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I am betting on Name-by-Push-Worth · thunderseethe’s devlog

I am betting on Name-by-Push-Worth · thunderseethe’s devlog

2024-03-09 12:56:56

You stumble upon a perform argument at a fork within the highway.
If it takes the left highway, it’ll consider itself after which be handed to its perform.
If it takes the suitable highway, it’ll cross itself to the perform to be evaluated someplace down the highway (🥁🐍).
Let’s guess on which highway might be sooner.

We’d suspect it is a relatively boring guess.
All we have now to do is look down every highway and see which one is shorter.
Thankfully for our wager (and to the dismay of theorists in all places), this isn’t the case.
We will at all times assemble a state of affairs the place evaluating both eagerly or lazily is best.

Our gamble touches on an age-old query in programming language semantics, to call-by-value
(CBV) or to call-by-name/call-by-need
(CBN).
They’re each analysis methods that decide the order during which expressions are evaluated.
CBV at all times evaluates a perform argument earlier than passing it to a perform (aka keen analysis).
CBN waits to judge perform arguments till they’re used within the perform physique (aka lazy analysis).

Languages choose one and use it for all their perform purposes.
Rust, Java, JavaScript, Python, and C/C++ use CBV as their analysis technique.
Haskell and…uh… Haskell use CBN for his or her analysis technique.
Alas, whichever name you make, the grass is at all times greener on the opposite aspect.
Our CBV languages introduce little spurts of lazy analysis (closures, iterators, and so forth.).
Our CBN language(s) introduce keen analysis; Haskell prolonged its language to make information varieties keen by default.

Given each CBV and CBN languages find yourself wanting each keen and lazy analysis, why are we pressured to select one and forgo the opposite solely?
It seems we’re not, we simply didn’t know that but after we designed all these languages. …Whoops.
Levy’s ‘99 paper Call by Push Value: A Subsuming Paradigm
introduces a 3rd choice, Name-by-Push-Worth (CBPV), to the CBV/CBN spectrum.
‘99 is principally the Cretaceous period if we’re releasing JavaScript frameworks, but it surely’s fairly current for releasing analysis.
CBPV has simply began to penetrate the zeitgeist, and it’s by far essentially the most promising method to calling-by.

Earlier than we are able to speak about why CBPV is cool, we have now to speak about what it’s.
The massive thought of CBPV is to assist each CBV and CBN with one set of semantics.
It accomplishes this by distinguishing between values and computations.
The paper offers a pleasant slogan to seize the instinct: “a computation does, a worth is”.

Nice, however what does that truly imply?
Let’s take a look at a standard lambda calculus, to supply distinction for our CBPV lambda calculus:

information Kind 
    | Int
    | Enjoyable Kind Kind

information Time period
    = Var Textual content
    | Int Int
    | Enjoyable Textual content Time period
    | App Time period Time period

Relying on how we execute our App time period, this may be both CBV or CBN (however not each).
If we consider our argument and apply it to our perform, that’s CBV.
If we apply our argument to our perform unevaluated, that’s CBN.

Nonetheless, we have now to select one: both CBV or CBN.
This is because of our values being all blended up with our computations underneath one time period.
CBN needs App to take a computation, however CBV needs App to take a worth.
As a result of the 2 are indistinguishable we’re pressured to select one.
Our CBPV lambda calculus fixes this by sundering worth and computation in two:

-- Kind of values
information ValType 
    = Int
    | Thunk CompType

-- Kind of computations
information CompType 
    = Enjoyable ValType CompType -- !!
    | Return ValType

-- A price time period
information Worth
    = Int Int
    | Var Textual content
    | Thunk Comp

-- A computation time period
information Comp
    = Enjoyable Textual content Comp
    | App Comp Worth
    | Return Worth

With that CPBV has lower the Gordian Knot, cementing its place as ruler of all Purposes.
And we love that for them, however wow, it took much more stuff to do it (we doubled our line depend).
It’s now exceedingly clear what’s a worth and what’s a computation.
One stunning factor is that variables are a worth.
What if our variable is certain to a computation?
CBPV has decreed: “we don’t have to fret about it” (though to be frank I’m a bit of apprehensive about it).

If we take a look at our new App node, it might probably additionally solely apply a worth.
What a reduction, which means we are able to nonetheless cross variables to capabilities.
However CBN has us cross round unevaluated arguments, the entire level is that they’re computations we haven’t evaluated to a worth but.
How are we going to do this if all our variables are values and all our perform arguments are values?
The reply lies in a brand new Worth node: Thunk.

A Thunk turns a computation into a worth.
Once we wish to apply a computation to a perform, we first have to show it into a worth utilizing Thunk.
This element is what makes CPBV so helpful.
Being pressured to be express about packaging our computations into values will increase our capacity to cause about work.

We will see one other instance of this in our new Comp node: Enjoyable.
Enjoyable can solely return a Comp.
We will nest Enjoyable nodes (since they’re computations) to create multi argument capabilities.
However what if we wish to return a perform from a perform?

For that we make use of our closing new node Return.
Return is the praise of Thunk.
It turns a Worth right into a Computation.
Utilizing Return we are able to create a perform that returns a perform like so:

(Enjoyable "x" (Return (Thunk (Enjoyable "y" (Var "x")))))

This may look like pageantry, and for a floor language people write I’d need to agree.
However in a compiler IR, this distinction permits us to generate way more environment friendly code.

Now that we all know what CBPV is, we are able to lastly speak about why CBPV is…the longer term.
We all know one massive benefit is being express about the place we flip computations into values (and again).
To assist put that in perspective, take a look at this monstrosity from Making a fast curry
required to use arguments to a perform at runtime:

Code snippet showing function application in making of a fast curry

Not solely do we have now to search for the arity of the perform, we have now to search for whether or not we’re calling a perform or a closure.
Even worse this all needs to be completed at runtime.
All these complications go away with CBPV.
If we see a:

(Enjoyable "x" (Enjoyable "y" (Var "x")))

we all know we have now to use two arguments. If as a substitute we see:

(Enjoyable "x" (Return (Thunk (Enjoyable "y (Var "x")))))

we are able to solely apply 1 argument, after which we have now a worth we have now to deal with earlier than we are able to do anymore.
It’s not even a legitimate time period to use two arguments to this time period

Being express about values and computations isn’t solely a useful optimization.
It opens the door to do new issues we couldn’t earlier than.
That is what truly led me to put in writing this text.
I saved seeing in any other case unrelated papers make use of CBPV to make their work doable.
Let’s take a look at these papers to see the various things CPBV can do:

Algebraic results are involved with monitoring uncomfortable side effects in varieties.
A difficulty you encounter instantly upon attempting to do that is: the place can results occur?
Capabilities can do results positive, that’s simple.
What about data, can they do results?
Nicely that appears sort of foolish, data are values, so let’s say no.
However what if the report comprises a perform that does an impact, what then?

CBPV deftly dispatches these quandaries.
Results can seem on any computation sort, and solely on computation varieties.
Capabilities return a computation, to allow them to do results.
However our data are values, to allow them to solely retailer different values, not results.

See Also

If we wish to put a perform in a report we first have to show it right into a Thunk.
So then our report can’t do results.
If we wish to carry out our report’s perform’s results, we first have to show it again right into a computation with Return.
CBPV makes it express and clear the place (and the place not) results can happen in a program.

This one has a frightening title, but it surely’s actually cool.
It’s speaking about sort inference (a topic we’re well versed in
).
A timeworn tradeoff for sort infer-ers is generic varieties.
When you enable a generic sort to be inferred to be one other generic sort, your sort inference is undecidable.
This places us in a bind although.
A number of cool varieties occur to contain these nested generics (known as Rank-2, Rank-N, or Impredicative varieties), and if we are able to’t infer them we’re pressured to put in writing them down by hand.
Really, a destiny worse than loss of life, so the kinds go sorely under-utilized.

This paper makes a dent in that downside by permitting us to deduce these varieties, generally.
Typically could appear underwhelming, however it’s important to take into account it’s infinitely higher than by no means.
It does this with, you guessed it, CBPV.
As we’ve seen, Name by push worth makes it express when a perform is saturated vs when it returns a closure.

This seems to be important data to have throughout sort inference.
Saturated perform calls have all their arguments, and these arguments can present sufficient data to deduce our perform sort.
Even when our perform sort consists of nested generics.
That’s fairly thrilling!
Impulsively our code requires fewer annotations as a result of we made a better alternative in language semantics.

Sorts Are Calling Conventions is an enchanting paper.
It employs sorts to unravel points which have plagued excessively generic languages for the reason that first beta redux:

  • Illustration – is my sort boxed or unboxed
  • Levity – is a generic argument evaluated lazily or eagerly
  • Arity – what number of arguments does a generic perform take earlier than doing actual work

To unravel these points, varieties are given extra refined sorts.
As a substitute of sort Int having variety TYPE, it will have variety TYPE Ptr.
Equally, we ascribe the sort Int -> Int -> Int the type TYPE Name[Int, Int].
Denoting that it’s a perform of arity 2 with its variety.
That is the place CBPV enters the story.

To have the ability to present the arity in a kind’s variety, we first need to know a perform’s arity.
This may be difficult in CBV or CBN languages that freely interchange capabilities and closures.
Fortunately, CBPV makes it abundantly clear what the arity of any perform is, based mostly purely on its sort.

Sorts Are Calling conventions makes use of this to nice impact to emit environment friendly calling code for greater order capabilities.
The paper additionally makes use of the truth that CBPV admits each keen and lazy analysis to trace how an argument is evaluated within the variety.
All in service of producing extra environment friendly machine code.
Who may’ve guessed such a theoretical method would serve such pragmatic targets.

If I had a nickel for each time CBPV exhibits up within the wild, I’d have 3 nickels.
That’s not lots, but it surely’s bizarre that it occurred 3 occasions.
Personally, I imagine it is because CBPV hits upon a kernel of reality within the universe.
Being express about what’s a computation and what’s a worth permits us to cause about extra properties of our applications.

Not solely does it allow us to optimize our applications higher, but it surely lets us do new sorts of polymorphism and resolve fancier varieties in finite time.
Given how current CBPV is when it comes to analysis, I believe we’re simply seeing begin of issues you are able to do with CBPV, and we’ll proceed to find extra issues shifting ahead.
I’m doing my half.
You higher imagine my language
might be constructed atop call-by-push-value.

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