Case Study: Pointers & Bytes

A large part of the allure of Haskell is its elegant, high-level ADTs that ensure that programs won't be plagued by problems like the infamous SSL heartbleed bug.1 However, another part of Haskell's charm is that when you really really need to, you can drop down to low-level pointer twiddling to squeeze the most performance out of your machine. But of course, that opens the door to the heartbleeds.

Wouldn't it be nice to have our cake and eat it too? Wouldn't it be great if we could twiddle pointers at a low-level and still get the nice safety assurances of high-level types? Lets see how LiquidHaskell lets us have our cake and eat it too.

HeartBleeds in Haskell


Modern Languages like Haskell are ultimately built upon the foundation of C. Thus, implementation errors could open up unpleasant vulnerabilities that could easily slither past the type system and even code inspection. As a concrete example, lets look at a function that uses the ByteString library to truncate strings:

chop' :: String -> Int -> String chop' s n = s' where b = pack s -- down to low-level b' = unsafeTake n b -- grab n chars s' = unpack b' -- up to high-level

First, the function packs the string into a low-level bytestring b, then it grabs the first n Characters from b and translates them back into a high-level String. Lets see how the function works on a small test:

ghci> let ex = "Ranjit Loves Burritos"

We get the right result when we chop a valid prefix:

ghci> chop' ex 10
"Ranjit Lov"

But, as illustrated in Figure 11.1, the machine silently reveals (or more colorfully, bleeds) the contents of adjacent memory or if we use an invalid prefix:

ghci> chop' ex 30
"Ranjit Loves Burritos\NUL\201\&1j\DC3\SOH\NUL"
Figure 11.1: Can we prevent the program from leaking secrets via overflows?


Types against Overflows Now that we have stared the problem straight in the eye, look at how we can use LiquidHaskell to prevent the above at compile time. To this end, we decompose the system into a hierarchy of levels (i.e. modules). Here, we have three levels:

  1. Machine level Pointers
  2. Library level ByteString
  3. User level Application

Our strategy, as before, is to develop an refined API for each level such that errors at each level are prevented by using the typed interfaces for the lower levels. Next, lets see how this strategy lets us safely manipulate pointers.

Low-level Pointer API

To get started, lets look at the low-level pointer API that is offered by GHC and the run-time. First, lets see who the dramatis personae are and how they might let heartbleeds in. Then we will see how to batten down the hatches with LiquidHaskell.


Pointers are an (abstract) type Ptr a implemented by GHC.

-- | A value of type `Ptr a` represents a pointer to an object,
--   or an array of objects, which may be marshalled to or from
--   Haskell values of type `a`.

data Ptr a


Foreign Pointers are wrapped pointers that can be exported to and from C code via the Foreign Function Interface.

data ForeignPtr a


To Create a pointer we use mallocForeignPtrBytes n which creates a Ptr to a buffer of size n and wraps it as a ForeignPtr

mallocForeignPtrBytes :: Int -> ForeignPtr a


To Unwrap and actually use the ForeignPtr we use

withForeignPtr :: ForeignPtr a     -- pointer
               -> (Ptr a -> IO b)  -- action
               -> IO b             -- result

That is, withForeignPtr fp act lets us execute a action act on the actual Ptr wrapped within the fp. These actions are typically sequences of dereferences, i.e. reads or writes.


To Dereference a pointer, i.e. to read or update the contents at the corresponding memory location, we use peek and poke respectively. 2

peek :: Ptr a -> IO a         -- Read
poke :: Ptr a -> a -> IO ()   -- Write


For Fine Grained Access we can directly shift pointers to arbitrary offsets using the pointer arithmetic operation plusPtr p off which takes a pointer p an integer off and returns the address obtained shifting p by off:

plusPtr :: Ptr a -> Int -> Ptr b


Example That was rather dry; lets look at a concrete example of how one might use the low-level API. The following function allocates a block of 4 bytes and fills it with zeros:

zero4 = do fp <- mallocForeignPtrBytes 4 withForeignPtr fp $ \p -> do poke (p `plusPtr` 0) zero poke (p `plusPtr` 1) zero poke (p `plusPtr` 2) zero poke (p `plusPtr` 3) zero return fp where zero = 0 :: Word8

While the above is perfectly all right, a small typo could easily slip past the type system (and run-time!) leading to hard to find errors:

zero4' = do fp <- mallocForeignPtrBytes 4 withForeignPtr fp $ \p -> do poke (p `plusPtr` 0) zero poke (p `plusPtr` 1) zero poke (p `plusPtr` 2) zero poke (p `plusPtr` 8) zero return fp where zero = 0 :: Word8

A Refined Pointer API

Wouldn't it be great if we had an assistant to helpfully point out the error above as soon as we wrote it? 3 We will use the following strategy to turn LiquidHaskell into such an assistant:

  1. Refine pointers with allocated buffer size,
  2. Track sizes in pointer operations,
  3. Enforce pointer are valid at reads and writes.


To Refine Pointers with the size of their associated buffers, we can use an abstract measure, i.e. a measure specification without any underlying implementation.

-- | Size of `Ptr`
measure plen  :: Ptr a -> Int

-- | Size of `ForeignPtr`
measure fplen :: ForeignPtr a -> Int

It is helpful to define aliases for pointers of a given size N:

type PtrN a N        = {v:Ptr a        | plen v  = N}
type ForeignPtrN a N = {v:ForeignPtr a | fplen v = N}


Abstract Measures are extremely useful when we don't have a concrete implementation of the underlying value, but we know that the value exists. Here, we don't have the value -- inside Haskell -- because the buffers are manipulated within C. However, this is no cause for alarm as we will simply use measures to refine the API, not to perform any computations. 4


To Refine Allocation we stipulate that the size parameter be non-negative, and that the returned pointer indeed refers to a buffer with exactly n bytes:

mallocForeignPtrBytes :: n:Nat -> ForeignPtrN a n


To Refine Unwrapping we specify that the action gets as input, an unwrapped Ptr whose size equals that of the given ForeignPtr.

withForeignPtr :: fp:ForeignPtr a
               -> (PtrN a (fplen fp) -> IO b)
               -> IO b

This is a rather interesting higher-order specification. Consider a call withForeignPtr fp act. If the act requires a Ptr whose size exceeds that of fp then LiquidHaskell will flag a (subtyping) error indicating the overflow. If instead the act requires a buffer of size less than fp then it is always safe to run the act on a larger buffer. For example, the below variant of zero4 where we only set the first three bytes is fine as the act, namely the function \p -> ..., can be typed with the requirement that the buffer p has size 4, even though only 3 bytes are actually touched.

zero3 = do fp <- mallocForeignPtrBytes 4 withForeignPtr fp $ \p -> do poke (p `plusPtr` 0) zero poke (p `plusPtr` 1) zero poke (p `plusPtr` 2) zero return fp where zero = 0 :: Word8


To Refine Reads and Writes we specify that they can only be done if the pointer refers to a non-empty (remaining) buffer. That is, we define an alias:

type OkPtr a = {v:Ptr a | 0 < plen v}

that describes pointers referring to non-empty buffers (of strictly positive plen), and then use the alias to refine:

peek :: OkPtr a -> IO a
poke :: OkPtr a -> a -> IO ()

In essence the above type says that no matter how arithmetic was used to shift pointers around, when the actual dereference happens, the size remaining after the pointer must be non-negative, so that a byte can be safely read from or written to the underlying buffer.


To Refine the Shift operations, we simply check that the pointer remains within the bounds of the buffer, and update the plen to reflect the size remaining after the shift: 5

plusPtr :: p:Ptr a -> off:BNat (plen p) -> PtrN b (plen p - off)

using the alias BNat, defined as:

type BNat N = {v:Nat | v <= N}

6


Types Prevent Overflows Lets revisit the zero-fill example from above to understand how the refinements help detect the error:

exBad = do fp <- mallocForeignPtrBytes 4 withForeignPtr fp $ \p -> do poke (p `plusPtr` 0) zero poke (p `plusPtr` 1) zero poke (p `plusPtr` 2) zero poke (p `plusPtr` 5) zero -- LH complains return fp where zero = 0 :: Word8

Lets read the tea leaves to understand the above error:

  Error: Liquid Type Mismatch
   Inferred type
     VV : {VV : Int | VV == ?a && VV == 5}

   not a subtype of Required type
     VV : {VV : Int | VV <= plen p}

   in Context
     zero : {zero : Word8 | zero == ?b}
     VV   : {VV : Int | VV == ?a && VV == (5  :  int)}
     fp   : {fp : ForeignPtr a | fplen fp == ?c && 0 <= fplen fp}
     p    : {p  : Ptr a | fplen fp == plen p && ?c <= plen p && ?b <= plen p && zero <= plen p}
     ?a   : {?a : Int | ?a == 5}
     ?c   : {?c : Int | ?c == 4}
     ?b   : {?b : Integer | ?b == 0}

The error says we're bumping p up by VV == 5 using plusPtr but the latter requires that bump-offset be within the size of the buffer referred to by p, i.e. VV <= plen p. Indeed, in this context, we have:

     p    : {p : Ptr a | fplen fp == plen p && ?c <= plen p && ?b <= plen p && zero <= plen p}
     fp   : {fp : ForeignPtr a | fplen fp == ?c && 0 <= fplen fp}

that is, the size of p, namely plen p equals the size of fp, namely fplen fp (thanks to the withForeignPtr call). The latter equals to ?c which is 4 bytes. Thus, since the offset 5 is not less than the buffer size 4, LiquidHaskell cannot prove that the call to plusPtr is safe, hence the error.

Assumptions vs Guarantees

At this point you ought to wonder: where is the code for peek, poke or mallocForeignPtrBytes and so on? How can we be sure that the types we assigned to them are in fact legitimate?


Frankly, we cannot as those functions are externally implemented (in this case, in C), and hence, invisible to the otherwise all-seeing eyes of LiquidHaskell. Thus, we are assuming or trusting that those functions behave according to their types. Put another way, the types for the low-level API are our specification for what low-level pointer safety. We shall now guarantee that the higher level modules that build upon this API in fact use the low-level function in a manner consistent with this specification.


Assumptions are a Feature and not a bug, as they let us to verify systems that use some modules for which we do not have the code. Here, we can assume a boundary specification, and then guarantee that the rest of the system is safe with respect to that specification. 7

ByteString API

Next, lets see how the low-level API can be used to implement to implement ByteStrings, in a way that lets us perform fast string operations without opening the door to overflows.


A ByteString is implemented as a record of three fields:

data ByteString = BS { bPtr :: ForeignPtr Word8 , bOff :: !Int , bLen :: !Int }
  • bPtr is a pointer to a block of memory,
  • bOff is the offset in the block where the string begins,
  • bLen is the number of bytes from the offset that belong to the string.

These entities are illustrated in Figure 11.2; the green portion represents the actual contents of a particular ByteString. This representation makes it possible to implement various operations like computing prefixes and suffixes extremely quickly, simply by pointer arithmetic.

Figure 11.2: Representing ByteStrings in memory.


In a Legal ByteString the start (bOff) and end (bOff + bLen) offsets lie inside the buffer referred to by the pointer bPtr. We can formalize this invariant with a data definition that will then make it impossible to create illegal ByteStrings:

{-@ data ByteString = BS { bPtr :: ForeignPtr Word8 , bOff :: {v:Nat| v <= fplen bPtr} , bLen :: {v:Nat| v + bOff <= fplen bPtr} } @-}

The refinements on bOff and bLen correspond exactly to the legality requirements that the start and end of the ByteString be within the block of memory referred to by bPtr.


For brevity lets define an alias for ByteStrings of a given size:

{-@ type ByteStringN N = {v:ByteString | bLen v = N} @-}


Legal Bytestrings can be created by directly using the constructor, as long as we pass in suitable offsets and lengths. For example,

{-@ good1 :: IO (ByteStringN 5) @-} good1 = do fp <- mallocForeignPtrBytes 5 return (BS fp 0 5)

creates a valid ByteString of size 5; however we need not start at the beginning of the block, or use up all the buffer, and can instead create ByteStrings whose length is less than the size of the allocated block, as shown in good2 whose length is 2 while the allocated block has size 5.

{-@ good2 :: IO (ByteStringN 2) @-} good2 = do fp <- mallocForeignPtrBytes 5 return (BS fp 3 2)


Illegal Bytestrings are rejected by LiquidHaskell. For example, bad1's length is exceeds its buffer size, and is flagged as such:

bad1 = do fp <- mallocForeignPtrBytes 3 return (BS fp 0 10)

Similarly, bad2 does have 2 bytes but not if we start at the offset of 2:

bad2 = do fp <- mallocForeignPtrBytes 3 return (BS fp 2 2)


Measures are generated from Fields in the datatype definition. As GHC lets us use the fields as accessor functions, we can refine the types of those functions to specify their behavior to LiquidHaskell. For example, we can type the (automatically generated) field-accessor function bLen so that it actually returns the exact size of the ByteString argument.

{-@ bLen :: b:ByteString -> {v: Nat | v = bLen b} @-}


To Safely Create a ByteString the implementation defines a higher order create function, that takes a size n and accepts a fill action, and runs the action after allocating the pointer. After running the action, the function tucks the pointer into and returns a ByteString of size n.

{-@ create :: n:Nat -> (Ptr Word8 -> IO ()) -> ByteStringN n @-} create n fill = unsafePerformIO $ do fp <- mallocForeignPtrBytes n withForeignPtr fp fill return (BS fp 0 n)


Exercise: (Create): Why does LiquidHaskell reject the following function that creates a ByteString corresponding to "GHC"?



bsGHC = create 3 $ \p -> do poke (p `plusPtr` 0) (c2w 'G') poke (p `plusPtr` 1) (c2w 'H') poke (p `plusPtr` 2) (c2w 'C')

Hint: The function writes into 3 slots starting at p. How big should plen p be to allow this? What type does LiquidHaskell infer for p above? Does it meet the requirement? Which part of the specification or implementation needs to be modified so that the relevant information about p becomes available within the do-block above? Make sure you figure out the above before proceeding.


To Pack a String into a ByteString we simply call create with the appropriate fill action:8

pack str = create' n $ \p -> go p xs where n = length str xs = map c2w str go p (x:xs) = poke p x >> go (plusPtr p 1) xs go _ [] = return ()


Exercise: (Pack): We can compute the size of a ByteString by using the function: Fix the specification for pack so that (it still typechecks!) and furthermore, the following QuickCheck style property is proved.



{-@ prop_pack_length :: String -> TRUE @-} prop_pack_length xs = bLen (pack xs) == length xs

Hint: Look at the type of length, and recall that len is a numeric measure denoting the size of a list.


The magic of inference ensures that pack just works. Notice there is a tricky little recursive loop go that is used to recursively fill in the ByteString and actually, it has a rather subtle type signature that LiquidHaskell is able to automatically infer.


Exercise: (Pack Invariant): Still, we're here to learn, so can you write down the type signature for the loop so that the below variant of pack is accepted by LiquidHaskell (Do this without cheating by peeping at the type inferred for go above!)



packEx str = create' n $ \p -> pLoop p xs where n = length str xs = map c2w str {-@ pLoop :: (Storable a) => p:Ptr a -> xs:[a] -> IO () @-} pLoop p (x:xs) = poke p x >> pLoop (plusPtr p 1) xs pLoop _ [] = return ()

Hint: Remember that len xs denotes the size of the list xs.


Exercise: (Unsafe Take and Drop): The functions unsafeTake and unsafeDrop respectively extract the prefix and suffix of a ByteString from a given position. They are really fast since we only have to change the offsets. But why does LiquidHaskell reject them? Can you fix the specifications so that they are accepted?



{-@ unsafeTake :: n:Nat -> b:_ -> ByteStringN n @-} unsafeTake n (BS x s _) = BS x s n {-@ unsafeDrop :: n:Nat -> b:_ -> ByteStringN {bLen b - n} @-} unsafeDrop n (BS x s l) = BS x (s + n) (l - n)

Hint: Under what conditions are the returned ByteStrings legal?


To Unpack a ByteString into a plain old String, we essentially run pack in reverse, by walking over the pointer, and reading out the characters one by one till we reach the end:

unpack :: ByteString -> String unpack (BS _ _ 0) = [] unpack (BS ps s l) = unsafePerformIO $ withForeignPtr ps $ \p -> go (p `plusPtr` s) (l - 1) [] where {-@ go :: p:_ -> n:_ -> acc:_ -> IO {v:_ | true } @-} go p 0 acc = peekAt p 0 >>= \e -> return (w2c e : acc) go p n acc = peekAt p n >>= \e -> go p (n-1) (w2c e : acc) peekAt p n = peek (p `plusPtr` n)


Exercise: (Unpack): Fix the specification for unpack so that the below QuickCheck style property is proved by LiquidHaskell.



{-@ prop_unpack_length :: ByteString -> TRUE @-} prop_unpack_length b = bLen b == length (unpack b)

Hint: You will also have to fix the specification of the helper go. Can you determine the output refinement should be (instead of just true?) How big is the output list in terms of p, n and acc.

Application API

Finally, lets revisit our potentially "bleeding" chop function to see how the refined ByteString API can prevent errors. We require that the prefix size n be less than the size of the input string s:

{-@ chop :: s:String -> n:BNat (len s) -> String @-} chop s n = s' where b = pack s -- down to low-level b' = unsafeTake n b -- grab n chars s' = unpack b' -- up to high-level


Overflows are prevented by LiquidHaskell, as it rejects calls to chop where the prefix size is too large which is what led to the overflow that spilled the contents of memory after the string (cf. Figure 11.1). In the code below, the first use of chop which defines ex6 is accepted as 6 <= len ex but the second call is rejected as 30 > len ex.

demo = [ex6, ex30] where ex = ['L','I','Q','U','I','D'] ex6 = chop ex 6 -- accepted by LH ex30 = chop ex 30 -- rejected by LH

Fix the specification for chop so that the following property is proved:

{-@ prop_chop_length :: String -> Nat -> TRUE @-} prop_chop_length s n | n <= length s = length (chop s n) == n | otherwise = True


Exercise: (Checked Chop): In the above, we know statically that the string is longer than the prefix, but what if the string and prefix are obtained dynamically, e.g. as inputs from the user? Fill in the implementation of ok below to ensure that chop is called safely with user specified values:



safeChop :: String -> Int -> String safeChop str n | ok = chop str n | otherwise = "" where ok = True queryAndChop :: IO String queryAndChop = do putStrLn "Give me a string:" str <- getLine putStrLn "Give me a number:" ns <- getLine let n = read ns :: Int return $ safeChop str n

Nested ByteStrings

For a more in-depth example, let's take a look at group, which transforms strings like "foobaaar" into lists of strings like ["f","oo", "b", "aaa", "r"]. The specification is that group should produce a

  1. list of non-empty ByteStrings,
  2. the sum of whose lengths equals that of the input string.


Non-empty ByteStrings are those whose length is non-zero:

{-@ predicate Null B = bLen B == 0 @-} {-@ type ByteStringNE = {v:ByteString | not (Null v)} @-}

We can use these to enrich the API with a null check

{-@ null :: b:_ -> {v:Bool | v <=> Null b} @-} null (BS _ _ l) = l == 0

This check is used to determine if it is safe to extract the head and tail of the ByteString. we can use refinements to ensure the safety of the operations and also track the sizes. 9

{-@ unsafeHead :: ByteStringNE -> Word8 @-} unsafeHead (BS x s _) = unsafePerformIO $ withForeignPtr x $ \p -> peekByteOff p s {-@ unsafeTail :: b:ByteStringNE -> ByteStringN {bLen b -1} @-} unsafeTail (BS ps s l) = BS ps (s + 1) (l - 1)


The Group` function recursively calls spanByte to carve off the next group, and then returns the accumulated results:

{-@ group :: b:_ -> {v: [ByteStringNE] | bsLen v = bLen b} @-} group xs | null xs = [] | otherwise = let y = unsafeHead xs (ys, zs) = spanByte y (unsafeTail xs) in (y `cons` ys) : group zs

The first requirement, that the groups be non-empty is captured by the fact that the output is a [ByteStringNE]. The second requirement, that the sum of the lengths is preserved, is expressed by a writing a numeric measure:

{-@ measure bsLen @-} bsLen :: [ByteString] -> Int bsLen [] = 0 bsLen (b:bs) = bLen b + bsLen bs


SpanByte does a lot of the heavy lifting. It uses low-level pointer arithmetic to find the first position in the ByteString that is different from the input character c and then splits the ByteString into a pair comprising the prefix and suffix at that point.

{-@ spanByte :: Word8 -> b:ByteString -> ByteString2 b @-} spanByte c ps@(BS x s l) = unsafePerformIO $ withForeignPtr x $ \p -> go (p `plusPtr` s) 0 where go p i | i >= l = return (ps, empty) | otherwise = do c' <- peekByteOff p i if c /= c' then return $ splitAt i else go p (i+1) splitAt i = (unsafeTake i ps, unsafeDrop i ps)

LiquidHaskell infers that 0 <= i <= l and therefore that all of the memory accesses are safe. Furthermore, due to the precise specifications given to unsafeTake and unsafeDrop, it is able to prove that the output pair's lengths add up to the size of the input ByteString.

{-@ type ByteString2 B = {v:_ | bLen (fst v) + bLen (snd v) = bLen B} @-}

Recap: Types Against Overflows

In this chapter we saw a case study illustrating how measures and refinements enable safe low-level pointer arithmetic in Haskell. The take away messages are that we can:

  1. compose larger systems from layers of smaller ones,
  2. refine APIs for each layer, which can be used to
  3. design and validate the layers above.

We saw this recipe in action by developing a low-level Pointer API, using it to implement fast ByteStrings API, and then building some higher-level functions on top of the ByteStrings.


The Trusted Computing Base in this approach includes exactly those layers for which the code is not available, for example, because they are implemented outside the language and accessed via the FFI as with mallocForeignPtrBytes and peek and poke. In this case, we can make progress by assuming the APIs hold for those layers and verify the rest of the system with respect to that API. It is important to note that in the entire case study, it is only the above FFI signatures that are trusted; the rest are all verified by LiquidHaskell.


  1. Assuming, of course, the absence of errors in the compiler and run-time...

  2. We elide the Storable type class constraint to strip this presentation down to the absolute essentials.

  3. In Vim or Emacs or online, you'd see the error helpfully highlighted.

  4. This is another ghost specification.

  5. This signature precludes left or backward shifts; for that there is an analogous minusPtr which we elide for simplicity.

  6. Did you notice that we have strengthened the type of plusPtr to prevent the pointer from wandering outside the boundary of the buffer? We could instead use a weaker requirement for plusPtr that omits this requirement, and instead have the error be flagged when the pointer was used to read or write memory.

  7. If we so desire, we can also check the boundary specifications at run-time, but that is outside the scope of LiquidHaskell.

  8. The code uses create' which is just create with the correct signature in case you want to skip the previous exercise. (But don't!)

  9. peekByteOff p i is equivalent to peek (plusPtr p i).