Cody Boone Ferguson
22e483723c
Instead of code blocks the bug / (mis)features statuses are quoted rather than in a code block. In the case that there is more than one a line break was added at the end of all but the last one. A bug status was renamed to be slightly more correct (maybe more than one was renamed for the same purpose but at least one was). The bug statuses in the quotes are now bold to let them stand out better.
569 lines
18 KiB
Markdown
569 lines
18 KiB
Markdown
## To build:
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``` <!---sh-->
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make all # On a 64-bit machine (default)
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make tromp32 # On a 32-bit machine
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```
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### Bugs and (Mis)features:
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The current status of this entry is:
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> **STATUS: INABIAF - please DO NOT fix**
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For more detailed information see [2012/tromp in bugs.html](../../bugs.html#2012_tromp).
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## To use:
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``` <!---sh-->
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./tromp [-b]
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```
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Use `./tromp32` as you would `./tromp` if on a 32-bit machine.
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## To use:
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``` <!---sh-->
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cat ascii-prog.blc data | ./tromp -b
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cat binary-prog.Blc data | ./tromp
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```
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## Try:
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``` <!---sh-->
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./try.sh
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```
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## Judges' remarks:
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The judges dare to say that the data files this entry is processing
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are more obfuscated than the entry itself.
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## Author's remarks:
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This program celebrates the close connection between obfuscation and conciseness,
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by implementing the most concise language known, BLC:
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[Binary Lambda Calculus](https://tromp.github.io/cl/Binary_lambda_calculus.html).
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[BLC](https://tromp.github.io/cl/Binary_lambda_calculus.html) was developed to
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make [Algorithmic Information
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Theory](https://en.wikipedia.org/wiki/Algorithmic_information_theory), the
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theory of smallest programs, more concrete. It starts with the simplest model of
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computation, the [lambda
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calculus](https://en.wikipedia.org/wiki/Lambda_calculus), and adds the minimum
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amount of machinery to enable binary input and output.
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More specifically, it defines a universal machine, which, from an input stream
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of bits, parses the binary encoding of a [lambda
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calculus](https://en.wikipedia.org/wiki/Lambda_calculus) term, applies that to
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the remainder of input (translated to a lazy list of
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[booleans](https://en.wikipedia.org/wiki/Boolean_algebra), which have a standard
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representation in lambda calculus), and translates the evaluated result back
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into a stream of bits to be output.
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Lambda is encoded as 00, application as 01, and the variable bound by the `n`th
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enclosing lambda (denoted `n` in so-called [De Bruijn](https://en.wikipedia.org/wiki/De_Bruijn_notation)
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notation) as `1^{n}0`.
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That's all there is to
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[BLC](https://tromp.github.io/cl/Binary_lambda_calculus.html)!
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For example the encoding of lambda term `S = \x \y \z (x z) (y z)`,
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with [De Bruijn notation](https://en.wikipedia.org/wiki/De_Bruijn_notation):
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```
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\ \ \ (3 1) (2 1)`, is `00 00 00 01 01 1110 10 01 110 10
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```
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In the closely related
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[BLC8](https://tromp.github.io/cl/Binary_lambda_calculus.html#BLC8:_byte_sized_I.2FO)
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language, I/O is byte oriented, translating between a stream of bytes and a list
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of length-8 lists of [booleans](https://en.wikipedia.org/wiki/Boolean_algebra).
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The submission implements the universal machine in the most concise manner conceivable.
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It lacks `#define`s and `#include`s, and compiles to a (stripped) executable of
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under 6K in size.
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Without arguments, it runs in byte mode, using standard input and output.
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With one (arbitrary) argument, it runs in bit mode, using only the least significant
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bit of input, and using characters `0` and `1` for output.
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The program uses the following exit codes:
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```
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0: OK; result is a finite list
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5: Out of term space
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6: Out of memory
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1,2,3,4,8,9: result not in list form
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```
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The size of the term space is fixed at compile time with `-DA`.
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### A half byte `cat`
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The shortest (closed) lambda calculus term is `\x x (\ 1` in
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[De Bruijn](https://en.wikipedia.org/wiki/De_Bruijn_notation) notation which is the
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identity function. When its encoding `0010` is fed into the universal machine,
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it will simply copy the input to the output (well, not that simply, since each
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byte is smashed to bits and rebuilt from scratch). Voila: a half byte cat:
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``` <!---sh-->
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$ echo " Hello, world" | ./tromp
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Hello, world
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```
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Since the least significant 4 bits of the first byte are just arbitrary padding
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that is ignored by the program, any character from ASCII 32 (space) through 47
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(`/`) will do, e.g.:
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``` <!---sh-->
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$ echo "*Hello, world" | ./tromp
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Hello, world
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```
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### Bad programs
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If the input doesn't start with a valid program, that is,
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if the interpreter reaches end-of-file during program parsing,
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it will crash in some way. E.g. the following might dump core:
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``` <!---sh-->
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echo -n "U" | ./tromp
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```
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Furthermore, the interpreter requires the initial encoded lambda term to be
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closed, that is, variable `n` can only appear within at least `n` enclosing
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lambdas. For instance, here the term `\ 5` is not closed, causing the
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interpreter to crash when looking into a null-pointer environment:
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``` <!---sh-->
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echo ">Hello, world" | ./tromp
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```
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will likely dump core.
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Since these properties can be checked when creating
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[BLC](https://tromp.github.io/cl/Binary_lambda_calculus.html) programs,
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the interpreter doesn't bother checking for it.
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### A Self Interpreter
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The [BLC](https://tromp.github.io/cl/Binary_lambda_calculus.html) universal
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machine may be small at 650 bytes of C (952 bytes including layout), but written
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as a self interpreter in BLC it is downright minuscule at 232 bits (29 bytes):
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```
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01010001
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10100000
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00010101
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10000000
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00011110
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00010111
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11100111
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10000101
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11001111
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000000111
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10000101101
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1011100111110
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000111110000101
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11101001 11010010
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11001110 00011011
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00001011 11100001
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11110000 11100110
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11110111 11001111
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01110110 00011001
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00011010 00011010
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```
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The byte oriented BLC8 version weighs in at 43 bytes (shown in hexadecimal).
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```
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19468
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05580
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05f00
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bfe5f
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85f3f
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03c2d
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b9fc3f8
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5e9d65e5f
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0decb f0fc3
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9befe 185f7
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0b7fb 00cf6
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7bb03 91a1a
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```
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``` <!---sh-->
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$ (cat uni8.Blc; echo " Ni hao") | ./tromp
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Ni hao
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```
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### A prime number sieve
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Even shorter than the self-interpreter is this prime number sieve in 167 bits
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(under 21 bytes):
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```
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000100011001100101000110100
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000000101100000100100010101
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11110111 101001000
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11010000 111001101
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000000000010110111001110011
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11111011110000000011111001
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10111000
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00010110
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0000110110
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```
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The `n`th bit in the output indicates whether n is prime:
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``` <!---sh-->
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$ cat primes.blc | ./tromp -b | head -c 70
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0011010100010100010100010000010100000100010100010000010000010100000100
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```
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For those who prefer to digest their primes in decimal, there is `oddindices.Blc`,
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which will print the indices of all odd characters (with
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[LSB](https://en.wikipedia.org/wiki/Bit_numbering) = 1)
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separated by a given character:
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```
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$ (cat oddindices.Blc; echo -n " "; cat primes.blc | ./tromp -b) | ./tromp | head -c 70
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2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
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```
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### A Space filling program
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The program `hilbert.Blc`, at 143 bytes, is a very twisty "one-liner" (shown in hexadecimal):
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```
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1818181 8111154 6806041 55ff041
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9d f9 de 16 ff fe 5f 3f
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ef f615ff9 46 84 058117e 05
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cb fe bc bf
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ee86cb9 4681600 5c0bfac bfbf71a
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85 e0 5c f4
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14d5fe0 8180b048d0800e078 016445f
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fe 5f
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f7 ffffe5fff2fc 02f7ad97f5bf ff
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ff bf ff ca af ff
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7817ffa df76695 4680601 57f7e16
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05 c1
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3fe80b2 2c18581 bfe5c10 42ff805
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de ec 06 c2 c0 c0
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60 8191a00167fb cbcfdf65f7c0 a20
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```
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It expects `n` arbitrary characters of input, and draws a space filling [Hilbert
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curve](https://en.wikipedia.org/wiki/Hilbert_curve) of order `n`:
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``` <!---sh-->
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$ (cat hilbert.Blc; echo -n "1") | ./tromp
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_
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$ (cat hilbert.Blc; echo -n "12") | ./tromp
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_ _
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_| |_
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$ (cat hilbert.Blc; echo -n "123") | ./tromp
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_ _ _ _
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| |_| | | |_| |
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|_ _| |_ _|
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_| |_____| |_
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| ___ ___ |
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|_| _| |_ |_|
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_ |_ _| _
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| |___| |___| |
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$ (cat hilbert.Blc; echo -n "1234") | ./tromp
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_ _ _ _ _ _ _ _
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| |_| | | |_| | | |_| | | |_| |
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|_ _| |_ _| |_ _| |_ _|
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_| |_____| |_ _| |_____| |_
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| ___ ___ | | ___ ___ |
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|_| _| |_ |_| |_| _| |_ |_|
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_ |_ _| _ _ |_ _| _
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| |___| |___| |_| |___| |___| |
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|_ ___ ___ ___ ___ _|
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_| |_ |_| _| |_ |_| _| |_
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| _ | _ |_ _| _ | _ |
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|_| |_| | |___| |___| | |_| |_|
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_ _ | ___ ___ | _ _
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| |_| | |_| _| |_ |_| | |_| |
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|_ _| _ |_ _| _ |_ _|
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_| |___| |___| |___| |___| |_
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```
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### A [Brainfuck](https://en.wikipedia.org/wiki/Brainfuck) interpreter
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The smallest known BF interpreter is written in... you guessed it,
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[BLC](https://tromp.github.io/cl/Binary_lambda_calculus.html),
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coming in at 112 bytes (including 3 bits of padding):
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```
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$ od -t x4 bf.Blc
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0000000 01a15144 02d55584 223070b7 00f032ff
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0000020 7f85f9bf 956fe15e c0ee7d7f 006854e5
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0000040 fbfd5558 fd5745e0 b6f0fbeb 07d62ff0
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0000060 d7736fe1 c0bc14f1 1f2eff0b 17666fa1
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0000100 2fef5be8 ff13ffcf 2034cae1 0bd0c80a
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0000120 e51fee99 6a5a7fff ff0fff1f d0049d87
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0000140 db0500ab 3bb74023 b0c0cc28 10740e6c
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0000160
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```
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It expects its input to consist of a
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[Brainfuck](https://en.wikipedia.org/wiki/Brainfuck) program
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(looking only at bits `0`, `1` and `4` to distinguish among `,-.+<>][ `)
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followed by a `]`, followed by the input for the Brainfuck program.
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```
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$ more hw.bf
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++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.>.]
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$ cat bf.Blc hw.bf | ./tromp
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Hello World!
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```
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Curiously, the interpreter `bf.Blc` is the exact same size as `hw.bf`.
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### A BLC assembler
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Writing BLC programs can be made slightly less painful with this parser that
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translates single-letter-variable lambda calculus into BLC:
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``` <!---sh-->
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$ echo "\f\x f (f (f x))" > three
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$ cat parse.Blc three | ./tromp
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000001110011100111010
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```
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### Converting between bits and bytes
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The program `inflate.Blc` and its inverse `deflate.Blc` allow us to translate between
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BLC and BLC8. If you assemble a byte oriented program, you'll need to compact it
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into BLC8:
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So we could assemble an input reversing program as
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``` <!---sh-->
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echo "\a a ((\b b b) (\b \c \d \e d (b b) (\f f c e))) (\b \c c)" > reverse
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cat parse.Blc reverse | ./tromp > reverse.blc
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```
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and change it to BLC8 with
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``` <!---sh-->
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$ cat deflate.Blc reverse.blc | ./tromp > rev.Blc
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$ wc rev.Blc
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0 1 9 rev.Blc
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```
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and then try it out with:
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``` <!---sh-->
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$ cat rev.Blc - | ./tromp
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Hello, world!
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^D
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!dlrow ,olleH
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```
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### Symbolic Lambda Calculus reduction
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BLC8 program `symbolic.Blc` shows individual reduction steps on symbolic lambda terms.
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Here it is used to show the calculation of 2^3 in Church numerals:
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``` <!---sh-->
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$ echo "(\f\x f (f (f x))) (\f\x f (f x))" > threetwo
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$ cat parse.Blc threetwo | ./tromp > threetwo.blc
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$ cat symbolic.Blc threetwo.blc | ./tromp
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(\a \b a (a (a b))) (\a \b a (a b))
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\a (\b \c b (b c)) ((\b \c b (b c)) ((\b \c b (b c)) a))
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\a \b (\c \d c (c d)) ((\c \d c (c d)) a) ((\c \d c (c d)) ((\c \d c (c d)) a) b)
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\a \b (\c (\d \e d (d e)) a ((\d \e d (d e)) a c)) ((\c \d c (c d)) ((\c \d c (c d)) a) b)
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\a \b (\c \d c (c d)) a ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b))
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\a \b (\c a (a c)) ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b))
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\a \b a (a ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
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\a \b a (a ((\c a (a c)) ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
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\a \b a (a (a (a ((\c \d c (c d)) ((\c \d c (c d)) a) b))))
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\a \b a (a (a (a ((\c (\d \e d (d e)) a ((\d \e d (d e)) a c)) b))))
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\a \b a (a (a (a ((\c \d c (c d)) a ((\c \d c (c d)) a b)))))
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\a \b a (a (a (a ((\c a (a c)) ((\c \d c (c d)) a b)))))
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\a \b a (a (a (a (a (a ((\c \d c (c d)) a b))))))
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\a \b a (a (a (a (a (a ((\c a (a c)) b))))))
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\a \b a (a (a (a (a (a (a (a b)))))))
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```
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As expected, the resulting normal form is [Church
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numeral](https://en.wikipedia.org/wiki/Church_encoding) 8.
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Taking only the first line of output gives us a sort of BLC disassembler, an
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exact inverse of the above assembler. The prime number sieve disassembles as
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follows:
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``` <!---sh-->
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$ cat symbolic.Blc primes.blc | ./tromp | head -1
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\a (\b b (b ((\c c c) (\c \d \e e (\f \g g) ((\f c c f ((\g g g) (\g f (g g)))) (\f \g \h \i i g (h (d f))))) (\c \d \e b (e c))))) (\b \c c (\d \e d) b)
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```
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Hardly any less obfuscated...
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The last line of
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``` <!---sh-->
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cat symbolic.Blc primes.blc | ./tromp | head -16
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```
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starts out as
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```
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\a \b b (\c \d c) (\c c (\d \e d) (\d d (\e \f f) (\e e (\f \g g) ((\f (\g \h \i
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```
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The `\a` is for ignoring the rest of the input (to which the universal machine
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applies the decoded lambda term). The `\b b (..) (...)` is the list constructor,
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usually called `cons`, applied to a head (a list element) and a tail (another list).
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In this case the element is `(\c \d c)`, which represents the boolean true, and
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which we use to represent a 0 bit. This is the bit that says 0 is not prime.
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The next list element (following another `cons`) is `(\d \e d)`. Another 0 bit,
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this time saying that 1 is not prime. The third list element is `(\e \f f)`,
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a 1 bit, confirming our suspicion that 2 is prime. As is the next number,
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according to `(\f \g g)`. We can see that the tail after the first 4 elements
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is still subject to further reduction. The bit for number 4 will show up
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for the first time in line 30, as `(\g \h g)`, or 0, as the result of zeroing
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out all multiples of the first prime, 2.
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Since my computer reaches swap hell before line 40, we can't see the next bit arriving,
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at least not in this symbolic reduction.
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### Performance
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Performance is quite decent, and amazingly good for such a tiny implementation,
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being roughly 50% slower than a Haskell implementation of the universal machine
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using so-called [Higher Order Abstract
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Syntax](https://en.wikipedia.org/wiki/Higher-order_abstract_syntax) which relies on the highly optimized
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Haskell runtime system for evaluation. Of course individual BLC programs running
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under the interpreter perform much worse than that same program written in Haskell.
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Our interpreter copes well with extra levels of interpretation:
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``` <!---sh-->
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$ time cat primes.blc | ./tromp -b | head -c 210 > /dev/null
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real 0m0.043s
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$ time cat uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
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real 0m0.191s
|
|
$ time cat uni.blc uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
|
|
real 0m1.919s
|
|
$ time cat uni.blc uni.blc uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
|
|
real 0m23.514s
|
|
$ time cat uni.blc uni.blc uni.blc uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
|
|
real 4m52.700s
|
|
```
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|
|
### Obfuscation
|
|
|
|
Obfuscation is due entirely to conciseness. Some questions to ponder:
|
|
|
|
Which of the term space codes `0`, `1`, `2`, `3` serve multiple purposes?
|
|
|
|
Why is the environment pointer pointing into the term space?
|
|
|
|
What does the test `u+m&1?` do?
|
|
|
|
How does the program reach exit code 0?
|
|
|
|
And how do any of those BLC programs work?
|
|
|
|
|
|
### Portability
|
|
|
|
The program freely (without casting) converts between `int` and `int *`, causing
|
|
many warnings;
|
|
|
|
```
|
|
note: expected 'int *' but argument is of type 'int'
|
|
warning: assignment from incompatible pointer type
|
|
warning: assignment makes integer from pointer without a cast
|
|
warning: assignment makes pointer from integer without a cast
|
|
warning: incompatible implicit declaration of built-in function 'calloc'
|
|
warning: incompatible implicit declaration of built-in function 'exit'
|
|
warning: passing argument 1 of 'd' makes pointer from integer without a cast
|
|
warning: passing argument 1 of 'p' makes pointer from integer without a cast
|
|
warning: pointer/integer type mismatch in conditional expression
|
|
```
|
|
|
|
Avoiding these would make the program substantially longer,
|
|
and detract from its single minded focus on conciseness.
|
|
|
|
It implicitly declares functions `read(2)`, `write(2)`, `exit(3)` and
|
|
`calloc(3)`, the latter two incompatibly. 32 bit and 64 bit executables are
|
|
separate [Makefile](%%REPO_URL%%/2012/tromp/Makefile) targets, involving a change from `int` to `long`
|
|
and from a hardcoded sizeof of 4 to 8.
|
|
|
|
The program has been tested to work correctly on Linux/Solaris/MacOSX both in 32
|
|
and 64 bits.
|
|
|
|
|
|
### Acknowledgements
|
|
|
|
Christopher Hendrie, Bertram Felgenhauer, Alex Stangl, Seong-hoon Kang,
|
|
and [Yusuke Endoh](../../authors.html#Yusuke_Endoh) have contributed ideas and
|
|
suggestions for improvement.
|
|
|
|
|
|
### References
|
|
|
|
Binary Lambda Calculus -
|
|
<https://tromp.github.io/cl/Binary_lambda_calculus.html>
|
|
|
|
G J Chaitin, Algorithmic information theory, Volume I,
|
|
Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, October 1987.
|
|
<https://web.archive.org/web/20121125233450/https://www.cs.auckland.ac.nz/~chaitin/cup.html>
|
|
|
|
Jean-Louis Krivine. 2007.
|
|
A call-by-name lambda-calculus machine
|
|
Higher Order Symbol. Comput. 20, 3 (September 2007), 199-207.
|
|
<http://www.pps.univ-paris-diderot.fr/~krivine/articles/lazymach.pdf>
|
|
|
|
|
|
### NOTICE to those who wish for a greater challenge:
|
|
|
|
**If you want a greater challenge, don't read any further**:
|
|
just try to understand the program via the source.
|
|
|
|
If you get stuck, come back and read below for additional hints and information.
|
|
|
|
|
|
### How this entry works:
|
|
|
|
See the file [how.html](how.html).
|
|
|
|
|
|
<!--
|
|
|
|
Copyright © 1984-2024 by Landon Curt Noll. All Rights Reserved.
|
|
|
|
You are free to share and adapt this file under the terms of this license:
|
|
|
|
Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
|
|
|
|
For more information, see:
|
|
|
|
https://creativecommons.org/licenses/by-sa/4.0/
|
|
|
|
-->
|