Inside 206-105

Existential Pontification and Generalized Abstract Digressions

HotOS “Unconference” report:
Verifying Systems

Ariel Rabkin has some code he'd like to verify, and at this year’s HotOS he appealed to participants of one “unconference” (informal breakout sessions to discuss various topics) to help him figure out what was really going on as far as formal verification went.

He had three questions: "What can we verify? What is impossible to verify? How can we tell that the verification is correct?" They seemed like impossibly large questions, so we drilled in a little bit, and found that Ariel had the very understandable question, "Say I have some C++ code implementing a subtle network protocol, and I'd like to prove that the protocol doesn't deadlock; how do I do that?"

I wish the formal verification community had a good answer to a question like this, but unfortunately we don't. The largest verification projects include things like verified kernels, which are written in fully specified subsets of C; which assume the translation performed by the compiler is correct, formalize C in a theorem prover, and then verify there. This is the "principled approach". It's just not feasible to take C or C++ in its entirety and try to formalize it; it's too complicated and too ill-specified. The easiest thing to do is formalize a small fragment of your algorithm and then make a hand-wavy argument that your implementation is adequate.

Martin Abadi remarked that before you embark on a verification project, you have to figure out where you'll get the most bang for your buck. Most of the time, a formalization won't get you "full correctness"; the "electrons may be faulty", as the case may be. But even a flawed verification forces you to state your assumptions explicitly, which is a good thing.

We then circled around to the subject of, well, what can be verified. Until the 90s, the formal verification community limited itself to only complete and sound analyses—and failed. The relaxation of this restriction lead to a renaissance of formal verification work. We talked about who was using formal verification, and the usual suspects showed up: safety critical software, cache coherence protocols (but one participant remarked that this was only a flash in the pan, as far as applications goes—he asserted that these companies are likely not going to use these methods any longer in the future), etc. Safety critical software is also likely to use coprocessors (since hardware failure is a very real issue), but Gernot Heiser noted that these folks are trying to get away from physical separation: it is expensive in terms of expense, weight and energy. Luckily, the costs of verification, as he recounted, are within a factor of two of normal industrial assurance, and half the cost of military assurance (though, he cautioned that this was for a specific project, and for a specific size of code.) He also remarked that as far as changes to code requiring changes to the proofs, the changes in the proofs seemed to be linear in the complexity (conceptual or implementation-wise) of the change, which is a good sign!

Well, supposing that you decide that you actually want to verify your software, how do you go about doing it? Unfortunately, it takes a completely different set of skills to build verified software versus normal software. Everyone agreed, "Yes, you need to hire a formal methods guy" if you're going to make any progress. But that's just not enough. The formal methods guy has to talk to the systems guy. Heiser recounted a very good experience hiring a formal methods person who was able to communicate with the other systems researchers working on the project; without this line of communication, he said, the project likely would have failed. And he mentioned another project, which had three times as much funding, but didn't accomplish nearly as much their team had. (Names not mentioned to protect the guilty.)

In the end, it seemed that we didn’t manage to give Ari a quite satisfactory answer. As one participant said, “You’ll probably learn the most by just sitting down and trying to formalize the thing you are interested in.” This is probably true, though I fear most will be scared off by the realization of how much work it actually takes to formalize software.

Hey guys, I’m liveblogging HotOS at my research Tumblr. The posts there are likely to be more fragmented than this, but if people are interested in any particular topics I can inflate them into full posts.

  • May 14, 2013

Category theory for loop optimizations

Christopher de Sa and I have been working on a category theoretic approach to optimizing MapReduce-like pipelines. Actually, we didn’t start with any category theory—we were originally trying to impose some structure on some of the existing loop optimizations that the Delite compiler performed, and along the way, we rediscovered the rich relationship between category theory and loop optimization.

On the one hand, I think the approach is pretty cool; but on the other hand, there’s a lot of prior work in the area, and it’s tough to figure out where one stands on the research landscape. As John Mitchell remarked to me when I was discussing the idea with him, “Loop optimization, can’t you just solve it using a table lookup?” We draw a lot of inspiration from existing work, especially the program calculation literature pioneered by Bird, Meertens, Malcom, Meijer and others in the early 90s. The purpose of this blog post is to air out some of the ideas we’ve worked out and get some feedback from you, gentle reader.

There are a few ways to think about what we are trying to do:

  • We would like to implement a calculational-based optimizer, targeting a real project (Delite) where the application of loop optimizations can have drastic impacts on the performance of a task (other systems which have had similar goals include Yicho, HYLO).
  • We want to venture where theorists do not normally tread. For example, there are many “boring” functors (e.g. arrays) which have important performance properties. While they may be isomorphic to an appropriately defined algebraic data type, we argue that in a calculational optimizer, we want to distinguish between these different representations. Similarly, many functions which are not natural transformations per se can be made to be natural transformations by way of partial application. For example, filter p xs is a natural transformation when map p xs is incorporated as part of the definition of the function (the resulting function can be applied on any list, not just the original xs). The resulting natural transformation is ugly but useful.
  • For stock optimizers (e.g. Haskell), some calculational optimizations can be supported by the use of rewrite rules. While rewrite rules are a very powerful mechanism, they can only describe “always on” optimizations; e.g. for deforestation, one always wants to eliminate as many intermediate data structures as possible. In many of the applications we want to optimize, the best performance can only be achieved by adding intermediate data structures: now we have a space of possible programs and rewrite rules are woefully inadequate for specifying which program is the best. What we’d like to do is use category theory to give an account for rewrite rules with structure, and use domain specific knowledge to pick the best programs.

I’d like to illustrate some of these ideas by way of an example. Here is some sample code, written in Delite, which calculates an iteration of (1-dimensional) k-means clustering:

(0 :: numClusters, *) { j =>
  val weightedPoints = sumRowsIf(0,m){i => c(i) == j}{i => x(i)};
  val points = c.count(_ == j);
  val d = if (points == 0) 1 else points
  weightedPoints / d

You can read it as follows: we are computing a result array containing the position of each cluster, and the outermost block is looping over the clusters by index variable j. To compute the position of a cluster, we have to get all of the points in x which were assigned to cluster j (that’s the c(i) == j condition) and sum them together, finally dividing by the sum by the number of points in the cluster to get the true location.

The big problem with this code is that it iterates over the entire dataset numClusters times, when we’d like to only ever do one iteration. The optimized version which does just that looks like this:

val allWP = hashreduce(0,m)(i => c(i), i => x(i), _ + _)
val allP = hashreduce(0,m)(i => c(i), i => 1, _ + _)
(0::numClusters, *) { j =>
    val weightedPoints = allWP(j);
    val points = allP(j);
    val d = if (points == 0) 1 else points
    return weightedpoints / d

That is to say, we have to precompute the weighted points and the point count (note the two hashreduces can and should be fused together) before generating the new coordinates for each of the clusters: generating more intermediate data structures is a win, in this case.

Let us now calculate our way to the optimized version of the program. First, however, we have to define some functors:

  • D_i[X] is an array of X of a size specified by i (concretely, we’ll use D_i for arrays of size numPoints and D_j for arrays of size numClusters). This family of functors is also known as the diagonal functor, generalized for arbitrary size products. We also will rely on the fact that D is representable, that is to say D_i[X] = Loc_D_i -> X for some type Loc_D_i (in this case, it is the index set {0 .. i}.
  • List[X] is a standard list of X. It is the initial algebra for the functor F[R] = 1 + X * R. Any D_i can be embedded in List; we will do such conversions implicitly (note that the reverse is not true.)

There are a number of functions, which we will describe below:

  • tabulate witnesses one direction of the isomorphism between Loc_D_i -> X and D_i[X], since D_i is representable. The other direction is index, which takes D_i[X] and a Loc_D_i and returns an X.
  • fold is the unique function determined by the initial algebra on List. Additionally, suppose that we have a function * which combines two algebras by taking their cartesian product,
  • bucket is a natural transformation which takes a D_i[X] and buckets it into D_j[List[X]] based on some function which assigns elements in D_i to slots in D_j. This is an example of a natural transformation that is not a natural transformation until it is partially applied: if we compute D_i[Loc_D_j], then we can create a natural transformation that doesn’t ever look at X; it simply “knows” where each slot of D_i needs to go in the resulting structure.

Let us now rewrite the loop in more functional terms:

tabulate (\j ->
  let weightedPoints = fold plus . filter (\i -> c[i] == j) $ x
      points = fold inc . filter (\i -> c[i] == j) $ x
  in divide (weightedPoints, points)

(Where divide is just a function which divides its arguments but checks that the divisor is not zero.) Eliminating some common sub-expressions and fusing the two folds together, we get:

tabulate (\j -> divide . fold (plus * inc) . filter (\i -> c[i] == j) $ x)

At this point, it is still not at all clear that there are any rewrites we can carry out: the filter is causing problems for us. However, because filter is testing on equality, we can rewrite it in a different way:

tabulate (\j -> divide . fold (plus * inc) . index j . bucket c $ x)

What is happening here? Rather than directly filtering for just items in cluster j, we can instead view this as bucketing x on c and then indexing out the single bucket we care about. This shift in perspective is key to the whole optimization.

Now we can apply the fundamental rule of natural transformations. Let phi = index j and f = divide . fold (plus * inc), then we can push f to the other side of phi:

tabulate (\j -> index j . fmap (divide . fold (plus * inc)) . bucket c $ x)

Now we can eliminate tabulate and index:

fmap (divide . fold (plus * inc)) . bucket c $ x

Finally, because we know how to efficiently implement fmap (fold f) . bucket c (as a hashreduce), we split up the fmap and join the fold and bucket:

fmap divide . hashreduce (plus * inc) c $ x

And we have achieved our fully optimized program.

All of this is research in progress, and there are lots of open questions which we have not resolved. Still, I hope this post has given you a flavor of the approach we are advocating. I am quite curious in your comments, from “That’s cool!” to “This was all done 20 years ago by X system.” Have at it!

  • May 12, 2013

The Difference between Recursion & Induction

Recursion and induction are closely related. When you were first taught recursion in an introductory computer science class, you were probably told to use induction to prove that your recursive algorithm was correct. (For the purposes of this post, let us exclude hairy recursive functions like the one in the Collatz conjecture which do not obviously terminate.) Induction suspiciously resembles recursion: the similarity comes from the fact that the inductive hypothesis looks a bit like the result of a “recursive call” to the theorem you are proving. If an ordinary recursive computation returns plain old values, you might wonder if an “induction computation” returns proof terms (which, by the Curry-Howard correspondence, could be thought of as a value).

As it turns out, however, when you look at recursion and induction categorically, they are not equivalent! Intuitively, the difference lies in the fact that when you are performing induction, the data type you are performing induction over (e.g. the numbers) appears at the type level, not the term level. In the words of a category theorist, both recursion and induction have associated initial algebras, but the carrier sets and endofunctors are different. In this blog post, I hope to elucidate precisely what the difference between recursion and induction is. Unfortunately, I need to assume some familiarity with initial algebras: if you don’t know what the relationship between a fold and an initial algebra is, check out this derivation of lists in initial algebra form.

When dealing with generalized abstract nonsense, the most important first step is to use a concrete example! So let us go with the simplest nontrivial data type one can gin up: the natural numbers (our examples are written in both Coq and Haskell, when possible):

Inductive nat : Set := (* defined in standard library *)
  | 0 : nat
  | S : nat -> nat.

data Nat = Z | S Nat

Natural numbers are a pretty good example: even the Wikipedia article on F-algebras uses them. To recap, an F-algebra (or sometimes simply “algebra”) has three components: an (endo)functor f, a type a and a reduction function f a -> a. For simple recursion over natural numbers, we need to define a functor NatF which “generates” the natural numbers; then our type a is Nat and the reduction function is type NatF Nat -> Nat. The functor is defined as follows:

Inductive NatF (x : Set) : Set :=
  | F0 : NatF x.
  | FS : x -> NatF x.

data NatF x = FZ | FS x

Essentially, take the original definition but replace any recursive occurrence of the type with a polymorphic variable. As an exercise, show that NatF Nat -> Nat exists: it is the (co)product of () -> Nat and Nat -> Nat. The initiality of this algebra implies that any function of type NatF x -> x (for some arbitrary type x) can be used in a fold Nat -> x: this fold is the homomorphism from the initial algebra (NatF Nat -> Nat) to another algebra (NatF x -> x). The take-away point is that the initial algebra of natural numbers consists of an endofunctor over sets.


Let’s look at the F-algebra for induction now. As a first try, let’s try to use the same F-algebra and see if an appropriate homomorphism exists with the “type of induction”. (We can’t write this in Haskell, so now the examples will be Coq only.) Suppose we are trying to prove some proposition P : nat -> Prop holds for all natural numbers; then the type of the final proof term must be forall n : nat, P n. We can now write out the morphism of the algebra: NatF (forall n : nat, P n) -> forall n : nat, P n. But this “inductive principle” is both nonsense and not true:

Hint Constructors nat NatF.
Goal ~ (forall (P : nat -> Prop), (NatF (forall n : nat, P n) -> forall n : nat, P n)).
  intro H; specialize (H (fun n => False)); auto.

(Side note: you might say that this proof fails because I’ve provided a predicate which is false over all natural numbers. But induction still “works” even when the predicate you’re trying to prove is false: you should fail when trying to provide the base case or inductive hypothesis!)

We step back and now wonder, “So, what’s the right algebra?” It should be pretty clear that our endofunctor is wrong. Fortunately, we can get a clue for what the right endofunctor might be by inspecting the type the induction principle for natural numbers:

(* Check nat_ind. *)
nat_ind : forall P : nat -> Prop,
  P 0 -> (forall n : nat, P n -> P (S n)) -> forall n : nat, P n

P 0 is the type of the base case, and forall n : nat, P n -> P (S n) is the type of the inductive case. In much the same way that we defined NatF nat -> nat for natural numbers, which was the combination of zero : unit -> nat and succ : nat -> nat, we need to define a single function which combines the base case and the inductive case. This seems tough: the result types are not the same. But dependent types come to the rescue: the type we are looking for is:

fun (P : nat -> Prop) => forall n : nat, match n with 0 => True | S n' => P n' end -> P n

You can read this type as follows: I will give you a proof object of type P n for any n. If n is 0, I will give you this proof object with no further help (True -> P 0). However, if n is S n', I will require you to furnish me with P n' (P n' -> P (S n')).

We’re getting close. If this is the morphism of an initial algebra, then the functor IndF must be:

fun (P : nat -> Prop) => forall n : nat, match n with 0 => True | S n' => P n' end

What category is this a functor over? Unfortunately, neither this post nor my brain has the space to give a rigorous treatment, but roughly the category can be thought of as nat-indexed propositions. Objects of this category are of the form forall n : nat, P n, morphisms of the category are of the form forall n : nat, P n -> P' n. [1] As an exercise, show that identity and composition exist and obey the appropriate laws.

Something amazing is about to happen. We have defined our functor, and we are now in search of the initial algebra. As was the case for natural numbers, the initial algebra is defined by the least fixed point over the functor:

Fixpoint P (n : nat) : Prop :=
  match n with 0 => True | S n' => P n' end.

But this is just True!

Hint Unfold P.
Goal forall n, P n = True.
  induction n; auto.

Drawing out our diagram:


The algebras of our category (downward arrows) correspond to inductive arguments. Because our morphisms take the form of forall n, P n -> P' n, one cannot trivially conclude forall n, P' n simply given forall n, P n; however, the presence of the initial algebra means that True -> forall n, P n whenever we have an algebra forall n, IndF n -> P n. Stunning! (As a side note, Lambek’s lemma states that Mu P is isomorphic to P (Mu P), so the initial algebra is in fact really really trivial.)

In conclusion:

  • Recursion over the natural numbers involves F-algebras with the functor unit + X over the category of Sets. The least fixed point of this functor is the natural numbers, and the morphism induced by the initial algebra corresponds to a fold.
  • Induction over the natural numbers involves F-algebras with the functor fun n => match n with 0 => True | S n' => P n' over the category of nat-indexed propositions. The least fixed point of this functor is True, and the morphism induced by the initial algebra establishes the truth of the proposition being inductively proven.

So, the next time someone tells asks you what the difference between induction and recursion is, tell them: Induction is just the unique homomorphism induced by an initial algebra over indexed propositions, what’s the problem?

Acknowledgements go to Conor McBride, who explained this shindig to me over ICFP. I promised to blog about it, but forgot, and ended up having to rederive it all over again.

[1] Another plausible formulation of morphisms goes (forall n : nat, P n) -> (forall n : nat, P' n). However, morphisms in this category are too strong: they require you to go and prove the result for all n... which you would do with induction, which misses the point. Plus, this category is a subcategory of the ordinary category of propositions.

  • April 27, 2013

Kindle is not good for textbooks

Having attempted to read a few textbooks on my Kindle, I have solemnly concluded that the Kindle is in fact a terrible device for reading textbooks. The fundamental problem is that, due to technological limitations, the Kindle is optimized for sequential reading. This can be seen in many aspects:

  • Flipping a page in the Kindle is not instantaneous (I don't have a good setup to time how long the screen refresh takes, but there is definitely a perceptible lag before when you swipe, and when the Kindle successfully redraws the screen—and it’s even worse if you try to flip backwards).
  • Rapidly flipping through pages in order to scan for a visual feature compounds the delay problem.
  • There is no way to take the “finger” approach to random access (i.e. wedge your finger between two pages to rapidly switch between them); jumping between bookmarks requires four presses with the current Kindle interface!
  • The screen size of the Kindle is dramatically smaller than that of an average textbook, which reduces the amount of information content that can be placed on one screen and further exacerbates slow page turns.

A textbook cannot be read as a light novel. So, while the Kindle offers the tantalizing possibility of carrying a stack of textbooks with you everywhere, in fact, you’re better off getting the actual dead tree version if you’re planning on doing some serious studying from it. That is not to say textbook ebooks are not useful; in fact, having a searchable textbook on your laptop is seriously awesome—but this is when you’re using the textbook as a reference material, and not when you’re trying to actually learn the material.

  • April 15, 2013

A Zerocoin puzzle

I very rarely post linkspam, but given that I’ve written on the subject of anonymizing Bitcoins in the past, this link seems relevant: Zerocoin: making Bitcoin anonymous. Their essential innovation is to have a continuously operating mixing pool built into the block chain itself; they pull this off using zero-knowledge proofs. Nifty!

Here is a puzzle for the readers of this blog. Suppose that I am a user who wants to anonymize some Bitcoins, and I am willing to wait expected time N before redeeming my Zerocoins. What is the correct probability distribution for me to pick my wait time from? Furthermore, suppose a population of Zerocoin participants, all of which are using this probability distribution. Furthermore, suppose that each participant has some utility function trading off anonymity and expected wait time (feel free to make assumptions that make the analysis easy). Is this population in Nash equilibrium?

  • April 11, 2013

A classical logic fairy tale

(Selinger) Here is a fairy tale: The evil king calls the poor shepherd and gives him these orders. “You must bring me the philosophers stone, or you have to find a way to turn the philosopher’s stone to gold. If you don’t, your head will be taken off tomorrow!” What can the poor shepherd do to save his life?

Hat tip to Chris for originally telling me a different variant of this story. Unfortunately, this quote from Lectures on the Curry-Howard Isomorphism was the only reference I could find. What should the shepherd do? Is there something a little odd about this story?

  • April 7, 2013

Resource limits for Haskell

Last week, I made my very first submission to ICFP! The topic? An old flame of mine: how to bound space usage of Haskell programs.

We describe the first iteration of a resource limits system for Haskell, taking advantage of the key observation that resource limits share semantics and implementation strategy with profiling. We pay special attention to the problem of limiting resident memory usage: we describe a simple implementation technique for carrying out incremental heap censuses and describe a novel information-flow control solution for handling forcible resource reclamation. This system is implemented as a set of patches to GHC.

You can get a copy of the submission here. I've reproduced below the background section on how profiling Haskell works; if this tickles your fancy, check out the rest of the paper!

Profiling in Haskell is performed by charging the costs of computation to the “current cost center.” A cost center is an abstract, programmer-specified entity to which costs can be charged; only one is active per thread at any given time, and the cost semantics determines how the current cost center changes as the program executes. For example, the scc cc e expression (set-cost-center) modifies the current cost center during evaluation of e to be cc. Cost centers are defined statically at compile time.

A cost semantics for Haskell was defined by Sansom et al. (1995) Previously, there had not been a formal account for how to attribute costs in the presence of lazy evaluation and higher-order functions; this paper resolved these questions. The two insights of their paper were the following: first, they articulated that cost attribution should be independent of evaluation order. For the sake of understandability, whether a thunk is evaluated immediately or later should not affect who is charged for it. Secondly, they observed that there are two ways of attributing costs for functions, in direct parallel to the difference between lexical scoping and dynamic scoping.

The principle of order-independent cost-attribution can be seen by this program:

f x = scc "f" (Just (x * x))
g x = let Just y = f x in scc "g" y

When g 4 is invoked, who is charged the cost of evaluating x * x? With strict evaluation, it is easy to see that f should be charged, since x * x is evaluated immediately inside the scc expression. Order-independence dictates, then, that even if the execution of x * x is deferred to the inside of scc "g" y, the cost should still be attributed to f. In general, scc "f" x on a variable x is a no-op. In order to implement such a scheme, the current cost-center at the time of the allocation of the thunk must be recorded with the thunk and restored when the thunk is forced.

The difference between lexical scoping and dynamic scoping for function cost attribution can be seen in this example:

f = scc "f" (\x -> x * x)
g = \x -> scc "g" (x * x)

What is the difference between these two functions? We are in a situation analogous to the choice for thunks: should the current cost-center be saved along with the closure, and restored upon invocation of the function? If the answer is yes, we are using lexical scoping and the functions are equivalent; if the answer is no, we are using dynamic scoping and the scc in f is a no-op. The choice GHC has currently adopted for scc is dynamic scoping.

  • April 2, 2013

The single export pattern

From the files of the ECMAScript TC39 proceedings

Single export refers to a design pattern where a module identifier is overloaded to also represent a function or type inside the module. As far as I can tell, the term “single export” is not particularly widely used outside the ECMAScript TC39 committee; however, the idea shows up in other contexts, so I’m hoping to popularize this particular name (since names are powerful).

The basic idea is very simple. In JavaScript, a module is frequently represented as an object:

var sayHello = require('./sayhello.js');;

The methods of sayHello are the functions exported by the module. But what about sayHello itself? Because functions are objects too, we could imagine that sayHello was a function as well, and thus:


would be a valid fragment of code, perhaps equivalent to Only one symbol can be exported this way, but in many modules, there is an obvious choice (think of jQuery’s $ object, etc).

This pattern is also commonly employed in Haskell, by taking advantage of the fact that types and modules live in different namespaces:

import qualified Data.Map as Map
import Data.Map (Map)

Map is now overloaded to be both a type and a module.

  • March 31, 2013

The duality of weak maps and private symbols

From the files of the ECMAScript TC39 proceedings

I want to talk about an interesting duality pointed out by Mark Miller between two otherwise different language features: weak maps and private symbols. Modulo implementation differences, they are the same thing!

A weak map is an ordinary associative map, with the twist that if the key for any entry becomes unreachable, then the value becomes unreachable too (though you must remember to ignore references to the key from the value itself!) Weak maps have a variety of use-cases, including memoization, where we’d like to remember results of a computation, but only if it will ever get asked for again! A weak map supports get(key) and set(key, value) operations.

A private symbol is an unforgeable identifier of a field on an object. Symbols are useful because they can be generated “fresh”; that is, they are guaranteed not to conflict with existing fields that live on an object (whereas one might get unlucky with _private_identifier_no_really); a private symbol has the extra stipulation that one cannot discover that it exists on an object without actually having the symbol—e.g. an object will refuse to divulge the existence of a private symbol while enumerating the properties of an object. A private symbol psym might be created, and then used just like an ordinary property name to get (obj[psym]) and set (obj[psym] = value) values.

To see why these are the same, lets implement weak maps in terms of private symbols, and vice versa (warning, pseudocode ahead):

function WeakMap() {
  var psym = PrivateSymbol();
  return {
    get: function(key) { return key[psym]; },
    set: function(key, value) { key[psym] = value; }

function PrivateSymbol() {
  return WeakMap();
// pretend that get/set are magical catch-all getters and setters
Object.prototype.get = function(key) {
  if (key instanceof PrivateSymbol) { return key.get(this); }
  else { return this.old_get(key); }
Object.prototype.set = function(key, value) {
  if (key instanceof PrivateSymbol) { return key.get(this, value); }
  else { return this.old_set(key, value); }

Notice, in particular, that it wouldn’t make sense to enumerate all of the entries of a weak map; such an enumeration would change arbitrarily depending on whether or not a GC had occurred.

If you look at this more closely, there is something rather interesting going on: the implementation strategies of weak maps and private symbols are the opposite of each other. With a weak map, you might imagine a an actual map-like data structure collecting the mappings from keys to values (plus some GC trickery); with a private symbol, you would expect the values to be stored on the object itself. That is to say, if we say “WeakMap = PrivateSymbol” and “key = this”, then the primary difference is whether or not the relationships are stored on the WeakMap/PrivateSymbol, or on the key/this. WeakMap suggests the former; PrivateSymbol suggests the latter.

Is one implementation or the other better? If objects in your system are immutable or not arbitrarily extensible, then the private symbol implementation may be impossible to carry out. But if both implementations are possible, then which one is better depends on the lifetimes of the objects in question. Garbage collecting weak references is expensive business (it is considerably less efficient than ordinary garbage collection), and so if you can arrange for your weak mappings to die through normal garbage collection, that is a win. Therefore, it’s better to store the mapping on the shorter-lived object. In the case of a memotable, the key is going to be a bit more ephemeral than the map, which results in a very strange consequence: the best implementation strategy for a weak map doesn’t involve creating a map at all!

Alas, as with many elegant results, there are some difficulties stemming from complexities in other parts of the ECMAScript specification. In particular, it is not at all clear what it means to have an “read-only weak map”, whereas an read-only private symbol has an obvious meaning. Furthermore, collapsing these two rather distinct concepts into a single language may only serve to confuse web developers; a case of a proposal being too clever for its own good. And finally, there is an ongoing debate about how to reconcile private state with proxies. This proposal was introduced to solve one particular aspect of this problem, but to our understanding, it only addresses a specific sub-problem, and only works when the proxy in question is a membrane.

  • March 19, 2013