The 1.x Files: A Primer for the Witness Specification

Since plenty of us have a bit extra time on our arms, I assumed now is perhaps a great alternative to proceed with one thing maybe slightly bit boring and tedious, however nonetheless fairly basic to the Stateless Ethereum effort: understanding the formal Witness Specification.

Like the captain of the Battleship in StarCraft, we’ll take it gradual. The witness spec shouldn’t be a very sophisticated idea, however it is extremely deep. That depth is slightly daunting, however is nicely price exploring, as a result of it’s going to present insights that, maybe to your nerdy delight, prolong nicely past the world of blockchains, and even software program!

By the finish of this primer, it’s best to have at the least minimum-viable-confidence in your capability to know what the formal Stateless Ethereum Witness Specification is all about. I will attempt to make it slightly extra enjoyable, too.

Recap: What you have to learn about State

Stateless Ethereum is, in fact, a little bit of a misnomer, as a result of the state is absolutely what this entire effort is about. Particularly, discovering a option to make retaining a duplicate of the entire Ethereum state an non-compulsory factor. If you have not been following this collection, it is perhaps price taking a look at my earlier primer on the state of stateless Ethereum. I will give a brief TL;DR right here although. Be happy to skim when you really feel such as you’ve already received a great deal with on this subject.

The full ‘state’ of Ethereum describes the present standing of all accounts and balances, in addition to the collective reminiscences of all good contracts deployed and working in the EVM. Each finalized block in the chain has one and just one state, which is agreed upon by all members in the community. That state is modified and up to date with every new block that’s added to the chain.

The Ethereum State is represented in silico as a Merkle-Patricia Trie: a hashed knowledge construction that organizes every particular person piece of knowledge (e.g. an account stability) into one huge related unit that may be verified for uniqueness. The full state trie is simply too huge to visualise, however here is a ‘toy model’ that will likely be useful once we get to witnesses:

Like magical cryptographic caterpillars, the accounts and code of good contracts reside in the leaves and branches of this tree, which by means of successive hashing ultimately results in a single root hash. If you wish to know that two copies of a state trie are the identical, you’ll be able to merely evaluate the root hashes. Sustaining comparatively safe and indeniable consensus over one ‘canonical’ state is the essence of what a blockchain is designed to do.

To be able to submit a transaction to be included in the subsequent block, or to validate {that a} specific change is in keeping with the final included block, Ethereum nodes should preserve a whole copy of the state, and re-compute the root hash (time and again). Stateless Ethereum is a set of modifications that may take away this requirement, by including what’s generally known as a ‘witness’.

A Witness Sketch

Earlier than we dive into the witness specification, it’s going to be useful to have an intuitive sense of what a witness is. Once more, there’s a extra thorough clarification in the submit on the Ethereum state linked above.

A witness is a bit like a cheat sheet for an oblivious (stateless) scholar (consumer). It is simply the minimal quantity of knowledge have to go the examination (submit a sound change of state for inclusion in the subsequent block). As a substitute of studying the entire textbook (retaining a duplicate of the present state), the oblivious scholar (stateless consumer) asks a good friend (full node) for a crib sheet to submit their solutions.

In very summary phrases, a witness gives all of the wanted hashes in a state trie, mixed with some ‘structural’ details about the place in the trie these hashes belong. This permits an ‘oblivious’ node to incorporate new transaction in its state, and to compute a brand new root hash regionally – with out requiring them to obtain a complete copy of the state trie.

Let’s transfer away from the cartoonish thought and in the direction of a extra concrete illustration. Here’s a “real” visualization of a witness:


I like to recommend opening this picture in a brand new tab in an effort to zoom in and actually respect it. This witness was chosen as a result of it is comparatively small and simple to pick options. Every little sq. on this picture represents a single ‘nibble’, or half of a byte, and you’ll confirm that your self by counting the variety of squares that it’s a must to ‘go by means of’, beginning at the root and ending at an Ether stability (it’s best to rely 64). Whereas we’re taking a look at this picture, discover the enormous chunk of code inside certainly one of the transactions that should be included for a contract name — code makes up a comparatively massive a part of the witness, and might be diminished by code merkleization (which we’ll discover one other day).

Some Formalities

Certainly one of the basic distinguishing options of Ethereum as a protocol is its independence from a selected implementation. This is the reason, reasonably than only one official consumer as we see in Bitcoin, Ethereum has a number of fully totally different variations of consumer. These shoppers, written in varied programming languages, should adhere to The Ethereum Yellow Paper, which explains in way more formal phrases how any consumer ought to behave with a view to take part in the Ethereum protocol. That means, a developer writing a consumer for Ethereum would not should cope with any ambiguity in the system.

The Witness Specification has this actual aim: to supply an unambiguous description of what a witness is, which can make implementing it easy in any language, for all shoppers. If and when Stateless Ethereum turns into ‘a factor’, the witness specification will be inserted into the Yellow Paper as an appendix.

Once we say unambiguous on this context, it means one thing stronger than what you would possibly imply in atypical speech. It is not that the formal specification is only a actually, actually, actually, detailed description of what a witness is and the way it behaves. It signifies that, ideally, there’s actually one and just one means describe a selected witness. That’s to say, when you adhere to the formal specification, it might be unimaginable for you to write down an implementation for Stateless Ethereum that generates witnesses totally different than every other implementation additionally following the guidelines. That is key, as a result of the witness goes to (hopefully) turn out to be a brand new cornerstone of the Ethereum protocol; It must be appropriate by building.

A Matter of Semantics (and Syntax)

Though ‘blockchain growth’ often implies one thing new and thrilling, it should be mentioned that plenty of it’s grounded in a lot older and wiser traditions of pc programming, cryptography, and formal logic. This actually comes out in the Witness Specification! To be able to perceive the way it works, we have to really feel comfy with a few of the technical phrases, and to do this we’ll should take slightly detour into linguistics and formal language concept.

Learn aloud the following two sentences, and pay specific consideration to your intonation and cadence:

  • furiously sleep concepts inexperienced colorless
  • colorless inexperienced concepts sleep furiously

I wager the first sentence got here out a bit robotic, with a flat emphasis and pause after every phrase. In contrast, the second sentence most likely felt pure, if a bit foolish. Despite the fact that it did not actually imply something, the second sentence made sense in a means that the first one did not. This can be a little instinct pump to attract consideration to the distinction between Syntax and Semantics. If you happen to’re an English speaker you have got an understanding of what the phrases characterize (their semantic content material), however that was largely irrelevant right here; what you seen was a distinction between legitimate and invalid grammar (their syntax).

This instance sentence is from a 1956 paper by one Noam Chomsky, which is a reputation you would possibly acknowledge. Though he’s now generally known as an influential political and social thinker, Chomsky’s first contributions as an educational had been in the area of logic and linguistics, and on this paper, he created certainly one of the most helpful classification programs for formal languages.

Chomsky was involved with the mathematical description of grammar, how one can categorize languages based mostly on their grammar guidelines, and what properties these classes have. One such property that’s related to us is syntactic ambiguity.

Ambiguous Buffalo

Think about the grammatically appropriate sentence “Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.” — it is a traditional instance that illustrates simply how ambiguous English syntax guidelines will be. If you happen to perceive that, relying on the context, the phrase ‘buffalo’ can be utilized as a verb (to intimidate), an adjective (being from Buffalo, NY), or a noun (a bison), you’ll be able to parse the sentence based mostly on the place every phrase belongs.

We may additionally use totally totally different phrases, and a number of sentences: “You know those NY bison that other NY bison intimidate? Well, they intimidate, too. They intimidate NY bison, to be exact.”

However what if we need to take away the ambiguity, however nonetheless prohibit our phrases to make use of solely ‘buffalo’, and preserve all of it as a single sentence? It is doable, however we have to modify the guidelines of English a bit. Our new “language” goes to be slightly extra actual. A method to do this could be to mark every phrase to point its a part of speech, like so:

Buffalo{pn} buffalo{n} Buffalo{pn} buffalo{n} buffalo{v} buffalo{v} Buffalo{pn} buffalo{n}

Maybe that is nonetheless not tremendous clear for a reader. To make it much more actual, let’s attempt utilizing a little bit of substitution to assist us herd a few of these “buffalo” into teams. Any bison from Buffalo, NY is absolutely only one particular model of what we’d name a “noun phrase”, or <NP>. We are able to substitute <NP> into the sentence every time we encounter the string Buffalo{pn} buffalo{n}. Since we’re getting a bit extra formal, we’d determine to make use of a shorthand notation for this and different future substitution guidelines, by writing:

<NP> ::= Buffalo{pn} buffalo{n}

the place ::= means “What’s on the left side can be replaced by what’s on the right side”. Importantly, we do not need this relationship to go the different means; think about how mad the Boulder buffalo would get!

Making use of our substitution rule to the full sentence, it might change to:

<NP> <NP> buffalo{v} buffalo{v} <NP>

Now, that is nonetheless a bit complicated, as a result of on this sentence there’s a sneaky relative clause, which will be seen much more clearly by inserting the phrase ‘that’ into the first half our sentence, i.e. <NP> *that* <NP> buffalo{v}….

So let’s make a substitution rule that teams the relative clause into <RC>, and say:

<RC> ::= <NP> buffalo{v}

Moreover, since a relative clause actually simply makes a clarification a few noun phrase, the two taken collectively are equal to only one other noun phrase:

<NP> ::= <NP><RC>

With these guidelines outlined and utilized, we will write the sentence as:

<NP> buffalo{v} <NP>

That appears fairly good, and actually will get at the core relationship this foolish sentence expresses: One specific group of bison intimidating one other group of bison.

We have taken it this far, so why not go all the means? At any time when ‘buffalo’ as a verb precedes a noun, we may name {that a} verb phrase, or <VP>, and outline a rule:

<VP> ::= buffalo{v}<NP>

And with that, we now have our single full legitimate sentence, which we may name S:

S ::= <NP><VP>

What we have accomplished right here is perhaps higher represented visually:


That construction seems to be curiously acquainted, would not it?

The buffalo instance is a bit foolish and never very rigorous, however it’s shut sufficient to reveal what is going on on with the bizarre mathematical language of the Witness Specification, which I’ve very sneakily launched in my rant about buffalo. It is known as Backus-Naur form notation, and it is typically utilized in formal specs like this, in quite a lot of real-world situations.

The ‘substitution guidelines’ we outlined for our restricted English language helped to ensure that, given a herd of “buffalo”, we may assemble a ‘legitimate’ sentence without having to know something about what the phrase buffalo means in the actual world. In the classification first elucidated by Chomsky, a language that has actual sufficient guidelines of grammar that let you do that is known as a context-free language.

Extra importantly, the guidelines make sure that for each doable sentence comprised of the phrase(s) buffalon, there’s one and just one option to assemble the knowledge construction illustrated in the tree diagram above. Un-ambiguity FTW!

Go Forth and Learn the Spec

Witnesses are at their core only a single massive object, encoded right into a byte array. From the (anthropomorphic) perspective of a stateless consumer, that array of bytes would possibly look a bit like an extended sentence comprised of very related trying phrases. As long as all shoppers observe the identical algorithm, the array of bytes ought to convert into one and just one hashed knowledge construction, no matter how the implementation chooses to characterize it in reminiscence or on disk.

The manufacturing guidelines, written out in part 3.2, are a bit extra complicated and much much less intuitive than the ones we used for our toy instance, however the spirit may be very a lot the identical: To be unambiguous pointers for a stateless consumer (or a developer writing a consumer) to observe and be sure they’re getting it proper.

I’ve glossed over rather a lot on this exposition, and the rabbit gap of formal languages goes far deeper, to make certain. My goal right here was to only present sufficient of an introduction and basis to beat that first hurdle of understanding. Now that you’ve got cleared that hurdle, it is time pop open wikipedia and deal with the relaxation your self!

As all the time, when you’ve got suggestions, questions, or requests for matters, please @gichiba or @JHancock on twitter.

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