Static pointers and serialisation

This longish post gives Simon's reflections on the implementation of Cloud-Haskell-style static pointers and serialiation. See also

Much of what is suggested here is implemented, in some form, in two existing projects

My goal here is to identify the smallest possible extension to GHC, with the smallest possible trusted code base, that would enable these libraries to be written in an entirely type-safe way.


Background: the trusted code base

The implementation Typeable class, and its associated functions, in GHC offers a type-safe abstraction, in the classic sense that "well typed programs won't go wrong". For example, we in Data.Typeable we have

cast :: forall a b. (Typeable a, Typeable b) => a -> Maybe b

We expect cast to be type-safe: if cast returns a value Just x then we really do know that x :: b. Let's remind ourselves of class Typeable:

class Typeable a where
  typeRep :: proxy a -> TypeRep

(It's not quite this, but close.) The proxy a argument is just a proxy for type argument; its value is never inspected and you can always pass bottom.

Under the hood, cast uses typeRep to get the runtime TypeRep for a and b, and compares them, thus:

cast :: forall a b. (Typeable a, Typeable b) => a -> Maybe b
cast x = if typeRep (Proxy :: Proxy a) == typeRep (Proxy :: Proxy b)
           then Just (unsafeCoerce x)
           else Nothing

Although cast is written in Haskell, it uses unsafeCoerce. For it to truly be type-safe, it must trust the Typeable instances. If the user could write a Typeable instance, they could write a bogus one, and defeat type safety. So only GHC is allowed write Typeable instances.

In short, cast and the Typeable instances are part of the trusted code base, or TCB:

  • The TCB should be as small as possible
  • The TCB should have a small, well-defined, statically-typed API used by client code
  • Client code is un-trusted; if the client code is well-typed, and the TCB is implemented correctly, nothing can go wrong

Background Typeable a and TypeRep

I'll use the Typeable a type class and values of type TypeRep more or less interchangeably. As you can see from the definition of class Typeable above, its payload is simply a constant function returning a TypeRep. So you can think of a Typeable a as simply a type-tagged version of TypeRep.

Of course, a Typeable a is a type class thing, which is hard to pass around explicitly like a value, but that is easily fixed using the "Dict Trick", well known in Haskell folk lore:

data Dict (c :: Constraint) where
  Dict :: forall c. c => Dict c

Now a value of type Dict (Typeable a) is an ordinary value that embodies a Typeable a dictionary. For example:

f :: Dict (Typeable a) -> Dict (Typeable b) -> a -> Maybe b
f Dict Dict val = cast val

The pattern-matches against the Dict constructor brings the Typeable dictionaries into scope, so they can be used to discharge the constraint arising from the call to cast.

Background: serialisation

I'm going to assume a a type class Serialisable, something like this:

class Serialisable a where
  encode :: a -> ByteString
  decode :: ByteString -> Maybe (a, ByteString)

'll use "encode" and "decode" as synonyms for "serialise" and "deserialise", because the former are easier to pronounce.

Here's an interesting question: are instances of Serialisable part of the TCB? No, they are not. Here is a tricky case:

  decode (encode [True,False]) :: Maybe (Int, ByteString)

Here I have encode a [Bool] into a ByteString, and then decoded an Int from that ByteString. This may be naughty or undesirable, but it cannot seg-fault: it is type-safe in the sense above. You can think of it like this: a decoder is simply a parser for the bits in the ByteString, so a decoder for (say) Int can fail to parse a full Int (returning Nothing), but it can't return a non-Int.

For the naughtiness, one could imagine that a Cloud Haskell library might send fingerprints or TypeReps or whatnot to eliminate potential naughtiness. But even then it is very valuable if the type-safety of the system does not rely on the CH library. Type safety depends only on the correctness of the (small) TCB; naughtiness-safety might additionally depend on the correctness of the CH library.

Background: static pointers

I'm taking for granted the basic design of the Cloud Haskell paper. That is,

  • A type constructor StaticPtr :: * -> *. Intuitively, a value of type StaticPtr t is represented by a static code pointer to a value of type t. Note "code pointer" not "heap pointer". That's the point!
  • A language construct static <expr>, whose type is StaticPtr t if <expr> has type t.
  • In static <expr>, the free variables of <expr> must all be bound at top level. The implementation almost certainly works by giving <expr> a top-level definition with a new name, static34 = <expr>.
  • A function unStatic :: StaticPtr a -> a, to unwrap a static pointer.
  • Static values are serialisable. Something like instance Serialisable (StaticPtr a). (This will turn out to be not quite right.) Operationally this works by serialising the code pointer, or top-level name (e.g "Foo.static34").

All of this is built-in. It is OK for the implementation of StaticPtr to be part of the TCB. But our goal is that no other code need be in the TCB.

A red herring. I'm not going to address the question of how to serialise a static pointer. One method would be to serialise a machine address, but that only works if the encoding and decoding ends are running identical binaries. But that's easily fixed: encode a static as the name of the static value e.g. "function foo from module M in package p". Indeed, I'll informally assume an implementation of this latter kind.

In general, I will say that what we ultimately serialise is a StaticName. You can think of a StaticName as package/module/function triple, or something like that. The implementation of StaticName is certainly not part of the client-visible API for StaticPtr; indeed, the type StaticName is not part of the API either. But it gives us useful vocabulary.

Serialising static pointers

We can see immediately that we cannot expect to have instance Serialisable (Static a), which is what the Cloud Haskell paper proposed. If we had such an instance we would have

encodeStatic :: forall a. StaticPtr a -> ByteString
decodeStatic :: forall a. ByteString -> Maybe (StaticPtr a, ByteString)

And it's immediately apparent that decodeStatic cannot be right. I could get a ByteString from anywhere, apply decodeStatic to it, and thereby get a StaticPtr a. Then use unStatic and you have a value of type a, for, for any type a!!

Plainly, what we need is (just in the case of cast) to do a dynamic typecheck, thus:

decodeStatic :: forall a. Typeable a 
                       => ByteString -> Maybe (StaticPtr a, ByteString)

Let's think operationally for a moment:

  • GHC collects all the StaticPtr values in a table, the static pointer table or SPT. Each row contains
    • The StaticName of the value
    • A pointer to closure for the value itself
    • A pointer to its TypeRep
  • decodeStatic now proceeds like this:
    • Parse a StaticName from the ByteString (failure => Nothing)
    • Look it up in table (not found => Nothing)
    • Compare the TypeRep passed to decodeStatic (via the Typeable a dictionary) with the one ine the table (not equal => Nothing)
    • Return the value

Side note. Another possibility is for decodeStatic not to take a Typeable a context but instead for unStatic to do so:: unStatic :: Typeable a => StaticPtr a -> Maybe a. But that seems a mess. Apart from anything else, it would mean that a value of type StaticPtr a might or might not point to a value of type a, so there's no point in having the type parameter in the first place. End of side note.

This design has some useful consequences that are worth calling out:

  • A StaticPtr is serialised simply to the StaticName; the serialised form does not need to contain a TypeRep. Indeed it would not even be type-safe to serialise a StaticPtr to a pair of a StaticName and a TypeRep, trusting that the TypeRep described the type of the named function. Why not? Think back to "Background: serialisation" above, and imagine we said
    decode (encode ["wibble", "wobble"]) 
      :: Typeable a => Maybe (StaticPtr a, ByteString)
    Here we create an essentially-garbage ByteString by encoding a [String], and try to decode it. If, by chance, we successfully parse a valid StaticName and TypeRep, there is absolutely no reason to suppose that the TypeRep will describe the type of the function.

    Instead, the TypeRep of the static pointer lives in the SPT, securely put there when the SPT was created. Not only is this type-safe, but it also saves bandwidth by not transmittingTypeReps.
  • Since clients can effectively fabricate a StaticName (by supplying decodeStatic with a bogus ByteString, a StaticName is untrusted. That gives the implementation a good deal of wiggle room for how it chooses to implement static names. Even a simple index in the range 0..N would be type-safe!

    The motivation for choosing a richer representation for StaticName (eg package/module/name) is not type-safety but rather resilience to change. For example, the Haskell programs at the two ends could be quite different, provided only that they agreed about what to call the static pointers that they want to exchange.

Statics and existentials

Here is something very reasonable:

data StaticApp b where
  SA :: StaticPtr (a->b) -> StaticPtr a -> StaticApp b

unStaticApp :: StaticApp a -> a
unStaticApp (SA f a) = unStatic f (unStatic a)

(We might want to add more constructors, but I'm going to focus only on SA.) A SA is just a pair of StaticPtrs, one for a function and one for an argument. We can securely unwrap it with unStaticApp.

Now, here is the question: can we serialise StaticApps? Operationally, of course yes: to serialise a SA, just serialise the two StaticPtrs it contains, and dually for deserialisation. But, as before, deserialisation is the hard bit. We seek:

decodeSA :: Typeable b => ByteString -> Maybe (StaticApp b, ByteString)

But how can we write decodeSA? Here is the beginning of an attempt:

decodeSA :: Typeable b => ByteString -> Maybe (StaticApp b, ByteString)
decodeSA bs
  = case decodeStatic bs :: Maybe (StaticPtr (a->b)) of
      Nothing -> Nothing
      Just (fun, bs1) -> ...

and you can immediately see that we are stuck. Type variable b is not in scope. More concretely, we need a Typeable (a->b) to pass in to decodeStatic, but we only have a Typeable b to hand.

What can we do? Tantalisingly, we know that if decodeStatic succeeds in parsing a static StaticName from bs then, when we look up that StaticName in the Static Pointer Table, we'll find a TypeRep for the value. So rather than passing a Typeable dictionary into decodeStatic, we'd like to get one out!

With that in mind, here is a new type signature for decodeStatic that returns both pieces:

data DynStaticPtr where
  DSP :: Typeable a => StaticPtr a -> DynStaticPtr

decodeStatic :: ByteString -> Maybe (DynStaticPtr, ByteString)

(The name DynStaticPtr comes from the fact that this data type is extremely similar to the library definition of Dynamic.)

Operationally, decodeStaticK bs fail cont works like this;

  • Parse a StaticName from bs (failure => return Nothing)
  • Look it up in the SPT (not found => return Nothing)
  • Return the TypeRep and the value found in the SPT, paired up with DSP. (Indeed the SPT could contain the DynStaticPtr values directly.)

For the construction of DynStaticPtr to be type-safe, we need to know that the TypeRep passed really is a TypeRep for the value; so the construction of the SPT is (unsurprisingly) part of the TCB.

Now we can write decodeSA (the monad is just the Maybe monad, nothing fancy):

decodeSA :: forall b. Typeable b => ByteString -> Maybe (StaticApp b, ByteString)
decodeSA bs
  = do { (DSP (fun :: StaticPtr tfun), bs1) <- decodeStatic bs
       ; (DSP (arg :: StaticPtr targ), bs2) <- decodeStatic bs1
            -- At this point we have 
            --     Typeable b      (from caller)
            --     Typeable tfun   (from first DSP)
            --     Typeable targ   (from second DSP)
       ; fun' :: StaticPtr (targ->b) <- cast fun   
       ; return (SA fun' arg, bs2) }

The call to cast needs Typeable tfun, and Typeable (targ->b). The former is bound by the first DSP pattern match. The latter is constructed automatically from Typeable targ and Typeable b, both of which we have. Bingo!

Notice that decodeSA is not part of the TCB. Clients can freely write code like decodeSA and be sure that it is type-safe.

From static pointers to closures

The original Cloud Haskell paper defines closures like this:

data Closure a where
  Clo :: StaticPtr (ByteString -> a) -> ByteString -> Closure a

It is easy to define

unClo :: Closure a -> a
unClo (Clo s e) = unStatic s e

Side note on HdpH

HdpH refines the Cloud Haskell Closure in (at least) two ways. I think (but I am not certain) that this declaration captures the essence:

data Closure a where
  Clo :: StaticPtr (ByteString -> a) -> Put () -> a -> Closure a

The refinements are:

  • The extra argument of type 'a' to avoid costs when we build a closure and then unwrap it with unClo locally, or repeatedly.
  • The use of Put () rather than a ByteString for the serialised environment, to avoid repeated copying when doing nested serialisation.

Both are importnat, but they are orthogonal to the discussion about static types, so I'll use the CH definition from here on.

Serialising closures

Just as in the case of StaticPtr, it is immediately clear that we cannot expect to have

decodeClo :: ByteString -> Maybe (Closure a, ByteString)

Instead we must play the same trick, and attempt to define

data DynClosure where
  DC :: Typeable a => Closure a -> DynClosure

decodeClo :: ByteString -> Maybe (DynClosure, ByteString)

But there's an immediate problem in writing decodeClo:

decodeClo bs
  = do { (DSP (fun :: StaticPtr tfun), bs1) <- decodeStatic bs
       ; (env, bs2)                         <- decodeByteString bs1
       ; return (DC (Clo fun env), bs2) }  -- WRONG

This won't typecheck because DC needs Typeable a, but we only have Typeable (ByteString -> a)`.

This is Jolly Annoying. I can see three ways to make progress:

  • Plan A: Provide some (type-safe) way to decompose TypeReps, to get from Typeable (a->b) to Typeable b (and presumably Typeable a as well).
  • Plan C: Serialise a TypeRep a with every Closure a.
  • Plan C: Generalise StaticPtr

I like Plan C best. They are each discussed next.

Plan A: Decomposing TypeRep

At the moment, GHC provides statically-typed ways to construct and compare a TypeRep (via cast), but no way to decompose one, at least not in a type-safe way. It is tempting to seek this function as part of the TCB:

class Typeable a where
  typeRep :: proxy a -> TypeRep
  decomposeTypeRep :: DecompTR a

data DecompTR a where
  TRApp :: (Typeable p, Typeable q) => DecompTR (p q)
  TRCon :: TyCon -> DecompTR a

This isn't a bad idea, but it does mean that Typeable a must be implemented (and presumably serialised) using a tree, whereas the current API would allow an implementation consisting only of a fingerprint.

(Oct 2014) I now think that Plan A is the right path. See Typeable for a design of Typeable that properly supports it.

(Thought experiment: maybe a Typeable a, and Dict (Typeable a) can be represented as a tree, but a TypeRep could be just a fingerprint?)

Plan B: serialise TypeRep with Closure

Since we need a Typeable a at the far end, we could just serialise it directly with the Closure, like this:

encodeClo :: forall a. Typeable a => Closure a -> ByteString
encodeClo (Clo fun env) 
  =  encodeTypeable (proxy :: a)
  ++ encodeStatic fun
  ++ encodeByteString env

Here I am assuming (as part of the TBC)

encodeTypeable :: Typeable a => proxy a -> ByteString
decodeTypeable :: ByteString -> Maybe (DynTypeable, ByteString)

data DynTypeable where
  DT :: Typeable a => proxy a -> DynTypeable

which serialises a TypeRep. (Or, operationally, perhaps just its fingerprint.) Now I think we can write decodeClo:

decodeClo :: ByteString -> Maybe (DynClosure, ByteString)
decodeClo bs
  = do { (DT (_ :: Proxy a),           bs1)  <- decodeTypeable
       ; (DSP (fun :: StaticPtr tfun), bs2)  <- decodeStatic bs1
       ; (env, bs3)                          <- decodeByteString bs2
       ; fun' :: StaticPtr (ByteString -> a) <- cast fun
       ; return (DC (Clo fun' env), bs2) }  -- WRONG

But this too is annoying: we have to send these extra TypeReps when morally they are already sitting there in the SPT.

Plan C: Generalising StaticPtr

Our difficulty is that we are deserialising StaticPtr (ByteString -> a) but we want to be given Typeable a not Typeable (ByteString -> a). So perhaps we can decompose the type into a type constructor and type argument, like this:

data StaticPtr (f :: *->*) (a :: *)

unStatic :: StaticPtr f a -> f a

decodeStatic :: ByteString -> Maybe (DynStaticPtr, ByteString)

data DynStaticPtr where
  DS :: (Typeable f, Typeable a) => StaticPtr (f a) -> DynStaticPtr

Each row of the SPT contains:

  • The StaticName
  • The value of type f a
  • The Typeable f dictionary
  • The Typeable a dictionary

Now we can define closures thus:

data Closure a where
  Clo :: StaticPtr (ByteString ->) a -> ByteString -> Closure a

and these are easy to deserialise:

decodeClo :: ByteString -> Maybe (DynClosure, ByteString)
decodeClo bs
  = do { (DSP (fun :: StaticPtr f a), bs1) <- decodeStatic bs
       ; (env, bs2)                        <- decodeByteString bs1
           -- Here we have Typeable f, Typeable a

       ; fun' :: StaticPtr (ByteString ->) a <- cast fun
           -- This cast checks that f ~ (ByteString ->)
           -- Needs Typeable f, Typealbe (ByteString ->)

       ; return (DC (Clo fun env), bs2) } 
           -- DC needs Typeable a

I like this a lot better, but it has knock on effects.

  • The old StaticPtr a is now StaticPtr Id a.
  • What becomes of our data type for StaticApply? Perhpas
    data StaticApp f b where
      SA :: StaticPtr f (a->b) -> StaticPtr f b -> StaticApp f b
    unStaticApp :: Applicative => StaticApp f b -> f b

Bottom line: I have not yet followed through all the details, and I think Plan A is better

Applying closures

Can we write closureApply? I'm hoping for a structure like this:

closureApply :: Closure (a->b) -> Closure a -> Closure b
closureApply fun arg = Clo (static caStatic) (fun, arg)

caStatic :: ByteString -> b  -- WRONG
caStatic bs = do { ((fun,arg), bs1) <- decode bs
                 ; return (unClo fun (unClo arg), bs1) }

This is obviously wrong. caStatic clearly cannot have that type. It would at least need to be

caStatic :: Typeable b => ByteString -> b

and now there is the thorny question of where the Typeable b dictionary comes from.

ToDo: ...I have stopped here for now

Polymorphism and serialisation

For this section I'll revert to the un-generalised single-parameter StaticPtr.

Parametric polymorphism

Consider these definitions:

rs1 :: Static ([Int] -> [Int])
rs1 = static reverse

rs2 :: Static ([Bool] -> [Bool])
rs2 = static reverse

rs3 :: forall a. Typeable a => Static ([a] -> [a])
rs3 = static reverse

The first two are clearly fine. The SPT will get one row for each of the two monomorphic calls to reverse, one with a TypeRep of [Int] -> [Int] and one with a TypeRep of [Bool] -> [Bool].

But both will have the same code pointer, namely the code for the polymorpic reverse function. Could we share just one StaticName for all instantiations of reverse, perhaps including rs3 as well?

I think we can. The story would be this:

  • The SPT has a row for reverse, containing
    • The StaticName for reverse
    • A pointer to the code for reverse (or, more precisely, its static closure).
    • A function of type TypeRep -> TypeRep that, given the TypeRep for a returns a TypeRep for [a] -> [a].
  • When we serialise a StaticPtr we send
    • The StaticName of the (polymorphic) function
    • A list of the TypeReps of the type arguments of the function
  • The rule for static <expr> becomes this: the free term variables <expr> must all be top level, but it may have free type variables, provided they are all Typeable.

All of this is part of the TCB, of course.

Type-class polymorphism

Consider static sort where sort :: Ord a => [a] -> [a]. Can we make such a StaticPtr. After all, sort gets an implicit value argument, namely an Ord a dictionary. If that dictionary can be defined at top level, well and good, so this should be OK:

ss1 :: StaticPtr ([Int] -> [Int])
ss1 = static sort

But things go wrong as soon as you have polymorphism:

ss2 :: forall a. Ord a => StaticPtr ([a] -> [a])
ss2 = static sort  -- WRONG

Now, clearly, the dictionary is a non-top-level free variable of the call to sort.

We might consider letting you write this:

ss3 :: forall a. StaticPtr (Ord a => [a] -> [a])
ss3 = static sort   -- ???

so now the static wraps a function expeting a dictionary. But that edges us uncomforatbly close to impredicative types, which is known to contain many dragons.

A simpler alternative is to use the Dict Trick (see Background above):

ss4 :: forall a. StaticPtr (Dict (Ord a) -> [a] -> [a])
ss4 = static sortD

sortD :: forall a. Dict (Ord a) -> [a] -> [a]
sortD Dict xs = sort xs

Now, at the call side, when we unwrap the StaticPtr, we need to supply an explicit Ord dictionary, like this:

...(unStatic ss4 Dict)....

For now, I propose to deal with type classes via the Dict Trick, which is entirely end-user programmable, leaving only parametric polymorphism for built-in support.

  • Posted: 2014-09-11 13:34 (Updated: 2014-10-07 10:43)
  • Author: simonpj
  • Categories: (none)


1. facundo.dominguez -- 2014-10-08 00:51

The rule for static <expr> becomes this: the free term variables <expr> must all be top level, but it may have free type variables, provided they are all Typeable.

If static <expr> must produce an entry in the SPT, the type a needs to be Typeable, or otherwise I don't see how the TypeRep in the SPT will be produced. A function from TypeRep -> TypeRep as explained here wouldn't be possible either.

2. facundo.dominguez -- 2014-10-08 00:56

Hit the submit button accidentally: the type a in the previous comment refers to the type of <expr>.