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Lambda Calculus in 400 Bytes
- Traubenfuchs 5y agoI remember memorizing how to solve (reduce? resolve? expand?) lambda calculus expressions by hand that went over multiple lines for my degree but I never had the faintest clue what it is and why I was learning this and quickly forgot how to do it.
- chriswarbo 5y ago> solve (reduce? resolve? expand?) Reduction (in particular "beta-reduction") is essentially 'calling a function with an argument' (just defined in a precise, mathematically-rigorous way). Since lambda calculus only has functions (AKA "lambdas"), "reducing an expression" is another way of saying "running/executing a program". "Expansion" would be going the other way; e.g. introducing an abstraction layer which, when reduced/executed, would result in the original expression.
- rpmuller 5y agoSlow down! I’m still catching up to sectorlisp!
- openfuture 5y agoEverything she touches is gold. Also: she would be the most fearsome cybercriminal I can imagine.
- ALLTaken 5y agoI was thinking of the same and also that this is just a glimpse of what's possible and possibly just intended this way to raise the interest in those genuinely curious. Unfortunately I don't fully understand from just glancing over the article (sorry, my bad), but I understand the implications. And these are incredibly fascinating to me. I was always thinking of living-code (just like DNA) living through the packet-state. Anyway I think abstracting away variables+lexer via sed and indexing is hot! My mind is so rusty, but I can imagine constructing an elegant & expressive language using "category theory + lambda calculus" and oh my god... instead of computing a single result using binary encoding we can compute all results in parallel (array-based) by using a lossless compressor (similar to data-fusion). A Finite State Entropy Encoder (FSE) with a multi-symbol alphabet (>2) can be used for this purpose. FSE is a very interesting development in ANS encoding (Asymmetric numeral systems). I need to put all these pieces together + self-modifying code. Because I don't have the feeling that this is a dumb idea at all. Maybe infecting any device like the skynet code isn't that far of a stretch away? Disregarding any malicious intent, this is simply inspiring. Maybe I'm just too much of a nerd though to enjoy this a bit too much.. idk.
- martyalain 5y agoEven if I'am far from understand your paper in deep, I like the way you explore new ways in lambda-calculus, mainly I think following John Tromp's works. I'm exploring lambda-calculus with binary numbers of any size using a home-made language, http://lambdaway.free.fr/lambdawalks http://lambdaway.free.fr/lambdawalks, in this wiki page, http://lambdaway.free.fr/lambdawalks/?view=oops6 http://lambdaway.free.fr/lambdawalks/?view=oops6, and it's funny. Your work is inspiring. Thank you.
- caaqil 5y agoJustine and making things ridiculously small. Maybe off-topic but seriously impressive projects by the author, consistently. It's amazing.
- ILMostro7 5y agoIIUC, this doesn't necessarily translate to more efficient programming, just because the program size is small. It's elegant. Just wondering about possible applications. Maybe I'm not understanding how currying works.
- ALLTaken 5y agoIndeed I wish there was a video of someone explaining this article on a whiteboard/chalkboard.
- CRConrad 5y agoMichael Penn, Burkard Polster, Matt Parker, or one of the Numberphile guys?
- jart 5y agoAuthor here. Love SectorLambda for its mathematical beauty. If you're hungry for more efficient practical computation, check out my C language projects like Cosmopolitan Libc and Redbean. For instance, rather than processing data at 16kbps it's able to do things like crc32 at 22gBps https://github.com/jart/cosmopolitan/blob/d6a039821f927cc81b71e11f21599ff93e1fed62/libc/nexgen32e/crc32-pclmul.S#L210 https://github.com/jart/cosmopolitan/blob/d6a039821f927cc81b... and memset goes 126gBps https://github.com/jart/cosmopolitan/blob/d6a039821f927cc81b71e11f21599ff93e1fed62/libc/intrin/memset.c#L110 https://github.com/jart/cosmopolitan/blob/d6a039821f927cc81b...
- montroser 5y agoThe Informal Description section on Wikipedia is good for more background on Lambda Calculus: https://en.m.wikipedia.org/wiki/Lambda_calculus https://en.m.wikipedia.org/wiki/Lambda_calculus
- User23 5y agoOne really interesting development of the Lambda calculus is the De Bruijn index. It does away with variable names altogether. It solves the name collision problem and would be an interesting way to write hygienic macros. [1] https://en.m.wikipedia.org/wiki/De_Bruijn_index https://en.m.wikipedia.org/wiki/De_Bruijn_index
- chalst 5y agoTromp's binary lambda calculus, which is what Justine is using, is based on de Bruijn indices. It works, but it's very fiddly. My favourite way of solving the problem of names in the lambda calculus is to use Pitts-Gabbay nominal syntax. Wikipedia has a weak article on them, which I mean someday to fix up: https://en.wikipedia.org/wiki/Nominal_terms_(computer_science) https://en.wikipedia.org/wiki/Nominal_terms_(computer_scienc...
- User23 5y agoInteresting! I hadn’t come across this. Thank you!
- chriswarbo 5y agoI really like de Bruijn indexes, but whenever alternatives are suggested I always like to mention the paper "I am not a number, I am a free variable", if only for the title ;) https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.365.2479&rep=rep1&type=pdf https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36...
- uncomputation 5y agoAnyone interested in BLC can find another introduction which I found personally helpful here: https://tromp.github.io/cl/Binary_lambda_calculus.html https://tromp.github.io/cl/Binary_lambda_calculus.html
- tromp 5y agoIndeed; that's one of the 3 references listed at the bottom of the article: > See Also > https://tromp.github.io/cl/Binary_lambda_calculus.html https://tromp.github.io/cl/Binary_lambda_calculus.html > https://www.ioccc.org/2012/tromp/hint.html https://www.ioccc.org/2012/tromp/hint.html > https://github.com/tromp/AIT https://github.com/tromp/AIT
- deleted 5y ago[deleted]
- simonw 5y agoI feel like you could build a semester-long university course out of this single web page, and it would be a really valuable way to spend that semester.
- igravious 5y agoAgreed. This is sheer brilliance. Technical work like this borders on art. It is inspiring in the traditional sense of the word, not in the Ted Talks sense of the word, as in it inspires me to blow the dust off old ideas I've had and get working on them and to set the quality bar high for myself.
- dukeofdoom 5y agoComputerphile has a great video on Lambda Calculus https://www.youtube.com/watch?v=eis11j_iGMs https://www.youtube.com/watch?v=eis11j_iGMs
- miovoid 5y agoIt looks like this it is great for FPGA.
- ncmncm 5y agoGreat for naked transistors.
- tonerow 5y agoDoes anyone know how the subroutine diagrams are generated, or have more info about these graphs in general?
- jart 5y agoBuild https://github.com/tromp/AIT https://github.com/tromp/AIT and you can use ./blc Pbm foo.lam >foo.pbm; convert foo.pbm -interpolate Nearest -filter point -resize 800% foo.png
- siddboots 5y agoThey're called "Lambda Diagrams". See the inventor's homepage [1], and some animations [2]. There's actually a long and obscure history of visualizations for lambda calculus. One of the originals is "To Dissect a Mockingbird" [3], which if I recall correctly, was the main thing on the internet in 1996. [1] https://tromp.github.io/ https://tromp.github.io/ [2] https://www.youtube.com/playlist?list=PLi8_XqluS5xc7GL-bgVrxpA2Uww6nK0gV https://www.youtube.com/playlist?list=PLi8_XqluS5xc7GL-bgVrx... [3] https://dkeenan.com/Lambda/ https://dkeenan.com/Lambda/
- tonerow 5y agoThank you!
- ravi-delia 5y agoI was about to mention SectorLisp as a somewhat related project when I noticed that it was written by the very same genius, not to mention Blinkenlights, which has provided many hours of delight. Incredible!
- smasher164 5y agoJustine, this is one of the coolest things I’ve ever seen! I’m flabbergasted. Are you a wizard?
- livinglist 5y agoshe surely is! this so far is the best thing I’ve seen on internet today.
- Shared404 5y ago*She Unless I've missed something. You should also check out the rest of her work! It's all amazing, SectorLISP, Blinkenlights and APE (Actually Portable Executable) are the really well known ones, but many of the other projects are things many programmers would have as the centerpiece of their portfolio.
- grimgrin 5y agoqueen justine
- fouronnes3 5y agoSlightly unrelated, but this thread is giving me a serious learning itch. Any book or online class recommendations on lambda calculus, combinators and that whole area of CS? Preferably written for the experienced programmer but very average mathematician.
- masklinn 5y agoIf you’re starting from zero this old classic could serve as an appetiser: https://tomstu.art/programming-with-nothing https://tomstu.art/programming-with-nothing
- arianvanp 5y agoI'd say https://www.cis.upenn.edu/~bcpierce/tapl/ https://www.cis.upenn.edu/~bcpierce/tapl/ is the ultimate bible on this topic. During my semester we only went through a few of its chapters but it was very enjoyable in my opinion.
- Verdex 5y agoAlso check out the "sequel" https://www.cis.upenn.edu/~bcpierce/attapl/ https://www.cis.upenn.edu/~bcpierce/attapl/. Pierce wrote the first book whereas this one is a series of articles edited by Pierce. However Advanced Topics covers a few areas that I have been hard pressed to find covered in other places. Row types, dependent types, linear types, etc.
- tomstuart 5y agoI wrote https://computationbook.com/ https://computationbook.com/ for that audience.
- arisbe__ 5y agoAn Introduction to Functional Programming Through Lambda Calculus by Greg Michaelson really spells out the lambda calculus. Regarding combinators the famous intro is the latter half of Raymond Smullyan's To Mock a Mockingbird.
- 5y ago
- alexshendi 5y agoI am so awestruck, I even quit doomscrolling.
- livinginfear 5y agoCool article. My first thought is that this might be a fun way to implement some really simple executable obfuscation.
- ncmncm 5y agoShould be trivial to add running off the end into into native code, presumably after decompressing it. Process is: 0. start a decompressor; 1. decompress a decryptor; 2. call that to decrypt a composite payload; 3. run off the end into a better, native decompressor to decompress the real payload, and write it out or; 4. run into that. I.e. it does not suffice to verify that the header is really a lambda calculus evaluator.
- tromp 5y agoThis is the best possible answer to my question at https://news.ycombinator.com/item?id=29631288 https://news.ycombinator.com/item?id=29631288
- steve76 5y ago
- pmarreck 5y agoI love this. I love this person's mind. I've seen her (assuming that is the correct pronoun) stuff before, always fascinating. And then I just discovered that for some unknown reason, this person has already blocked me on Twitter (I can recall exactly zero interactions with them, but I must have followed them already due to things like APE). Not sure if she sees this but I'm sorry about whatever I said that I don't recall? Twitter username is same as this one here. Would love to see you in my feed again, will promise to keep big mouth shut
- javajosh 5y ago>you could prefix the compressed file with this 400 byte interpreter to get autonomous self-extracting archives that anyone can use. What could possibly go wrong?
- tromp 5y agoAssuming you verified that it's this particular 400 byte interpreter, which is as sandboxed as it gets, then the worst that can happen is hogging all your memory and cpu.
- javajosh 5y agoGiven SPECTRE and rowhammer, I just don't believe that. This gives attackers full degrees of freedom to reactively search for a crack in the process space. With a normal statically compiled decoder, as an attacker you have a certain degree of freedom, but it is far less (unless one of your formats is a programmable environment, e.g. NGO's iOS exploit). I, for one, would not be comfortable having content distributed as a blob that runs as a virtual machine that builds the software that decodes the content. Justine has made this practical. I can see the appeal. I just worry that we're trading in our jpgs for exes in a sandbox, and I'm not sure its worth the risk.
- edgyquant 5y agoI wouldn’t say that the OP has made this possible, there is nothing groundbreaking here it’s a cool trick that isn’t widely employed for the exact reasons you mentioned.
- jart 5y agoI'm flattered you think my hobby project might replace jpeg. Maybe one day we'll figure out how to do discrete cosine transform as a lambda expression. All I'm trying to accomplish here is sharing interesting ideas and inspiring the curiosity of programmers who dare to dream that things can be better than they are. It's not the the responsibility of the educational materials I provide free of charge to folks who love computer science to help you comply with hardening policies aimed at reducing risks relating to malicious actors exploiting the most recently disclosed weaknesses in your hardware. Powerful knowledge has many applications so it always makes me sad when people choose to focus on the negative ones. If you want something that can provide that level of assurance then I'd suggest looking into Blinkenlights, which can be retooled to abstract a level of memory obfuscation and processor insulation that effectively neutralizes such threats, much stronger than alternatives like docker/gvisor/vms/etc., but at a cost of performance.
- ncmncm 5y agoCan I just say this whole presentation (like the previous Lisp boot-sector one) is just astonishingly well put-together, on top of the tour-de-force achievement.
- deleted 5y ago[deleted]
- rbsmith 5y agoThe blc.S didn’t build for me using `-oformat:binary` . Changing to `--oformat=binary` it compiled, but then get core dumps. Running Linux x86_64 up to date Ubuntu 20.04.4 . for cc in cc gcc clang do echo "## $cc" $cc -no-pie -static -nostdlib -o blc -Wl,--oformat=binary blc.S || exit 1 { printf 0010; printf 0101; } | ./blc; echo done Any suggestions?
- jart 5y agoSorry about that! wget https://justine.lol/lambda/blc.S wget https://justine.lol/lambda/flat.lds cc -c -o blc.o blc.S ld.bfd -o blc blc.o -T flat.lds Just tested myself on Linux with both GCC and Clang. Whatever you do, do not use any linker except big deal.
- rbsmith 5y agoYes! Thank you. On to exploring!