Abstractions work by restricting the domain of what you can do, then building on those restrictions. For example, raw hardware can jump anywhere, but structured programming constrains you to jump only to certain locations in order to implement if, for, functions, etc. It is precisely those restrictions that bring the benefits of structured programming; if you still frequently dipped into jumping around directly structured programming would fail to provide the guarantees it is supposed to provide. CRUD frameworks provide their power by restricting you to CRUD operations, then building on that. Immutable data is accomplished by forbidding you from updating values even though the hardware will happily do it. And so on.

Escape hatches under the abstractions are generally there precisely to break the abstractions, and break them they do.

Abstractions necessarily involve being irreversible, or, to forestall a tedious discussion of the definition of "irreversible", necessarily involve making it an uphill journey to violate and go under the abstraction. There's no way around it. Careful thought can make using an escape hatch less pain than it might otherwise be (such as the ORM that makes it virtually impossible to use SQL by successfully hiding everything about the SQL tables from you so you're basically typing table and column names by dead reckoning), but that's all that can be done.

One thing to do about this is that just as in the past few years the programming community has started to grapple with the fact that libraries aren't free but come with a certain cost that really adds up once you're pulling in a few thousand libraries for a framework's "hello world", abstractions that look really useful but whose restrictions don't match your needs need to be looked at a lot more closely.

I had something like that happen to me just this week. I needed a simple byte ring buffer. I looked in my language's repos for an existing one. I found them. But they were all super complicated, offering tons of features I didn't need, like being a writethrough buffer (which involved taking restrictions I didn't want), or where the simple task of trying to understand the API was quite literally on par with implementing one myself. So I just wrote the simple thing. (Aiding this decision is that broadly speaking if this buffer does fail or have a bug it's not terribly consequential, in my situation it's only for logging output and only effectively at a very high DEBUG level.) It wasn't worth the restrictions to build up stuff I didn't even want.

> It is precisely those restrictions that bring the benefits [...]

Wouldn't it be possible to say "ok, I'll take those restrictions as long as they benefit me, but once I notice that they no longer do, I'll break them and drop down to the lower layer. But only for those parts that actually require it"?

> Abstractions necessarily involve being irreversible, or, to forestall a tedious discussion of the definition of "irreversible", necessarily involve making it an uphill journey to violate and go under the abstraction.

Why? Not being snarky, I'm genuinely trying to understand this better.

I added 2 numbers and came up with 5. What numbers did I add?

You can’t know, because the abstraction (add) destroys information. A “good “ abstraction destroys information that doesn’t matter, or maybe matter in a given context.

You can hang on to all of that extra detail, but it seems like that extra detail slows down drawing inferences.

When I claimed adding resulted in 5, you probably didn’t care if it was 5 apples or 5 skyscrapers. The addition results of 5 are the important part.

Kinda hand waving, but what is included and what is left out is the heart of abstraction imho. And when it’s left out, you can’t get it back.

I think there is something to the nature of your addition example that is counter to your point. Addition being an "abstraction" doesn't make it destroy information it's just an algebraic property of addition. If you instead took multiplication of prime numbers as your "abstraction", no less abstract than addition, then every product would have a unique factorization in the primes. Whether either of these operations makes sense for your problem and thus whether their limitations apply doesn't have anything to do with what "abstraction" you choose. They are either isomorphic to some aspect of your problem or they aren't.

You are right.

How Aristotle illustrated abstraction – by extracting the definition of triangle. Reversible abstraction would mean the possibility of taking a triangle in the Cartesian space and reconstructing the actual object that includes an instance of this triangle. We’d have to be able to reconstruct its material properties.

It is precisely this impossibility that is essential to abstraction. It involves the removal of properties of a particular to arrive at the abstract – the common, the universal.

Now, it is possible to arrive at a poor, incomplete abstraction. Imagine if we dealt with red triangles and green triangles, as opposed to just triangles. If we wished to operate on the its underlying triangle, we would have to remove the colour at each operation. It would be an unused variable. We don’t want that – so we remove the property of colour from our triangle operations entirely. And thatbis the only way to deal with triangles.

Reversibility is simply a different property that can’t be attached to abstraction is if we wish precision at all.

I think the parent's point is that it doesn't need to be like that.

You might be an abstracted adding thingy that adds two numbers to get some other number. But you could also implement a visitor pattern that hooks into the guts of your implementation, allowing me, for example, to inject a logger to record what those numbers were.

Likewise, some ORMs have some abilities to bypass the query engine to hand-write a query, or change the way data types are serialized/deserialized - the key here is basically providing an API to peek under the hood when the user needs to do some stuff at a lower level than the abstraction dictates

There actually is such a thing as reversible computing(?) that keeps around enough intermediate values to run the code backwards to the inputs. Not sure what it is actually good for. Not to be confused with time travel debuggers, though they are similar in spirit.

Yes, it would be OK to do that. One of the worst things abstractions can do is seal you away from the lower level even though you still need to get there. Another example I recently used was a CRUD framework that 100% took over the routing of URLs and had no callouts whatsoever for a non-CRUD-framework page. A CRUD framework may do many wonderful things for my CRUD pages but I may still need a URL to go somewhere else.

"Why? Not being snarky, I'm genuinely trying to understand this better."

It's almost a definitional issue, honestly. If you aren't doing some sort of limiting and building on limitations, you don't have an abstraction, you just have a library. A library is just a whole bunch of programming you could have done yourself, but doesn't impose any further restrictions on you. A classic example would be an image decoding library. They generally do not impose anything on you. They're just huge bits of code that turns images into pixels. You justifiably pull one in because why would you want to write that code again when battle-tested code already exists, but it doesn't impose anything on your code.

Now, when you start getting an "abstraction" that tries to make it so you can operate on multiple types of images at once, you're going to have some restrictions. Your abstraction is going to make some choices about the color spaces you can operate on. Your abstraction is going to make choices about what features they expose from the underlying graphics formats. For example, consider how a generalized "operate on all images" library will handle animated formats. It's a very sensible answer to say it won't operate on them at all. Or perhaps it offers animation support and errors out if you choose a format that doesn't support them. Can it export SVGs? Can it export SVGs with any sort of embedded Javascript? Does it do anything sensible with imported SVGs with embedded Javascript? What does it do with vector versus pixel based images?

You may say "ah, but jerf, I can easily provide a library that simply allows all those things no matter what... or, well, at least I can hypothesize such a library, providing it would actually be a pain... but there's no reason it couldn't exist". Exist, yes, but what you'd find is that if it let you do everything to every image format that it actually wouldn't do much! You can provide a library that takes a file, figures out what kind of image it is, and hands back a specific instance of a *JPEG or *GIF or *TIFF or *SVG, but if your supposed abstraction lets you do anything with anything, if you sit down and work out what it actually means for my JPEG support to give you access to the DCT tables directly and the GIF library to support the exact GIF animations and SVGs to offer direct manipulation of the SVG DOM and PNGs to offer direct access to all the frame elements in a PNG is that you don't have an "abstraction" anymore! Your "abstraction" is just a whole bunch of libraries bundled together with a thin abstraction around loading a file, and programmers using it this way get no ability to work across file types because they all have a completely different API.

And then you say "But I could offer a subset", which is 100% true, and that would be an abstraction. But then that abstraction would offer no access to PNG frames or JPG DCT tables.

And that's fine. There's no law whatsoever that a single "thing" must either be an abstraction or a library. It would be perfectly sensible to offer a total image solution that had a series of abstractions of varying level of restrictions and varying corresponding levels of power, and also include a full library for deep manipulation of every individual type. It's fine to offer a generalized "Image" type that has a ".ConcreteImage()" method that returns a concrete image that can be used with the libraries and "penetrate the abstraction". My point here is about the fact that if you want more "power", to operate on multiple image types with the same code, to take advantage of simply committing to a page-based interface to the Web and thereby being able to take advantage of the resulting simplifications it offers, to be able to plug arbitrary compression algorithms on to an IO stream, you always have to build these things on a reduction of power of some sort because you can't get any "abstractive" power if you're trying to offer everything to everybody. It's a fundamental fact of abstractions, it's precisely where they get their power from in the first place, and there is no option where you get those benefits without paying the price.

Oh, forgot to mention: Trying to offer everything to everybody has its own antipattern name, the Inner Platform effect. https://en.wikipedia.org/wiki/Inner-platform_effect

One way of viewing an Inner Platform is when you have an abstraction that is so "powerful" in the process of doing everything for everybody that it fails to offer any of the advantages of imposing the restrictions, but it still manages to deliver the disadvantages of abstractions! (Alternatively it can come from having some layer reduced power in the wrong way, and then having a layer above it trying to recover the original power. Either way these are always, always disasters.)

Thank you very much for this detailed explanation! I'll have to let it sink in a bit.

Lots of abstractions have an escape hatch down to the lower level, you can put assembly in your C code, most ORMs have some way to just run a query, etc.

I think the question I have is, what benefit does this provide? Let's say we could wave a magic wand and you can operate at any layer of abstraction. Is this beneficial in some way? The article is about leaky abstractions and states

> One reason the law of leaky abstractions is problematic is that it means that abstractions do not really simplify our lives as much as they were meant to.

I think I'm just struggling to understand how this would help with that.

It would help because you could tackle the problem at hand always at the right layer of abstraction.

If a certain aspect of the problem can be solved easily in a higher layer of abstraction, great! Let's solve it at that layer, because it's usually easier and allows for more expressiveness.

But whenever we need more control, we can seamlessly drop down to the lower layer and work there.

I think we need to find a fundamental principle that allows this. But I see barely anyone working on this - instead we keep trying to find higher and higher layers of abstractions (LLMs being the most recent addition) in the hopes they will get rid of the need of dealing with the lower layers. Which is a false hope, I feel.

The best paradigm for understanding abstractions is not the theory-and-model style (which requires hiding details irreversibly), but the equivalence style.

A good abstraction is e.g. summing a list whose elements are a monoid - summing the list is equivalent to adding up all the elements in a loop. Crucially, this doesn't require you to "forget" the specific type of element that your list has - a bad version of this library would say that your list elements have to be subtypes of some "number" type and the sum of your list came back as a "number", permanently destroying the details of the specific type that it actually is. But with the monoid model your "sum" is still whatever complex type you wanted it to be - you've just summed it up in the way appropriate to that type.

Interesting! Can you point me to some further reading or resources on these different paradigms?

> My hunch is that this constraint should be that abstractions must be reversible.

> Here's an example: When you use a compiler, you can work at a higher layer of abstraction (the higher-level language). But, this means you're now locked into that layer of abstraction. By that I mean, you can no longer work at the lower layer (assembly), even if you wanted to. You could in theory of course modify the compiler output after it's been generated, but then you'd have to somehow manually keep that work in sync whenever you want to re-generate. Using an abstraction kinda locks you into that layer.

Just to make sure I understand, you're proposing a constraint that would rule out every compiler in existence today? I feel like overall I think compilers have worked out well, but if I'm not misunderstanding and this is how you actually feel, I guess I at least should comment your audacity, because I don't think I'd be willing to seriously propose something that radical.

A lot of languages allow in-line assembly

I'm repeating the claim that the parent comment made; the assertion that compilers lock you into a level of abstraction is theirs, not mine.

Yes, you understood correctly.

What I'm saying is extremely radical and would require rethinking and rebuilding practically everything we have.

Thanks for the clarification! I'm probably too far into the orthodoxy to seriously consider something like this, but I admire your willingness to question things that most of us probably take for granted.

No, reversible abstractions are just one kind of abstraction. For instance, a machine code sequence to a linear sequence of assembly instructions is a reversible abstraction. Not every machine code sequence is expressible as a linear sequence of assembly instructions, but every linear sequence of assembly instructions has a trivial correspondence to a machine code sequence.

However, consider the jump to a C-like language. The key abstraction provided there is the abstraction of infinite local variables. The compiler manages this through a stack, register allocation, and stack spilling to provide the abstraction and consumes your ability to control the registers directly to provide this abstraction. To interface at both levels simultaneously requires the leakage of the implementation details of the abstraction and careful interaction.

What you can do easily is what I call a separable abstraction, a abstraction that can be restricted to just the places it is needed/removed where unneeded. In certain cases in C code you need to do some specific assembly instruction, sequence, or even function. This can be easily done by writing a assembly function that interfaces with the C code via the C ABI. What is happening there is that the C code defines a interface allowing you to drop down or even exit the abstraction hierarchy for the duration of that function. The ease of doing so makes C highly separable and is part of the reason why it is so easy to call out to C, but you hardly ever see anybody calling out to say Java or Haskell.

Of course, that is just one of the many properties of abstractions that can make them easier to use, simpler, and more robust.

There's a well-written article by Bret Victor on climbing the ladder of abstraction. It makes the same argument you made, in that climbing "down" the ladder is just as important as going "up"

https://worrydream.com/LadderOfAbstraction/

Thank you for posting, I love that article. Bret Victor is a genius in my opinion and his writings and talks have inspired many of the thoughts I've written above.

I work on programming languages and systems (virtual machines). A key thing with a systems programming language is that you need to be able to do things at the machine level. Here's a talk I gave a year ago about it: https://www.youtube.com/watch?v=jNcEBXqt9pU

That's not really true of, at least C compilers. Because compilers have ABI's and fixed calling conventions, it's straightforward, documented, and not uncommon (depending on your application area/deployment target) to drop down to the ASM layer if you need to do that.

It's definitely one of those things that makes C nice for bare metal programming.

Interesting, I'm curious though, once you do drop down to the ASM layer, how do you ensure that this code doesn't get overwritten by new compiler output? Or is this something you somehow include in the compile step?

Typically you'd have some assembly functions in a separate file. Compile to an object file and link it, as you'd do with a separate C file.

If you want to insert assembly snippets inside a C function, many C compilers have an inline assembly feature. For simple snippets, the C compiler can figure it out. For more complex things, you there are ways to tell the C compilers which registers you're using, so it does not step on your toes.

Thank you for explaining!

In my experience (admittedly limited) you include the assembly in the compile step. Your linker hopefully puts everything together so you can talk to yourself

Assembly can either be inline with the C code or in a separate file. It's just source. Of course, if you really want to have fun with breaking abstractions, check out linker script files. That's for when you absolutely need different bits of code and data in specific parts of the application. Fun!

Most ORMs give a way to integrate nicely with SQL if you need to reach down to that layer and still use the rest of the ORM features.

There is no silver bullet; everything is a trade off. Almost all of the time, the trade off is entirely worth it even if that gets you locked into that solution.

> Most ORMs give a way to integrate nicely with SQL if you need to reach down to that layer and still use the rest of the ORM features.

Agreed, that's a good thing, in my experience.

> Almost all of the time, the trade off is entirely worth it even if that gets you locked into that solution.

I wish this would match my experience.

What's funny is that ORMs giving you directly access to SQL is a leaky part of the abstraction but in this case that's good!

I think being locked into a some abstraction is so common place that you don't even consider it being a thing until you have a problem with it. Look at your examples: compilers, libraries, frameworks, etc. As an example, is anyone truly upset that coding in Python locks you into the Python ecosystem? Yet, I've used libraries/frameworks that didn't win the war of popularity and I'm still unfortunately committed. I think there's a bias at play in how we look at these things.

> Here's an example: When you use a compiler, you can work at a higher layer of abstraction (the higher-level language). But, this means you're now locked into that layer of abstraction. By that I mean, you can no longer work at the lower layer (assembly), even if you wanted to.

Native-code compilers commonly allow emitting assembly directly, but now your source code isn't portable between CPUs. Many interpreted languages, even most, allow FFI code to be imported, modifying the runtime accordingly, but now your program isn't portable between implementations of that language, and you have to be careful to make sure the behavior you've introduced doesn't mess with other parts of the system in unexpected ways.

Generalizing, it's often possible to drill down beneath the abstraction layer, but there's often an inherent price to be paid, whether it be taking pains to preserve the invariants of the abstraction, losing some of the benefits of it, or both.

There are better and worse versions of this layer, I would point to Lua as a language which is explicitly designed to cross the C/Lua boundary in both directions, and which did a good job of it. But nothing can change the fact that pure-Lua code simply won't segfault, but bring in userdata and it very easily can; the problems posed are inherent.

I think this is a good way to frame abstraction vs macro

Babel towers of macro edsls, aka learn lisp. https://github.com/combinatorylogic/mbase

You can probably find an IDE plugin that inlines the assembly for a c function. Most ids can show the assembly side by side with your c code so it wouldn't be that much of a step. To fulfill your vision you would also need a decompiler (and an inliner) to convert a block of assembly back into C if a corresponding C routine exists.

This is something I think a lot about.

I spend a lot of time trying to think of something that composes. Monads are one answer.

I think we need advanced term rewriting systems that also optimize and equivalise.

I really enjoy Joel on Software blog posts from this era.