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20 September 2022 — by Mahmoud Mazouz
Optimizing Nickel's Array Contracts
nickelinternship

Nickel is a gradually-typed, purely functional configuration language with contracts and lazy evaluation.

My internship at Tweag consisted of (attempts at) performance improvements in the Nickel reference interpreter. In this article, I will describe what I think is the most interesting problem I had on my hands: array operations like head were sometimes running in linear time instead of constant time.

What do I mean by “sometimes”? Well, to answer that, we need some familiarity with contract application and lazy evaluation.

Contract application

Contracts are a key feature of Nickel that empowers you to write correct configurations in a flexible way by extending the type system with your custom dynamically-checked properties. Thus you can write types for TCP ports, email addresses, or even the Cargo Manifest format, using runtime checks on your data.

Prime numbers are cool. Let’s write a contract for them1:

let Prime = fun label value =>
  if is_prime value then value
  else contract.blame_with label "not a prime number"

An expression such as 42 | Prime will expectedly fail, i.e. the interpreter will run the “function” Prime on the blame label, a special value containing error-reporting information, and the value 42. This is syntactic sugar — before evaluation, this expression will be transformed into contract.apply Prime label 42.

For arrays, we can use the constructor Array and write [3, 19] | Array Prime to enforce the prime number contract on all elements of the array. In this case, the expression will be roughly transformed into:

array.map (contract.apply Prime label) [3, 19]

This is not completely accurate: the interpreter uses unique labels for each element to avoid blaming the entire array for a contract violation, as that would result in poor error messages.

At this point, you can already see where the linear behavior might come from. Since evaluating:

array.head (array.map (contract.apply Prime label) [3, 19])

will involve two contract applications, instead of one. The argument of array.head will first be evaluated to [3 | Prime, 19 | Prime], meaning that Prime will be applied on both 3 and 19. Only then can we retrieve 3 | Prime.

This effect gets amplified for recursive functions guarded by an array contract, such as:

let rec product
  | Array Prime -> Num
  = fun ps =>
    if array.length ps == 0 then 1
    else array.head ps * product (array.tail ps)

Here, every recursive call will apply the Array Prime contract to the tail of the input array. Consequently, every call to product will be done in linear time, making the full operation quadratic.

Unfortunately, this reasoning doesn’t completely explain the observed behavior, because Nickel is lazy.

Lazy evaluation

During evaluation, Nickel expressions are put behind thunks. Thunks are mutable memory locations that initially hold unevaluated expressions, and are only updated with evaluation results if some part of the program forces them.

This means that evaluating:

let ps = [3, 9 + 10] | Array Prime in array.head ps

will mean mapping Prime over [3, 9 + 10] to get something that resembles [3 | Prime, (9 + 10) | Prime]. Next, 3 | Prime would be extracted and evaluated.

Hence the evaluation result will be 3 and (9 + 10) | Prime won’t be computed. In fact, one could replace 9 + 10 with a computation which never succeeds, such as 0 / 0, and the above snippet will still evaluate to 3.

Thanks to lazy evaluation, array contracts are mapped in linear time but the resulting contract applications are not evaluated unless they’re needed. If you wish to force the entire array to be fully evaluated, you can use builtin.deep_seq. This special function will make sure that the thunk behind each of the array’s elements is updated.

A solution

Instead of mapping contract application on arrays, the interpreter should make the array hold on to its contract, and only apply it when data leaves the array. This came in the form of a new internal operation which I will refer to as contract.lazy_apply. This means that our [3, 19] | Array Prime example will be equivalent to:

contract.lazy_apply Prime label [3, 19]

This time, array.head ([3, 19] | Prime) will return contract.apply Prime 3 in constant time, even if the thunk corresponding to the array had never been updated before.

After refactoring the interpreter to use the new machinery, I realized that builtin.deep_seq was subtly broken. Given arbitrary terms x and y, builtin.deep_seq x y recursively traverses all the thunks of x so that nested records and arrays will be fully evaluated. Once that’s done, builtin.deep_seq makes the interpreter resume normal evaluation of y.

To preserve the semantics of array contracts, any pending contract should be applied during the builtin.deep_seq operation. At first, I made it so that when builtin.deep_seq is called on an array, the interpreter will evaluate each element with the array’s contract applied to it. This worked in the majority of cases, except for record contracts.

The problem with record contracts was that, under certain conditions2, they have to clone their thunks. Which led to cases where calling builtin.deep_seq on a record with a contract applied, such as { x = y + 1, y = 1 } | { x | Num, y | Num }, updated the newly cloned thunks and not the original thunks.

Therefore, in some cases builtin.deep_seq x y left x with unevaluated thunks: x doesn’t “see” the cloned thunks. This isn’t the desired behaviour. Furthermore, serialization functions to JSON and friends, as well as the pretty-printer in the REPL assume that they are given values without thunks, which I couldn’t guarantee anymore.

To address this, I introduced a new internal operator.

Yet another operator

Because of how record contracts work, applying a contract to an arbitrary term may yield a version of said term where some thunks have been cloned. And so given a term t, when builtin.deep_seq t t recursively evaluates arrays with their contracts mapped, some contract application results will not be reflected in t as they live in cloned thunks.

This is where a new internal unary operation comes into the picture: builtin.force.

How it works, is that builtin.force t not only evaluates t, but also returns a new copy of t where everything is guaranteed to be evaluated. In particular, when t is an array or records, builtin.force t will return a new array filled with the records’ (evaluated) cloned thunks, rather than the original, unevaluated thunks.

Future opportunities

Because array contracts are now saved in a pending state for later application, it’s possible to eliminate duplicates using a limited notion of contract equality. I say limited because the terms inside a contract can be arbitrarily complex. Still, it might be worth the effort to optimize for the common cases such as name aliases, and the Nickel Team recently made some headway towards deciding contract equality in many of those cases.

Benchmarks

It turns out that this is one of those cases where the obtained performance improvement is significant. Let’s write a function for computing array slices by generating a range of indices from a from index and to index. For simplicity’s sake, an empty array is returned if the provided range is invalid.

let slice
  | Num -> Num -> Array Num -> Array Num
  = fun from to xs =>
    if to < array.length xs && from >= 0 && from <= to then
      let range = array.generate ((+) from) (to - from)
      in array.map (fun idx => array.elem_at idx xs) range
    else []

I ran slice 200 800 on an array of 1000 elements and obtained the following results, courtesy of the excellent command-line tool hyperfine:

Version Mean [ms] Min [ms] Max [ms] Relative
Without array.lazy_apply 618.9 ± 21.2 601.3 670.1 7.59 ± 0.36
With array.lazy_apply 81.6 ± 2.6 78.8 94.5 1.00

  1. A more idiomatic way of writing this contract is: contract.from_predicate is_prime. Of course, the two styles are equivalent.
  2. This is due to the interaction between Nickel’s merging primitive with recursive records. As documented in this Pull Request
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