In real life, I’m not a mathematician; I’m a computer scientist. Still a math geek, mind you, but what I really do is very much in the realm of applied math, researching how to build systems to help people program.
\nOne of my pathological obsessions is programming languages. Since I first got exposed to TRS-80 Model 1 BASIC back in middle school, I’ve been absolutely nuts programming languages. Last time I counted, I’d learned about 130 different languages; and I’ve picked up more since then. I’ve written programs most of them. Like I said, I’m nuts.
\nAnyway, I decided that it would be amusing to inflict my obsession on you, my readers, with a new feature: the friday pathological programming language. You see, there are plenty of *crazy* people out there; and many of them like to invent programming languages. Some very small number of them try to design good languages and succeed; a much larger number try to design good languages and fail; and *then* there are the folks who design the languages I’m going to talk about. They’re the ones who set out to design *bizzare* programming languages, and succeed brilliantly. They call them “esoteric” programming languages. I call them evil.
\nToday, the beautiful grand-daddy of the esoteric language family: the one, the only, the truly and deservedly infamous: [Brainfuck!][bf], designed by Urban M\u00fcller. (There are a number of different implementations available; just follow the link.)
\nOnly 8 commands – including input and output – all written using symbols. And yet Turing complete; and not just Turing complete, but actually based on a *real* [formal theoretical design][pprimeprime]. And it’s even been implemented [*in hardware*!][bf-hard]
\nBrainFuck is based on something very much like a twisted cross between a [Turing machine][turing] and a [Minsky machine][minsky]. It’s got the idea of an input tape, like the turing machine. But unlike the turing machine, each cell of the tape stores a number, which can be incremented or decremented, like a Minsky machine. And like a Minsky, the only control flow is a test for zero.
\nThe 8 instructions:
\n1. **>**: move the tape head one cell forward.
\n2. **+++++++++.++++++-.+++++++..+++.>++++<>.<——.++++++
\n.+++.——.——–.>+.
\nLet’s pull that apart just a bit so that we can hope to understand.
\n* “++++++++”: store the number “8” in the current tape cell. We’re going to use that as a loop index, so the loop is going to repeat 8 times.
\n* “[>+++++++++.”: go to the cell after the loop index, and output what’s there. That outputs the “72” as a character: “H”.
\n* “++++++-.”: Advance past the index, subtract one, and output. That’s 101, or “e”.
\nContinues in pretty much the same vein, using a couple of tape cells, and running loops to generate the values of the characters. Beautiful, eh?
\nIf that didn’t seem impressive enough, [here][bf-fib] is a really gorgeous implementation of a fibonacci sequence generator, with documentation. The BF compiler used to write this ignores any character other than the 8 commands, so the comments don’t need to be marked in any way; they just need to be really careful not to use punctuation.<\/p>\n
\n+++++++++++ number of digits to output\n> #1\n+ initial number\n>>>> #5\n++++++++++++++++++++++++++++++++++++++++++++ (comma)\n> #6\n++++++++++++++++++++++++++++++++ (space)\n<<<<< #1\ncopy #1 to #7\n[>>>>>>+>+<<<<<<>>>>>>[<<<<<<>>>>>>-]\n\n++++++++++ set the divisor #8\n[\nsubtract from the dividend and divisor\n->+>+<<>>[<<>>-]\nset #10\n+\nif #9 clear #10\n[-][<>>+<<>[-]]\njump back to #8 (divisor possition)\n<>> #11\ncopy to #13\n[>>+>+<<>>[<<>>-]\nset #14\n+\nif #13 clear #14\n[-][<>[-]]\n<<<<<<>>>> #12\nif #12 output value plus offset to ascii 0\n[++++++++++++++++++++++++++++++++++++++++++++++++.[-]]\nsubtract #11 from 10\n++++++++++ #12 is now 10\n- #12\noutput #12 even if it's zero\n++++++++++++++++++++++++++++++++++++++++++++++++.[-]\n<<<<<<<<<<< #1\ncheck for final number\ncopy #0 to #3\n>>+>+<<<>>>[<<<>>>-]\n>.>.<<<[-]]\n<>+>+<<>>[<<>>-]<<[-]>[-]<<<-\n]\n<\/pre>\n[bf]: http:\/\/www.muppetlabs.com\/~breadbox\/bf\/
\n[bf-fib]: http:\/\/esoteric.sange.fi\/brainfuck\/bf-source\/prog\/fibonacci.txt
\n[turing]: http:\/\/goodmath.blogspot.com\/2006\/03\/playing-with-mathematical-machines.html
\n[minsky]: http:\/\/goodmath.blogspot.com\/2006\/05\/minsky-machine.html
\n[bf-hard]: http:\/\/www.robos.org\/?bfcomp
\n[pprimeprime]: http:\/\/en.wikipedia.org\/wiki\/P_prime_prime<\/p>\n","protected":false},"excerpt":{"rendered":"In real life, I’m not a mathematician; I’m a computer scientist. Still a math geek, mind you, but what I really do is very much in the realm of applied math, researching how to build systems to help people program. One of my pathological obsessions is programming languages. Since I first got exposed to TRS-80 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[92],"tags":[],"class_list":["post-73","post","type-post","status-publish","format-standard","hentry","category-pathological-programming"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-1b","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/73","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=73"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/73\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=73"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=73"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=73"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}