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How I program with LLMs 2025-01-06 This document is a summary of my personal experiences using generative models while programming over the past year. It has not been a passive process. I have intentionally sought ways to use LLMs while programming to learn about them. The result has been that I now regularly use LLMs while working and I consider their benefits net-positive on my productivity. (My attempts to go back to programming without them are unpleasant.) Along the way I have found oft-repeated steps that can be automated, and a few of us are working on building those into a tool specifically for Go programming: . It’s very early but so far the experience has been positive.sketch.dev I am typically curious about new technology. It took very little experimentation with LLMs for me to want to see if I could extract practical value. There is an allure to a technology that can (at least some of the time) craft sophisticated responses to challenging questions. It is even more exciting...
8 months ago

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More from David Crawshaw

jsonfile: a quick hack for tinkering

jsonfile: a quick hack for tinkering Consider your requirements! A reference implementation A final thought 2024-02-06 The year is 2024. I am on vacation and dream up a couple of toy programs I would like to build. It has been a few years since I built a standalone toy, I have . So instead of actually building any of the toys I think of, I spend my time researching if anything has changed since the last time I did it. Should pick up new tools or techniques?been busy It turns out lots of things have changed! There’s some great stuff out there, including decent quorum-write regional cloud databases now. Oh and the ability to have a fascinating hour-long novel conversation with transistors. But things are still awkward for small fast tinkering. Going back in time, I struggled constantly rewriting the database for the prototype for Tailscale, so I ended up writing my in-memory objects out as . It went far further than I planned. Somewhere in the intervening years I convinced myself it must have been a bad idea even for toys, given all the pain migrating away from it caused. But now that I find myself in an empty text editor wanting to write a little web server, I am not so sure. The migration was painful, and a lot of that pain was born by others (which is unfortunate, I find handing a mess to someone else deeply unpleasant). Much of that pain came from the brittle design of the caching layers on top (also my doing), which came from not moving to an SQL system soon enough.a JSON file I suspect, considering the process retrospect, a great deal of that pain can be avoided by committing to migrating directly to an SQL system the moment you need an index. You can pay down a lot of exploratory design work in a prototype before you need an index, which n is small, full scans are fine. But you don’t make it very far into production before one of your values of n crosses something around a thousand and you long for an index. With a clear exit strategy for avoiding big messes, that means the JSON file as database is still a valid technique for prototyping. And having spent a couple of days remembering what a misery it is to write a unit test for software that uses postgresql (mocks? docker?? for a database program I first ran on a computer with less power than my 2024 wrist watch?) and struggling figuring out how to make my cgo sqlite cross-compile to Windows, I’m firmly back to thinking a JSON file can be a perfectly adequate database for a 200-line toy. Before you jump into this and discover it won’t work, or just as bad, dismiss the small and unscaling as always a bad idea, consider the requirements of your software. Using a JSON file as a database means your software: Programming is the art of tradeoffs. You have to decide what matters and what does not. Some of those decisions need to be made early, usually with imperfect information. You may very well need a powerful SQL DBMS from the moment you start programming, depending on the kind of program you’re writing! An implementation of jsonfile (which Brad called JSONMutexDB, which is cooler because it has an x in it, but requires more typing) can fit in about 70 lines of Go. But there are a couple of lessons we ran into in the early days of Tailscale that can be paid down relatively easily, growing the implementation to 85 lines. (More with comments!) I think it’s worth describing the interesting things we ran into, both in code and here. You can find the implementation of jsonfile here: . The interface is:https://github.com/crawshaw/jsonfile/blob/main/jsonfile.go There is some experience behind this design. In no particular order: One of the early pain points in the transition was figuring out the equivalent of when to , , and . The first version exposed the mutex directly (which was later converted into a RWMutex).BEGINCOMMITROLLBACK There is no advantage to paying this transition cost later. It is easy to box up read/write transactions with a callback. This API does that, and provides a great point to include other safety mechanisms. There are two forms of this. The first is if the write fn fails half-way through, having edited the db object in some way. To avoid this, the implementation first creates an entirely new copy of the DB before applying the edit, so the entire change set can be thrown away on error. Yes, this is inefficient. No, it doesn’t matter. Inefficiency in this design is dominated by the I/O required to write the entire database on every edit. If you are concerned about the duplicate-on-write cost, you are not modeling I/O cost appropriately (which is important, because if I/O matters, switch to SQL). The second is from a full disk. The easy to write a file in Go is to call os.WriteFile, which the first implementation did. But that means: A failure can occur in any of those system calls, resulting in a corrupt DB. So this implementation creates a new file, loads the DB into it, and when that has all succeeded, uses . It is not a panacea, our operating systems do not make all the promises we wish they would about rename. But it is much better than the default.rename(2) A nasty issue I have run into twice is aliasing memory. This involves doing something like: An intermediate version of this code kept the previous database file on write. But there’s an easier and even more robust strategy: never rename the file back to the original. Always create a new file, . On starting, load the most recent file. Then when your data is worth backing up (if ever), have a separate program prune down the number of files and send them somewhere robust.Backups.mydb.json.<timestamp> Not in this implementation but you may want to consider, is removing the risk of a Read function editing memory. You can do that with View* types generated by the tool. It’s neat, but more than quadruples the complexity of JSONFileDB, complicates the build system, and initially isn’t very important in the sorts of programs I write. I have found several memory aliasing bugs in all the code I’ve written on top of a JSON file, but have yet to accidentally write when reading. Still, for large code bases Views are quite pleasant and well-worth considering about the point when a project should move to a real SQL.Constant memory.viewer There is some room for performance improvements too (using cloner instead of unmarshalling a fresh copy of the data for writing), though I must point out again that needing more performance is a good sign it is time to move on to SQLite, or something bigger. It’s a tiny library. Copy and edit as needed. It is an all-new implementation so I will be fixing bugs as I find them. (As a bonus: this was my first time using a Go generic! 👴 It went fine. Parametric polymorphism is ok.) Why go out of my way to devise an inadequate replacement for a database? Most projects fail before they start. They fail because the is too high. Our dreams are big and usually too much, as dreams should be.activation energy But software is not building a house or traveling the world. You can realize a dream with the tools you have on you now, in a few spare hours. This is the great joy of it, you are free from physical and economic constraint. If you start. Be willing to compromise almost everything to start. Doesn’t have a lot of data. Keep it to a few megabytes. The data structure is boring enough not to require indexes. You don’t need something interesting like full-text search. You do plenty of reads, but writes are infrequent. Ideally no more than one every few seconds. Truncating the database file Making multiple system calls to .write(2) Calling .close(2) type JSONFile[Data any] struct { … } func New[Data any](path string) (*JSONFile[Data], error) func Load[Data any](path string) (*JSONFile[Data], error) func (p *JSONFile[Data]) Read(fn func(data *Data)) func (p *JSONFile[Data]) Write(fn func(*Data) error) error list := []int{1, 2, 3} db.Write(func() { db.List = list }) list[0] = 10 // editing the database! Transactions Database corruption through partial writes Memory aliasing Some changes you may want to consider

a year ago 32 votes
new year, same plan

new year, same plan 2022-12-31 Some months ago, the bill from GCE for hosting this blog jumped from nearly nothing to far too much for what it is, so I moved provider and needed to write a blog post to test it all. I could have figured out why my current provider hiked the price. Presumably I was Holding It Wrong and with just a few grip adjustments I could get the price dropped. But if someone mysteriously starts charging you more money, and there are other people who offer the same service, why would you stay? This has not been a particularly easy year, for a variety of reasons. But here I am at the end of it, and beyond a few painful mistakes that in retrospect I did not have enough information to get right, I made mostly the same decisions I would again. There were a handful of truly wonderful moments. So the plan for 2023 is the same: keep the kids intact, and make programming more fun. There is also the question of Twitter. It took me a few years to develop the skin to handle the generally unpleasant environment. (I can certainly see why almost no old Twitter employees used their product.) The experience recently has degraded, there are still plenty of funny tweets, but far less moments of interesting content. Here is a recent exception, but it is notable because it's the first time in weeks I learned anything from twitter: . I now find more new ideas hiding in HN comments than on Twitter.https://twitter.com/lrocket/status/1608883621980704768 Many people I know have sort-of moved to Mastodon, but it has a pretty horrible UX that is just enough work that I, on the whole, don't enjoy it much. And the fascinating insights don't seem to be there yet, but I'm still reading and waiting. On the writing side, it might be a good idea to lower the standards (and length) of my blog posts to replace writing tweets. But maybe there isn't much value in me writing short notes anyway, are my contributions as fascinating as the ones I used to sift through Twitter to read? Not really. So maybe the answer is to give up the format entirely. That might be something new for 2023. Here is something to think about for the new year: http://www.shoppbs.pbs.org/now/transcript/transcriptNOW140_full.html DAVID BRANCACCIO: There's a little sweet moment, I've got to say, in a very intense book– your latest– in which you're heading out the door and your wife says what are you doing? I think you say– I'm getting– I'm going to buy an envelope. KURT VONNEGUT: Yeah. DAVID BRANCACCIO: What happens then? KURT VONNEGUT: Oh, she says well, you're not a poor man. You know, why don't you go online and buy a hundred envelopes and put them in the closet? And so I pretend not to hear her. And go out to get an envelope because I'm going to have a hell of a good time in the process of buying one envelope. I meet a lot of people. And, see some great looking babes. And a fire engine goes by. And I give them the thumbs up. And, and ask a woman what kind of dog that is. And, and I don't know. The moral of the story is, is we're here on Earth to fart around. And, of course, the computers will do us out of that. And, what the computer people don't realize, or they don't care, is we're dancing animals. You know, we love to move around. And, we're not supposed to dance at all anymore.

over a year ago 30 votes
log4j: between a rock and a hard place

log4j: between a rock and a hard place 2021-12-11 What does backwards compatibility mean to me? Backwards compatibility should not have forced log4j to keep LDAP/JNDI URLs The other side of compatibility: being cautious adding features There is more than enough written on the mechanics of and mitigations for the recent . On prevention, this is the most interesting widely-reshared I have seen:severe RCE in log4jinsight This is making the rounds because highly-profitable companies are using infrastructure they do not pay for. That is a worthy topic, but not the most interesting thing in this particular case because it would not clearly have contributed to preventing this bug. It is the second statement in this tweet that is worthy of attention: the long ago, but could not because of the backwards compatibility promises they are held to.maintainers of log4j would have loved to remove this bad feature I am often heard to say that I love backwards compatibility, and that it is underrated. But what exactly do I mean? I don't mean that whenever I upgrade a dependency, I expect zero side effects. If a library function gets two times faster in an upgrade, that is a change in behavior that might break my software! But obviously the exact timings of functions can change between versions. In some extreme cases I need libraries to promise the algorithmic complexity of run time or memory usage, where I am providing extremely large inputs, or need constant-time algorithms to avoid timing attacks. But I don't need that from a logging library. So let me back up and describe what is important. The ideal version of this is I run my package manager's upgrade command, execute the tests, commit the output, and not think about it any more. This means the API/ABI stays similar enough that the compiler won't break, the behavior of the library routines is similar enough the tests will pass, and no other constraints, such as total binary size limits, are exceeded. This is impossible in the general case. The only way to achieve it is to not make any changes at all. When we write down a promise, we leave lots of definitional holes in the promise. E.g. take the (generally excellent) :Go compatibility promise Here "correctly" means according to the Go language specification and the API documentation. The spec and the docs do not cover run time, memory use, or binary size. The next version of Go can be 10x slower and be compatible! But I can assure you if that were the case I would fail my goal of not spending much time upgrading a dependency. But the Go team know this, and work to the spirit of their promise. Very occasionally they break things, for security reasons, and when they do I have to spend time upgrading a dependency for a really good reason: my program needs it.very If I want my program to work correctly I should write tests for all the behaviors I care about. But like all programmers, I am short on hours in the day to do all that needs doing, and never have enough tests. So whenever a change in behavior happens in an upstream library that my tests don't catch but makes it into production, my instinct is to blame upstream. This is of course unfair, the burden for releasing good programs is borne by the person pressing the release button. But it is an expression of a programming social contract that has taken hold: a good software project tries to break downstream as little as possible, and when we do break downstream, we should do our best to make the breakage obvious and easy to fix. No compatibility promise I have seen covers the spirit of minimizing breakage and moving it to the right part of the process. As far as I can tell, engineers aren't taught this in school, and many have never heard the concept articulated. So much of best practice in releasing libraries is learned on the job and not well communicated (yet). Good upstream dependencies are maintained by people who have figured this out the hard way and do their best by their users. As a user, it is extremely hard to know what kind of library you are getting when you first consider a dependency, unless it is a very old and well established project. This is where software goes wrong the most for me. I want, year after year, to come back to a tool and be able to apply the knowledge I acquired the last time I used it, to new things I learn, and build on it. I want to hone my craft by growing a deep understanding of the tools I use. Some new features are additive. If I buy a new for framing, and it has a notch on it my old one didn't that I can use as a shortcut in marking up a beam, its presence does not invalidate my old knowledge. If the new interior notch replaces a marking that was on the outside of the square, then when I go to find my trusty marking I remember from years ago, and it's missing, I need to stop and figure out a new way to solve this old problem. Maybe I will notice the new feature, or, more likely, I'll pull out the tape measure measure I know how to use and find my mark that (slower) way. If someone who knew what they were doing saw me they could correct me! But like programming, I'm usually making a mess with wood alone in a few spare hours on a Saturday.speed square When software "upgrades" invalidate my old knowledge, it makes me a worse programmer. I can spend time getting back to where I was, but that's time I am not spending improving on where I was. To give a concrete example: I will never be an expert at developing for macOS or iOS. I bounce into and out of projects for Apple devices, spending no more than 10% of my hours on their platform. Their APIs change constantly. The buttons in Xcode move so quickly I sometimes wonder if it's happening before my eyes. Try looking up some Swift syntax on stack overflow and you'll find the answers are constantly edited for the latest version of Swift. At this point, I assume every time I come back to macOS/iOS, that I know nothing and I am learning the platform for the first time. Compare the shifting sands of Swift with the stability of awk. I have spent not a tenth of the time learning awk that I have spent relearning Swift, and yet I am about as capable in each language. An awk one-liner I learned 20 years ago still works today! When I see someone use awk to solve a problem, I'm enthusiastic to learn how they did it, because I know that 20 years from now the trick will work. By what backwards compatibility means to me, a project like log4j will break fewer people by removing a feature like the JNDI URLs than by marking an old API method with some mechanical deprecation notice that causes a build process's equivalent of to fail and moving it to a new name. They will in practice, break fewer people removing this feature than they would by slowing down a critical path by 10%, which is the sort of thing that can trivially slip into a release unnoticed.-Wall But the spirit of compatibility promises appears to be poorly understood across our industry (as software updates demonstrate to me every week), and so we lean on the pseudo-legalistic wording of project documentation to write strongly worded emails or snarky tweets any time a project makes work for us (because most projects don't get it, so surely every example of a breakage must be a project that doesn't get it, not a good reason), and upstream maintainers become defensive and overly conservative. The result is now everyone's Java software is broken! We as a profession misunderstand and misuse the concept of backwards compatibility, both upstream and downstream, by focusing on narrow legalistic definitions instead of outcomes. This is a harder, longer topic that maybe I'll find enough clarity to write properly about one day. It should be easy to hack up code and share it! We should also be cautious about adding burdensome features. This particular bug feels impossibly strange to me, because my idea of a logging API is file descriptor number 2 with the system call. None of the bells and whistles are necessary and we should be conservative about our core libraries. Indeed libraries like these are why I have been growing ever-more skeptical of using any depdendencies, and now force myself to read a big chunk of any library before adding it to a project.write But I have also written my share of misfeatures, as much as I would like to forget them. I am thankful my code I don't like has never achieved the success or wide use of log4j, and I cannot fault diligent (and unpaid!) maintainers doing their best under those circumstances. Log4j maintainers have been working sleeplessly on mitigation measures; fixes, docs, CVE, replies to inquiries, etc. Yet nothing is stopping people to bash us, for work we aren't paid for, for a feature we all dislike yet needed to keep due to backward compatibility concerns. It is intended that programs written to the Go 1 specification will continue to compile and run correctly, unchanged, over the lifetime of that specification. I want to not spend much time upgrading a dependency I want any problems caused by the upgrade to be caught early, not in production. I want to be able to build knowledge of the library over a long time, to hone my craft

over a year ago 35 votes
Software I’m thankful for

Software I’m thankful for 2021-11-25 A few of the things that come to mind, this thanksgiving. Most Unix-ish APIs, from files to sockets are a bit of a mess today. Endless poorly documented sockopts, unexpected changes in write semantics across FSs and OSes, good luck trying to figure out . But despite the mess, I can generally wrap my head around open/read/write/close. I can strace a binary and figure out the sequence and decipher what’s going on. Sprinkle in some printfs and state is quickly debuggable. Stack traces are useful!mtimes Enormous effort has been spent on many projects to replace this style of I/O programming, for efficiency or aesthetics, often with an asynchronous bent. I am thankful for this old reliable standby of synchronous open/read/write/close, and hope to see it revived and reinvented throughout my career to be cleaner and simpler. Goroutines are coroutines with compiler/runtime optimized yielding, to make them behave like threads. This breathes new life into the previous technology I’m thankful for: simple blocking I/O. With goroutines it becomes cheap to write large-scale blocking servers without running out of OS resources (like heavy threads, on OSes where they’re heavy, or FDs). It also makes it possible to use blocking interfaces between “threads” within a process without paying the ever-growing price of a context switch in the post- world.spectre This is the first year where the team working on Tailscale has outgrown and eclipsed me to the point where I can be thankful for Tailscale without feeling like I’m thanking myself. Many of the wonderful new features that let me easily wire machines together wherever they are, like userspace networking or MagicDNS, are not my doing. I’m thankful for the product, and the opportunity to work with the best engineering team I’ve ever had the privilege of being part of. Much like open/read/write/close, SQLite is an island of stability in a constantly changing technical landscape. Techniques I learned 10 or 15 years ago using SQLite work today. As a bonus, it does so much more than then: WAL mode for highly-concurrent servers, advanced SQL like window functions, excellent ATTACH semantics. It has done all of this while keeping the number of, in the projects own language, “goofy design” decisions to a minimum and holding true to its mission of being “lite”. I aspire to write such wonderful software. JSON is the worst form of encoding — except for all the others that have been tried. It’s complicated, but not too complicated. It’s not easily read by humans, but it can be read by humans. It is possible to extend it in intuitive ways. When it gets printed onto your terminal, you can figure out what’s going on without going and finding the magic decoder ring of the week. It makes some things that are extremely hard with XML or INI easy, without introducing accidental Turing completeness or turning . Writing software is better for it, and shows the immense effect carefully describing something can do for programming. JSON was everywhere in our JavaScript before the term was defined, the definition let us see it and use it elsewhere.country codes into booleans WireGuard is a great demonstration of why the total complexity of the implementation ends up affecting the UX of the product. In theory I could have been making tunnels between my devices for years with IPSec or TLS, in practice I’d completely given it up until something came along that made it easier. It didn’t make it easier by putting a slick UI over complex technology, it made the underlying technology simpler, so even I could (eventually) figure out the configuration. Most importantly, by not eating my entire complexity budget with its own internals, I could suddenly see it as a building block in larger projects. Complexity makes more things possible, and fewer things possible, simultaneously. WireGuard is a beautiful example of simplicity and I’m thankful for it. Before Go became popular, the fast programming language compilers of the 90s had mostly fallen by the wayside, to be replaced with a bimodal world of interpreters/JITs on one side and creaky slow compilers attempting to produce extremely optimal code on the other. The main Go toolchain found, or rediscovered, a new optimal point in the plane of tradeoffs for programming languages to sit: ahead of time compiled, but with a fast less-than-optimal compiler. It has managed to continue to hold that interesting, unstable equilibrium for a decade now, which is incredibly impressive. (E.g. I personally would love to improve its inliner, but know that it’s nearly impossible to get too far into that project without sacrificing a lot of the compiler’s speed.) I’ve always been cranky about GCC: I find its codebase nearly impossible to modify, it’s slow, the associated ducks I need to line up to make it useful (binutils, libc, etc) blow out the complexity budget on any project I try to start before I get far, and it is associated with GNU, which I used to view as an oddity and now view as a millstone around the neck of an otherwise excellent software project. But these are all the sorts of complaints you only make when using something truly invaluable. GCC is invaluable. I would never have learned to program if a free C compiler hadn’t been available in the 90s, so I owe it my career. To this day, it vies neck-and-neck with LLVM for best performing object code. Without the competition between them, compiler technology would stagnate. And while LLVM now benefits from $10s or $100s of millions a year in Silicon Valley salaries working on it, GCC does it all with far less investment. I’m thankful it keeps on going. I keep trying to quit vim. I keep ending up inside a terminal, inside vim, writing code. Like SQLite, vim is an island of stability over my career. While I wish IDEs were better, I am extremely thankful for tools that work and respect the effort I have taken to learn them, decade after decade. SSH gets me from here to there, and has done since ~1999. There is a lot about ssh that needs reinventing, but I am thankful for stable, reliable tools. It takes a lot of work to keep something like ssh working and secure, and if the maintainers are ever looking for someone to buy them a round they know where to find me. How would I get anything done without all the wonderful information on the public web and search engines to find it? What an amazing achievement. Thanks everyone, for making computers so great. open/read/write/close goroutines Tailscale SQLite JSON WireGuard The speed of the Go compiler GCC vim ssh The public web and search engines

over a year ago 35 votes

More in programming

Apologies and forgiveness

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12 hours ago 4 votes
Understanding Bazel remote caching

A deep dive into the Action Cache, the CAS, and the security issues that arise from using Bazel with a remote cache but without remote execution

13 hours ago 4 votes
Trying to Make Sense of Casing Conventions on the Web

(I present to you my stream of consciousness on the topic of casing as it applies to the web platform.) I’m reading about the new command and commandfor attributes — which I’m super excited about, declarative behavior invocation in HTML? YES PLEASE!! — and one thing that strikes me is the casing in these APIs. For example, the command attribute has a variety of values in HTML which correspond to APIs in JavaScript. The show-popover attribute value maps to .showPopover() in JavaScript. hide-popover maps to .hidePopover(), etc. So what we have is: lowercase in attribute names e.g. commandfor="..." kebab-case in attribute values e.g. show-popover camelCase for JS counterparts e.g. showPopover() After thinking about this a little more, I remember that HTML attributes names are case insensitive, so the browser will normalize them to lowercase during parsing. Given that, I suppose you could write commandFor="..." but it’s effectively the same. Ok, lowercase attribute names in HTML makes sense. The related popover attributes follow the same convention: popovertarget popovertargetaction And there are many other attribute names in HTML that are lowercase, e.g.: maxlength novalidate contenteditable autocomplete formenctype So that all makes sense. But wait, there are some attribute names with hyphens in them, like aria-label="..." and data-value="...". So why isn’t it command-for="..."? Well, upon further reflection, I suppose those attributes were named that way for extensibility’s sake: they are essentially wildcard attributes that represent a family of attributes that are all under the same namespace: aria-* and data-*. But wait, isn’t that an argument for doing popover-target and popover-target-action? Or command and command-for? But wait (I keep saying that) there are kebab-case attribute names in HTML — like http-equiv on the <meta> tag, or accept-charset on the form tag — but those seem more like legacy exceptions. It seems like the only answer here is: there is no rule. Naming is driven by convention and decisions are made on a case-by-case basis. But if I had to summarize, it would probably be that the default casing for new APIs tends to follow the rules I outlined at the start (and what’s reflected in the new command APIs): lowercase for HTML attributes names kebab-case for HTML attribute values camelCase for JS counterparts Let’s not even get into SVG attribute names We need one of those “bless this mess” signs that we can hang over the World Wide Web. Email · Mastodon · Bluesky

2 days ago 6 votes
The Angels and Demons of Nondeterminism

Greetings everyone! You might have noticed that it's September and I don't have the next version of Logic for Programmers ready. As penance, here's ten free copies of the book. So a few months ago I wrote a newsletter about how we use nondeterminism in formal methods. The overarching idea: Nondeterminism is when multiple paths are possible from a starting state. A system preserves a property if it holds on all possible paths. If even one path violates the property, then we have a bug. An intuitive model of this is that for this is that when faced with a nondeterministic choice, the system always makes the worst possible choice. This is sometimes called demonic nondeterminism and is favored in formal methods because we are paranoid to a fault. The opposite would be angelic nondeterminism, where the system always makes the best possible choice. A property then holds if any possible path satisfies that property.1 This is not as common in FM, but it still has its uses! "Players can access the secret level" or "We can always shut down the computer" are reachability properties, that something is possible even if not actually done. In broader computer science research, I'd say that angelic nondeterminism is more popular, due to its widespread use in complexity analysis and programming languages. Complexity Analysis P is the set of all "decision problems" (basically, boolean functions) can be solved in polynomial time: there's an algorithm that's worst-case in O(n), O(n²), O(n³), etc.2 NP is the set of all problems that can be solved in polynomial time by an algorithm with angelic nondeterminism.3 For example, the question "does list l contain x" can be solved in O(1) time by a nondeterministic algorithm: fun is_member(l: List[T], x: T): bool { if l == [] {return false}; guess i in 0..<(len(l)-1); return l[i] == x; } Say call is_member([a, b, c, d], c). The best possible choice would be to guess i = 2, which would correctly return true. Now call is_member([a, b], d). No matter what we guess, the algorithm correctly returns false. and just return false. Ergo, O(1). NP stands for "Nondeterministic Polynomial". (And I just now realized something pretty cool: you can say that P is the set of all problems solvable in polynomial time under demonic nondeterminism, which is a nice parallel between the two classes.) Computer scientists have proven that angelic nondeterminism doesn't give us any more "power": there are no problems solvable with AN that aren't also solvable deterministically. The big question is whether AN is more efficient: it is widely believed, but not proven, that there are problems in NP but not in P. Most famously, "Is there any variable assignment that makes this boolean formula true?" A polynomial AN algorithm is again easy: fun SAT(f(x1, x2, …: bool): bool): bool { N = num_params(f) for i in 1..=num_params(f) { guess x_i in {true, false} } return f(x_1, x_2, …) } The best deterministic algorithms we have to solve the same problem are worst-case exponential with the number of boolean parameters. This a real frustrating problem because real computers don't have angelic nondeterminism, so problems like SAT remain hard. We can solve most "well-behaved" instances of the problem in reasonable time, but the worst-case instances get intractable real fast. Means of Abstraction We can directly turn an AN algorithm into a (possibly much slower) deterministic algorithm, such as by backtracking. This makes AN a pretty good abstraction over what an algorithm is doing. Does the regex (a+b)\1+ match "abaabaabaab"? Yes, if the regex engine nondeterministically guesses that it needs to start at the third letter and make the group aab. How does my PL's regex implementation find that match? I dunno, backtracking or NFA construction or something, I don't need to know the deterministic specifics in order to use the nondeterministic abstraction. Neel Krishnaswami has a great definition of 'declarative language': "any language with a semantics has some nontrivial existential quantifiers in it". I'm not sure if this is identical to saying "a language with an angelic nondeterministic abstraction", but they must be pretty close, and all of his examples match: SQL's selects and joins Parsing DSLs Logic programming's unification Constraint solving On top of that I'd add CSS selectors and planner's actions; all nondeterministic abstractions over a deterministic implementation. He also says that the things programmers hate most in declarative languages are features that "that expose the operational model": constraint solver search strategies, Prolog cuts, regex backreferences, etc. Which again matches my experiences with angelic nondeterminism: I dread features that force me to understand the deterministic implementation. But they're necessary, since P probably != NP and so we need to worry about operational optimizations. Eldritch Nondeterminism If you need to know the ratio of good/bad paths, the number of good paths, or probability, or anything more than "there is a good path" or "there is a bad path", you are beyond the reach of heaven or hell. Angelic and demonic nondeterminism are duals: angelic returns "yes" if some choice: correct and demonic returns "no" if !all choice: correct, which is the same as some choice: !correct. ↩ Pet peeve about Big-O notation: O(n²) is the set of all algorithms that, for sufficiently large problem sizes, grow no faster that quadratically. "Bubblesort has O(n²) complexity" should be written Bubblesort in O(n²), not Bubblesort = O(n²). ↩ To be precise, solvable in polynomial time by a Nondeterministic Turing Machine, a very particular model of computation. We can broadly talk about P and NP without framing everything in terms of Turing machines, but some details of complexity classes (like the existence "weak NP-hardness") kinda need Turing machines to make sense. ↩

2 days ago 6 votes
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2 days ago 9 votes