10 February 2021 — by Divesh Otwani, Utku Demir
linear-base makes writing Linear Haskell easy and fun
haskelllinear-types

We’re announcing linear-base, a standard library for Linear Haskell programs. Our release accompanies the release of GHC 9.0 which supports -XLinearTypes. Linear base has been written by Bhavik Mehta, a former Tweag intern, Arnaud Spiwack, and ourselves.

In the spirit of a standard library, linear-base is not a strict replica of base with linearly-typed variants of all the facilities in base. Instead, linear-base focuses on the abstractions one naturally needs and desires when programming with linear types.

It does include some linear variants from base, but the library ranges from mutable data structures with a pure API to a resource-safe I/O monad, to linear-streams. It’s a “base” library, a helpful prelude to programming using -XLinearTypes.

Of course this raises the question, what does a linear Haskell program look like? And, how does linear-base provide what we need and what we want to write one?

Envisioning Linear Haskell Programs

If you’re unfamiliar with -XLinearTypes, you can learn more by browsing our examples and README. At a bare-bones level, linear types simply provide some further properties that a function declared with a signature like f :: A %1-> B must satisfy. Namely, to type-check the body of f, the A must be consumed exactly once. We are then able to leverage this type-checking power to write functions that would have been unsafe to write before (e.g., a pure interface to mutable data structures) or provide alternative APIs to existing ones that place an obligation on the programmer to ensure they avoid certain errors (such as reading from a closed file handle). For more information about how -XLinearTypes works see our earlier posts.

There are two main families of motivations for this additional type-checking discussed in the Linear Haskell paper. First, we can write pure APIs for mutable data structures such as arrays. As discussed in the paper, this approach is sometimes more convenient to work with than using the ST monad, and even makes unsafeFreeze safe.

Second, -XLinearTypes enables us to type-check usage protocols. An example discussed in the paper is the protocol of file handles, namely, that file handles must be closed and then cannot be written to or read from1.

Thus, a typical linear program would likely be one that

  • is mostly pure, but has a piece of state to use throughout. Using linear types avoids that an ST monad invades the larger, pure, part of the program
  • is resource-heavy and requires a non-trivial amount of reasoning on the part of the programmer to ensure resource protocols are upheld.

With this in mind, we can envision a standard library as one that has the linear gadgets we want, like pure-interfaced mutable data structures and resource-safe APIs, and the utilities we need, like a linear ($), to write a typical linear program.

What we want: linear abstractions or use-cases!

  • linear-base comes equipped with a pure API for mutable arrays, vectors, hashmaps and sets. These enable us to write a mutable implementation of quicksort in a few lines:
  quicksort :: Array Int %1-> Array Int
  quicksort arr = Array.size arr & \case
    (arr', Ur len) -> go 0 (len-1) arr'

  go :: Int -> Int -> Array Int %1-> Array Int
  go lo hi arr = case lo >= hi of
    True -> arr
    False -> Array.read arr lo & \case
      (arr0, Ur pivot) -> partition arr0 pivot lo hi & \case
        (arr1, Ur ix) -> swap arr1 lo ix & \case
          arr2 -> go lo ix arr2 & \case
            arr3 -> go (ix+1) hi arr3

  partition :: Array Int %1-> Int -> Int -> Int -> (Array Int, Ur Int)
  partition arr pivot lx rx
    | (rx < lx) = (arr, Ur rx)
    | otherwise = Array.read arr lx & \case
        (arr1, Ur lVal) -> Array.read arr1 rx & \case
          (arr2, Ur rVal) -> case (lVal <= pivot, pivot < rVal) of
            (True, True) -> partition arr2 pivot (lx+1) (rx-1)
            (True, False) -> partition arr2 pivot (lx+1) rx
            (False, True) -> partition arr2 pivot (lx-1) (rx-1)
            (False, False) -> swap arr2 lx rx & \case
              arr3 -> partition arr3 pivot (lx+1) (rx-1)

This code reads rather like an imperative program, where arr is updated through arr, arr1, arr2 and so on. Compared to using the ST monad, we lose the ability to share the effect of mutations, in exchange we gain a pure interface, which can be less invasive.

  • linear-base has a resource-safe File I/O API that ensures that file handles, for instance, are closed and then no longer used.
  • linear-base includes a linear variant of the streaming library, which is compatible with the resource-safe I/O monad, to ensure that resources accessed in the monadic layers of streams have their protocols obeyed and that the protocols of streams themselves are enforced. If the effects in streams can be repeated more than once, we could, say, repeat the effect of reading from a file handle after that handle is closed. Hence, we use control monads inside linear streams to ensure monadic effects are performed exactly once. This is based on the work of Edvard Hübinette, for the Haskell Summer of Code of 2018.
  • In order to define such resource-safe protocols, linear-base provides control monads and related monadic functions like foldM.

What we need: linear utilities!

Of course, linear-base includes various abstractions that many linear programs will end up using, namely:

  • Variants of base abstractions like a linear Num, linear Functors (in two flavors), a linear Data.List API, and linear versions of standard Prelude functions like ($).

    We need these because functions as simple as

  f :: Int %1-> Int %1-> Int
  f a b = (a * 4) + b

will only type-check if (*) and (+) have linear arrows. Similarly, using standard abstractions from base, like functors, ($), map, foldl, will not work inside many functions that have linear arguments.

As a special note, we use a linear (&) for a workaround to the current limitation that all case statements consume the scrutinee (the x in case x of) unrestrictedly. See the user guide for more.

  • Mechanisms to interface linear and non-linear code: linear-base comes with Ur, which stands for unrestricted and lets you manipulate a non-linear value in a linear context. Hence, a function f :: Ur a %1-> b can use the a unrestrictedly after pattern matching on (Ur x). Alongside this, linear-base comes with the classes Consumable, Dupable and Movable which allow non-linear use of linearly-bound values; one can consume, duplicate (possibly with dup2 :: a %1-> (a,a)) or, move a linearly bound value.
  consume :: Consumable a => a %1-> ()
  dup2 :: Dupable a => a %1-> (a,a)
  move :: Movable a => a %1-> Ur a

These are used throughout linear-base itself and are likely to show up in linearly typed programs. For instance, the linearly-typed streaming function chain has the following type

  chain :: forall a m r y . (Control.Monad m, Consumable y) =>
    (a -> m y) -> Stream (Of a) m r %1-> Stream (Of a) m r

because the y must be discarded as the monadic effect is chained after each a in the stream.

Advanced abstractions & sneak peeks

Finally, linear-base has several features still in the works. Please note that some of these features like non-GC memory allocation, destination arrays and push-pull arrays are still very experimental and likely to change.

  • Linear optics are optics re-designed to work in linear contexts.
  • Non-GC memory allocation. We can use linear types to enforce the protocols for using memory outside of GHC’s garbage collector and on the system heap, i.e., that we allocate before use, necessarily free and do not use after that. Hence, the GC has less work to do and we as programmers have the control over some allocation which could impact the performance of our program.
  • Destination arrays. Destination arrays, provide a way to write code in destination-passing-style. This lets us decide when we allocate space for a write-only array that’s threaded throughout our program. If we instead had just used a vector, we might not have had all the fusion we’d like and might have had extra allocations which impact memory use and performance.
  • Push-pull arrays. We can use linear-types to represent polarized arrays. This enables us to provide a vector-like API but explicitly control when allocation occurs. With the existing vector library, one is often relying on array fusion to avoid unnecessary allocations, but it can be hard to predict when array fusion occurs. Polarized arrays can be either output-friendly (a push array) or input-friendly (a pull array) and neither form allocates. Only when a regular array is needed does one explicitly allocate. So, controlling allocation is done by the programmer, not the compiler.

Community first

Our goal with linear-base is to make it easy and fun for the community to write Linear Haskell programs. The first release is available on Hackage and comes with examples from the repository, and, in addition to the haddock, a short user guide. Please feel welcome to point out bugs or request features. To check out the latest update, see our GitHub repository.


  1. Of course, these are not the only uses, though many use-cases of linear types can be seen as a combination of these two aspects. Notably, computations on serialized data could be represented with an API similar to that of mutable arrays, with a usage protocol layered on top; the API ensures a legal and complete write to a memory block that has a serialized representation of some data type.

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