell records aren't really "less structural" than the rest of the type system. Every type is either completely specified, or "specifically vague" (i.e. defined with a typeclass).
To allow both HRec and HRec2 to f, you have a couple of options:
Algebraic types:
Here, you define HRec and HRec2 records to both be part of the HRec type:
data HRec = HRec { x :: Int, y :: Bool }
| HRec2 { p :: Int, q :: Bool }
foo :: HRec -> Bool
(alternately, and maybe more idiomatic:)
data HRecType = Type1 | Type2
data HRec = HRec { hRecType :: HRecType, x :: Int, y :: Bool }
Typeclasses
Here, you define foo as able to accept any type as input, as long as a typeclass instance has been written for that type:
data HRec = HRec { x :: Int, y :: Bool }
data HRec2 = HRec2 { p :: Int, q :: Bool }
class Flexible a where
foo :: a -> Bool
instance Flexible HRec where
foo (HRec a _) = a == 5 -- or whatever
instance Flexible HRec2 where
foo (HRec2 a _) = a == 5
Using typeclasses allows you to go further than regular structural typing -- you can accept types that have the necessary information embedded in them, even if the types don't superficially look similar, e.g.:
data Foo = Foo { a :: String, b :: Float }
data Bar = Bar { c :: String, d :: Integer }
class Thing a where
doAThing :: a -> Bool
instance Thing Foo where
doAThing (Foo x y) = (x == "hi") && (y == 0)
instance Thing Bar where
doAThing (Bar x y) = (x == "hi") && ((fromInteger y) == 0)
We can run fromInteger (or any arbitrary function) to get the data we need from what we have!
I'm aware of two library implementations of structurally typed records in Haskell:
HList is older, and is explained in an excellent paper: Haskell's overlooked object system (free online, but SO won't let me include more links)
vinyl is newer, and uses fancy new GHC features. There's at least one library, vinyl-gl, using it.
I cannot answer the language-design part of your question, though.
To answer your last question, Go and Scalas definitely have structural typing. Some people (including me) would call that "statically unsafe typing", since it implicitly declares all samely- named methods in a program to have the same semantics, which implies "spooky action at a distance", relating code in on source file to code in some library that the program has never seen.
IMO, better to require that the same-named methods to explicitly declare that they conform to a named semantic "model" of behavior.
Yes, the compiler would guarantee that the method is callable, but it isn't much safer than saying:
f :: [a] -> Int
And letting the compiler choose an arbitrary implementation that may or may not be length.
(A similar idea can be made safe with Scala "implicits" or Haskell (GHC?) "reflection" package.)
In Scrap your boilerplate reloaded, the authors describe a new presentation of Scrap Your Boilerplate, which is supposed to be equivalent to the original.
However, one difference is that they assume a finite, closed set of "base" types, encoded with a GADT
data Type :: * -> * where
Int :: Type Int
List :: Type a -> Type [a]
...
In the original SYB, type-safe cast is used, implemented using the Typeable class.
My questions are:
What is the relationship between these two approaches?
Why was the GADT representation chosen for the "SYB Reloaded" presentation?
[I am one of the authors of the "SYB Reloaded" paper.]
TL;DR We really just used it because it seemed more beautiful to us. The class-based Typeable approach is more practical. The Spine view can be combined with the Typeable class and does not depend on the Type GADT.
The paper states this in its conclusions:
Our implementation handles the two central ingredients of generic programming differently from the original SYB paper: we use overloaded functions with
explicit type arguments instead of overloaded functions based on a type-safe
cast 1 or a class-based extensible scheme [20]; and we use the explicit spine
view rather than a combinator-based approach. Both changes are independent
of each other, and have been made with clarity in mind: we think that the structure of the SYB approach is more visible in our setting, and that the relations
to PolyP and Generic Haskell become clearer. We have revealed that while the
spine view is limited in the class of generic functions that can be written, it is
applicable to a very large class of data types, including GADTs.
Our approach cannot be used easily as a library, because the encoding of
overloaded functions using explicit type arguments requires the extensibility of
the Type data type and of functions such as toSpine. One can, however, incorporate Spine into the SYB library while still using the techniques of the SYB
papers to encode overloaded functions.
So, the choice of using a GADT for type representation is one we made mainly for clarity. As Don states in his answer, there are some obvious advantages in this representation, namely that it maintains static information about what type a type representation is for, and that it allows us to implement cast without any further magic, and in particular without the use of unsafeCoerce. Type-indexed functions can also be implemented directly by using pattern matching on the type, and without falling back to various combinators such as mkQ or extQ.
Fact is that I (and I think the co-authors) simply were not very fond of the Typeable class. (In fact, I'm still not, although it is finally becoming a bit more disciplined now in that GHC adds auto-deriving for Typeable, makes it kind-polymorphic, and will ultimately remove the possibility to define your own instances.) In addition, Typeable wasn't quite as established and widely known as it is perhaps now, so it seemed appealing to "explain" it by using the GADT encoding. And furthermore, this was the time when we were also thinking about adding open datatypes to Haskell, thereby alleviating the restriction that the GADT is closed.
So, to summarize: If you actually need dynamic type information only for a closed universe, I'd always go for the GADT, because you can use pattern matching to define type-indexed functions, and you do not have to rely on unsafeCoerce nor advanced compiler magic. If the universe is open, however, which is quite common, certainly for the generic programming setting, then the GADT approach might be instructive, but isn't practical, and using Typeable is the way to go.
However, as we also state in the conclusions of the paper, the choice of Type over Typeable isn't a prerequisite for the other choice we're making, namely to use the Spine view, which I think is more important and really the core of the paper.
The paper itself shows (in Section 8) a variation inspired by the "Scrap your Boilerplate with Class" paper, which uses a Spine view with a class constraint instead. But we can also do a more direct development, which I show in the following. For this, we'll use Typeable from Data.Typeable, but define our own Data class which, for simplicity, just contains the toSpine method:
class Typeable a => Data a where
toSpine :: a -> Spine a
The Spine datatype now uses the Data constraint:
data Spine :: * -> * where
Constr :: a -> Spine a
(:<>:) :: (Data a) => Spine (a -> b) -> a -> Spine b
The function fromSpine is as trivial as with the other representation:
fromSpine :: Spine a -> a
fromSpine (Constr x) = x
fromSpine (c :<>: x) = fromSpine c x
Instances for Data are trivial for flat types such as Int:
instance Data Int where
toSpine = Constr
And they're still entirely straightforward for structured types such as binary trees:
data Tree a = Empty | Node (Tree a) a (Tree a)
instance Data a => Data (Tree a) where
toSpine Empty = Constr Empty
toSpine (Node l x r) = Constr Node :<>: l :<>: x :<>: r
The paper then goes on and defines various generic functions, such as mapQ. These definitions hardly change. We only get class constraints for Data a => where the paper has function arguments of Type a ->:
mapQ :: Query r -> Query [r]
mapQ q = mapQ' q . toSpine
mapQ' :: Query r -> (forall a. Spine a -> [r])
mapQ' q (Constr c) = []
mapQ' q (f :<>: x) = mapQ' q f ++ [q x]
Higher-level functions such as everything also just lose their explicit type arguments (and then actually look exactly the same as in original SYB):
everything :: (r -> r -> r) -> Query r -> Query r
everything op q x = foldl op (q x) (mapQ (everything op q) x)
As I said above, if we now want to define a generic sum function summing up all Int occurrences, we cannot pattern match anymore, but have to fall back to mkQ, but mkQ is defined purely in terms of Typeable and completely independent of Spine:
mkQ :: (Typeable a, Typeable b) => r -> (b -> r) -> a -> r
(r `mkQ` br) a = maybe r br (cast a)
And then (again exactly as in original SYB):
sum :: Query Int
sum = everything (+) sumQ
sumQ :: Query Int
sumQ = mkQ 0 id
For some of the stuff later in the paper (e.g., adding constructor information), a bit more work is needed, but it can all be done. So using Spine really does not depend on using Type at all.
Well, obviously the Typeable use is open -- new variants can be added after the fact, and without modifying the original definitions.
The important change though is that in that TypeRep is untyped. That is, there is no connection between the runtime type , TypeRep, and the static type it encodes. With the GADT approach we can encode the mapping between a type a and its Type, given by the GADT Type a.
We thus bake in evidence for the type rep being statically linked to its origin type, and can write statically typed dynamic application (for example) using Type a as evidence that we have a runtime a.
In the older TypeRep case, we have no such evidence and it comes down to runtime string equality, and a coerce and hope for the best through fromDynamic.
Compare the signatures:
toDyn :: Typeable a => a -> TypeRep -> Dynamic
versus GADT style:
toDyn :: Type a => a -> Type a -> Dynamic
I can't fake my type evidence, and I can use that later when reconstructing things, to e.g. lookup the type class instances for a when all I have is a Type a.
When metaprogramming, it may be useful (or necessary) to pass along to Haskell's type system information about types that's known to your program but not inferable in Hindley-Milner. Is there a library (or language extension, etc) that provides facilities for doing this—that is, programmatic type annotations—in Haskell?
Consider a situation where you're working with a heterogenous list (implemented using the Data.Dynamic library or existential quantification, say) and you want to filter the list down to a bog-standard, homogeneously typed Haskell list. You can write a function like
import Data.Dynamic
import Data.Typeable
dynListToList :: (Typeable a) => [Dynamic] -> [a]
dynListToList = (map fromJust) . (filter isJust) . (map fromDynamic)
and call it with a manual type annotation. For example,
foo :: [Int]
foo = dynListToList [ toDyn (1 :: Int)
, toDyn (2 :: Int)
, toDyn ("foo" :: String) ]
Here foo is the list [1, 2] :: [Int]; that works fine and you're back on solid ground where Haskell's type system can do its thing.
Now imagine you want to do much the same thing but (a) at the time you write the code you don't know what the type of the list produced by a call to dynListToList needs to be, yet (b) your program does contain the information necessary to figure this out, only (c) it's not in a form accessible to the type system.
For example, say you've randomly selected an item from your heterogenous list and you want to filter the list down by that type. Using the type-checking facilities supplied by Data.Typeable, your program has all the information it needs to do this, but as far as I can tell—this is the essence of the question—there's no way to pass it along to the type system. Here's some pseudo-Haskell that shows what I mean:
import Data.Dynamic
import Data.Typeable
randList :: (Typeable a) => [Dynamic] -> IO [a]
randList dl = do
tr <- randItem $ map dynTypeRep dl
return (dynListToList dl :: [<tr>]) -- This thing should have the type
-- represented by `tr`
(Assume randItem selects a random item from a list.)
Without a type annotation on the argument of return, the compiler will tell you that it has an "ambiguous type" and ask you to provide one. But you can't provide a manual type annotation because the type is not known at write-time (and can vary); the type is known at run-time, however—albeit in a form the type system can't use (here, the type needed is represented by the value tr, a TypeRep—see Data.Typeable for details).
The pseudo-code :: [<tr>] is the magic I want to happen. Is there any way to provide the type system with type information programatically; that is, with type information contained in a value in your program?
Basically I'm looking for a function with (pseudo-) type ??? -> TypeRep -> a that takes a value of a type unknown to Haskell's type system and a TypeRep and says, "Trust me, compiler, I know what I'm doing. This thing has the value represented by this TypeRep." (Note that this is not what unsafeCoerce does.)
Or is there something completely different that gets me the same place? For example, I can imagine a language extension that permits assignment to type variables, like a souped-up version of the extension enabling scoped type variables.
(If this is impossible or highly impractical,—e.g., it requires packing a complete GHCi-like interpreter into the executable—please try to explain why.)
No, you can't do this. The long and short of it is that you're trying to write a dependently-typed function, and Haskell isn't a dependently typed language; you can't lift your TypeRep value to a true type, and so there's no way to write down the type of your desired function. To explain this in a little more detail, I'm first going to show why the way you've phrased the type of randList doesn't really make sense. Then, I'm going to explain why you can't do what you want. Finally, I'll briefly mention a couple thoughts on what to actually do.
Existentials
Your type signature for randList can't mean what you want it to mean. Remembering that all type variables in Haskell are universally quantified, it reads
randList :: forall a. Typeable a => [Dynamic] -> IO [a]
Thus, I'm entitled to call it as, say, randList dyns :: IO [Int] anywhere I want; I must be able to provide a return value for all a, not simply for some a. Thinking of this as a game, it's one where the caller can pick a, not the function itself. What you want to say (this isn't valid Haskell syntax, although you can translate it into valid Haskell by using an existential data type1) is something more like
randList :: [Dynamic] -> (exists a. Typeable a => IO [a])
This promises that the elements of the list are of some type a, which is an instance of Typeable, but not necessarily any such type. But even with this, you'll have two problems. First, even if you could construct such a list, what could you do with it? And second, it turns out that you can't even construct it in the first place.
Since all that you know about the elements of the existential list is that they're instances of Typeable, what can you do with them? Looking at the documentation, we see that there are only two functions2 which take instances of Typeable:
typeOf :: Typeable a => a -> TypeRep, from the type class itself (indeed, the only method therein); and
cast :: (Typeable a, Typeable b) => a -> Maybe b (which is implemented with unsafeCoerce, and couldn't be written otherwise).
Thus, all that you know about the type of the elements in the list is that you can call typeOf and cast on them. Since we'll never be able to usefully do anything else with them, our existential might just as well be (again, not valid Haskell)
randList :: [Dynamic] -> IO [(TypeRep, forall b. Typeable b => Maybe b)]
This is what we get if we apply typeOf and cast to every element of our list, store the results, and throw away the now-useless existentially typed original value. Clearly, the TypeRep part of this list isn't useful. And the second half of the list isn't either. Since we're back to a universally-quantified type, the caller of randList is once again entitled to request that they get a Maybe Int, a Maybe Bool, or a Maybe b for any (typeable) b of their choosing. (In fact, they have slightly more power than before, since they can instantiate different elements of the list to different types.) But they can't figure out what type they're converting from unless they already know it—you've still lost the type information you were trying to keep.
And even setting aside the fact that they're not useful, you simply can't construct the desired existential type here. The error arises when you try to return the existentially-typed list (return $ dynListToList dl). At what specific type are you calling dynListToList? Recall that dynListToList :: forall a. Typeable a => [Dynamic] -> [a]; thus, randList is responsible for picking which a dynListToList is going to use. But it doesn't know which a to pick; again, that's the source of the question! So the type that you're trying to return is underspecified, and thus ambiguous.3
Dependent types
OK, so what would make this existential useful (and possible)? Well, we actually have slightly more information: not only do we know there's some a, we have its TypeRep. So maybe we can package that up:
randList :: [Dynamic] -> (exists a. Typeable a => IO (TypeRep,[a]))
This isn't quite good enough, though; the TypeRep and the [a] aren't linked at all. And that's exactly what you're trying to express: some way to link the TypeRep and the a.
Basically, your goal is to write something like
toType :: TypeRep -> *
Here, * is the kind of all types; if you haven't seen kinds before, they are to types what types are to values. * classifies types, * -> * classifies one-argument type constructors, etc. (For instance, Int :: *, Maybe :: * -> *, Either :: * -> * -> *, and Maybe Int :: *.)
With this, you could write (once again, this code isn't valid Haskell; in fact, it really bears only a passing resemblance to Haskell, as there's no way you could write it or anything like it within Haskell's type system):
randList :: [Dynamic] -> (exists (tr :: TypeRep).
Typeable (toType tr) => IO (tr, [toType tr]))
randList dl = do
tr <- randItem $ map dynTypeRep dl
return (tr, dynListToList dl :: [toType tr])
-- In fact, in an ideal world, the `:: [toType tr]` signature would be
-- inferable.
Now, you're promising the right thing: not that there exists some type which classifies the elements of the list, but that there exists some TypeRep such that its corresponding type classifies the elements of the list. If only you could do this, you would be set. But writing toType :: TypeRep -> * is completely impossible in Haskell: doing this requires a dependently-typed language, since toType tr is a type which depends on a value.
What does this mean? In Haskell, it's perfectly acceptable for values to depend on other values; this is what a function is. The value head "abc", for instance, depends on the value "abc". Similarly, we have type constructors, so it's acceptable for types to depend on other types; consider Maybe Int, and how it depends on Int. We can even have values which depend on types! Consider id :: a -> a. This is really a family of functions: id_Int :: Int -> Int, id_Bool :: Bool -> Bool, etc. Which one we have depends on the type of a. (So really, id = \(a :: *) (x :: a) -> x; although we can't write this in Haskell, there are languages where we can.)
Crucially, however, we can never have a type that depends on a value. We might want such a thing: imagine Vec 7 Int, the type of length-7 lists of integers. Here, Vec :: Nat -> * -> *: a type whose first argument must be a value of type Nat. But we can't write this sort of thing in Haskell.4 Languages which support this are called dependently-typed (and will let us write id as we did above); examples include Coq and Agda. (Such languages often double as proof assistants, and are generally used for research work as opposed to writing actual code. Dependent types are hard, and making them useful for everyday programming is an active area of research.)
Thus, in Haskell, we can check everything about our types first, throw away all that information, and then compile something that refers only to values. In fact, this is exactly what GHC does; since we can never check types at run-time in Haskell, GHC erases all the types at compile-time without changing the program's run-time behavior. This is why unsafeCoerce is easy to implement (operationally) and completely unsafe: at run-time, it's a no-op, but it lies to the type system. Consequently, something like toType is completely impossible to implement in the Haskell type system.
In fact, as you noticed, you can't even write down the desired type and use unsafeCoerce. For some problems, you can get away with this; we can write down the type for the function, but only implement it with by cheating. That's exactly how fromDynamic works. But as we saw above, there's not even a good type to give to this problem from within Haskell. The imaginary toType function allows you to give the program a type, but you can't even write down toType's type!
What now?
So, you can't do this. What should you do? My guess is that your overall architecture isn't ideal for Haskell, although I haven't seen it; Typeable and Dynamic don't actually show up that much in Haskell programs. (Perhaps you're "speaking Haskell with a Python accent", as they say.) If you only have a finite set of data types to deal with, you might be able to bundle things into a plain old algebraic data type instead:
data MyType = MTInt Int | MTBool Bool | MTString String
Then you can write isMTInt, and just use filter isMTInt, or filter (isSameMTAs randomMT).
Although I don't know what it is, there's probably a way you could unsafeCoerce your way through this problem. But frankly, that's not a good idea unless you really, really, really, really, really, really know what you're doing. And even then, it's probably not. If you need unsafeCoerce, you'll know, it won't just be a convenience thing.
I really agree with Daniel Wagner's comment: you're probably going to want to rethink your approach from scratch. Again, though, since I haven't seen your architecture, I can't say what that will mean. Maybe there's another Stack Overflow question in there, if you can distill out a concrete difficulty.
1 That looks like the following:
{-# LANGUAGE ExistentialQuantification #-}
data TypeableList = forall a. Typeable a => TypeableList [a]
randList :: [Dynamic] -> IO TypeableList
However, since none of this code compiles anyway, I think writing it out with exists is clearer.
2 Technically, there are some other functions which look relevant, such as toDyn :: Typeable a => a -> Dynamic and fromDyn :: Typeable a => Dynamic -> a -> a. However, Dynamic is more or less an existential wrapper around Typeables, relying on typeOf and TypeReps to know when to unsafeCoerce (GHC uses some implementation-specific types and unsafeCoerce, but you could do it this way, with the possible exception of dynApply/dynApp), so toDyn doesn't do anything new. And fromDyn doesn't really expect its argument of type a; it's just a wrapper around cast. These functions, and the other similar ones, don't provide any extra power that isn't available with just typeOf and cast. (For instance, going back to a Dynamic isn't very useful for your problem!)
3 To see the error in action, you can try to compile the following complete Haskell program:
{-# LANGUAGE ExistentialQuantification #-}
import Data.Dynamic
import Data.Typeable
import Data.Maybe
randItem :: [a] -> IO a
randItem = return . head -- Good enough for a short and non-compiling example
dynListToList :: Typeable a => [Dynamic] -> [a]
dynListToList = mapMaybe fromDynamic
data TypeableList = forall a. Typeable a => TypeableList [a]
randList :: [Dynamic] -> IO TypeableList
randList dl = do
tr <- randItem $ map dynTypeRep dl
return . TypeableList $ dynListToList dl -- Error! Ambiguous type variable.
Sure enough, if you try to compile this, you get the error:
SO12273982.hs:17:27:
Ambiguous type variable `a0' in the constraint:
(Typeable a0) arising from a use of `dynListToList'
Probable fix: add a type signature that fixes these type variable(s)
In the second argument of `($)', namely `dynListToList dl'
In a stmt of a 'do' block: return . TypeableList $ dynListToList dl
In the expression:
do { tr <- randItem $ map dynTypeRep dl;
return . TypeableList $ dynListToList dl }
But as is the entire point of the question, you can't "add a type signature that fixes these type variable(s)", because you don't know what type you want.
4 Mostly. GHC 7.4 has support for lifting types to kinds and for kind polymorphism; see section 7.8, "Kind polymorphism and promotion", in the GHC 7.4 user manual. This doesn't make Haskell dependently typed—something like TypeRep -> * example is still out5—but you will be able to write Vec by using very expressive types that look like values.
5 Technically, you could now write down something which looks like it has the desired type: type family ToType :: TypeRep -> *. However, this takes a type of the promoted kind TypeRep, and not a value of the type TypeRep; and besides, you still wouldn't be able to implement it. (At least I don't think so, and I can't see how you would—but I am not an expert in this.) But at this point, we're pretty far afield.
What you're observing is that the type TypeRep doesn't actually carry any type-level information along with it; only term-level information. This is a shame, but we can do better when we know all the type constructors we care about. For example, suppose we only care about Ints, lists, and function types.
{-# LANGUAGE GADTs, TypeOperators #-}
import Control.Monad
data a :=: b where Refl :: a :=: a
data Dynamic where Dynamic :: TypeRep a -> a -> Dynamic
data TypeRep a where
Int :: TypeRep Int
List :: TypeRep a -> TypeRep [a]
Arrow :: TypeRep a -> TypeRep b -> TypeRep (a -> b)
class Typeable a where typeOf :: TypeRep a
instance Typeable Int where typeOf = Int
instance Typeable a => Typeable [a] where typeOf = List typeOf
instance (Typeable a, Typeable b) => Typeable (a -> b) where
typeOf = Arrow typeOf typeOf
congArrow :: from :=: from' -> to :=: to' -> (from -> to) :=: (from' -> to')
congArrow Refl Refl = Refl
congList :: a :=: b -> [a] :=: [b]
congList Refl = Refl
eq :: TypeRep a -> TypeRep b -> Maybe (a :=: b)
eq Int Int = Just Refl
eq (Arrow from to) (Arrow from' to') = liftM2 congArrow (eq from from') (eq to to')
eq (List t) (List t') = liftM congList (eq t t')
eq _ _ = Nothing
eqTypeable :: (Typeable a, Typeable b) => Maybe (a :=: b)
eqTypeable = eq typeOf typeOf
toDynamic :: Typeable a => a -> Dynamic
toDynamic a = Dynamic typeOf a
-- look ma, no unsafeCoerce!
fromDynamic_ :: TypeRep a -> Dynamic -> Maybe a
fromDynamic_ rep (Dynamic rep' a) = case eq rep rep' of
Just Refl -> Just a
Nothing -> Nothing
fromDynamic :: Typeable a => Dynamic -> Maybe a
fromDynamic = fromDynamic_ typeOf
All of the above is pretty standard. For more on the design strategy, you'll want to read about GADTs and singleton types. Now, the function you want to write follows; the type is going to look a bit daft, but bear with me.
-- extract only the elements of the list whose type match the head
firstOnly :: [Dynamic] -> Dynamic
firstOnly [] = Dynamic (List Int) []
firstOnly (Dynamic rep v:xs) = Dynamic (List rep) (v:go xs) where
go [] = []
go (Dynamic rep' v:xs) = case eq rep rep' of
Just Refl -> v : go xs
Nothing -> go xs
Here we've picked a random element (I rolled a die, and it came up 1) and extracted only the elements that have a matching type from the list of dynamic values. Now, we could have done the same thing with regular boring old Dynamic from the standard libraries; however, what we couldn't have done is used the TypeRep in a meaningful way. I now demonstrate that we can do so: we'll pattern match on the TypeRep, and then use the enclosed value at the specific type the TypeRep tells us it is.
use :: Dynamic -> [Int]
use (Dynamic (List (Arrow Int Int)) fs) = zipWith ($) fs [1..]
use (Dynamic (List Int) vs) = vs
use (Dynamic Int v) = [v]
use (Dynamic (Arrow (List Int) (List (List Int))) f) = concat (f [0..5])
use _ = []
Note that on the right-hand sides of these equations, we are using the wrapped value at different, concrete types; the pattern match on the TypeRep is actually introducing type-level information.
You want a function that chooses a different type of values to return based on runtime data. Okay, great. But the whole purpose of a type is to tell you what operations can be performed on a value. When you don't know what type will be returned from a function, what do you do with the values it returns? What operations can you perform on them? There are two options:
You want to read the type, and perform some behaviour based on which type it is. In this case you can only cater for a finite list of types known in advance, essentially by testing "is it this type? then we do this operation...". This is easily possible in the current Dynamic framework: just return the Dynamic objects, using dynTypeRep to filter them, and leave the application of fromDynamic to whoever wants to consume your result. Moreover, it could well be possible without Dynamic, if you don't mind setting the finite list of types in your producer code, rather than your consumer code: just use an ADT with a constructor for each type, data Thing = Thing1 Int | Thing2 String | Thing3 (Thing,Thing). This latter option is by far the best if it is possible.
You want to perform some operation that works across a family of types, potentially some of which you don't know about yet, e.g. by using type class operations. This is trickier, and it's tricky conceptually too, because your program is not allowed to change behaviour based on whether or not some type class instance exists – it's an important property of the type class system that the introduction of a new instance can either make a program type check or stop it from type checking, but it can't change the behaviour of a program. Hence you can't throw an error if your input list contains inappropriate types, so I'm really not sure that there's anything you can do that doesn't essentially involve falling back to the first solution at some point.