improved indentation and whitespace for markdown code blocks
All code blocks in markdown have been intended by at least 4 spaces. We add `--tab-stop=8` to all `pandoc(1)` executions in order to set a better tab stop indentation, especially for tab intended code blocks. Changed `bin/pandoc-wrapper.sh` VERSION from "1.5.3 2024-03-26" to "1.6 2024-03-31". Fixed `1991/brnstnd/sorta.README.md` so that the sorta code is code blocks. Removed unneeded paragraph group in copyright in `inc/footer.default.html`. Fixed excess whitespace after list Author on entry `index.html` page. Changed `bin/output-index-author.sh` VERSION from "1.5.2 2024-03-26" to "1.6 2024-03-31". Performed `make www` to perform the above and test under macOS. TODO: Fix the problem of the initial line of code being extra intended. TODO: Fix excess whitespace around code that is inline.
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+123
-125
@@ -1,9 +1,9 @@
|
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## To build:
|
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|
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```sh
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make all # On a 64-bit machine (default)
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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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make tromp32 # On a 32-bit machine
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```
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@@ -12,7 +12,7 @@ make tromp32 # On a 32-bit machine
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The current status of this entry is:
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```
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STATUS: INABIAF - please **DO NOT** fix
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STATUS: INABIAF - please **DO NOT** fix
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```
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For more detailed information see [2012 tromp bugs](../../bugs.html#2012_tromp).
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@@ -21,7 +21,7 @@ For more detailed information see [2012 tromp bugs](../../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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./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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@@ -30,15 +30,15 @@ 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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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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./try.sh
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```
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@@ -96,10 +96,10 @@ 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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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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@@ -114,8 +114,8 @@ 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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|
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```sh
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$ echo " Hello, world" | ./tromp
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Hello, world
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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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@@ -123,8 +123,8 @@ 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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$ echo "*Hello, world" | ./tromp
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Hello, world
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```
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@@ -135,7 +135,7 @@ 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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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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@@ -144,7 +144,7 @@ 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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echo ">Hello, world" | ./tromp
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```
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will likely dump core.
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@@ -201,8 +201,8 @@ The byte oriented BLC8 version weighs in at 43 bytes (shown in hexadecimal).
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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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$ (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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@@ -226,8 +226,8 @@ Even shorter than the self-interpreter is this prime number sieve in 167 bits
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The `n`th bit in the output indicates whether n is prime:
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|
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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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$ 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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@@ -236,8 +236,8 @@ which will print the indices of all odd characters (with
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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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$ (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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@@ -266,44 +266,43 @@ 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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| |
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$ (cat hilbert.Blc; echo -n "1") | ./tromp
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_
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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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|_ _|
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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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|_ _|
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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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|
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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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$ (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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| |___| |___| |
|
||||
|
||||
$ (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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### A [Brainfuck](https://en.wikipedia.org/wiki/Brainfuck) interpreter
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@@ -313,15 +312,15 @@ The smallest known BF interpreter is written in... you guessed it,
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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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$ 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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@@ -330,10 +329,10 @@ It expects its input to consist of a
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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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$ 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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@@ -346,10 +345,9 @@ translates single-letter-variable lambda calculus into BLC:
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|
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|
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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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$ 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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@@ -361,24 +359,24 @@ into BLC8:
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So we could assemble an input reversing program as
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|
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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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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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||||
|
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and change it to BLC8 with
|
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|
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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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||||
$ cat deflate.Blc reverse.blc | ./tromp > rev.Blc
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$ wc rev.Blc
|
||||
0 1 9 rev.Blc
|
||||
```
|
||||
and then try it out with:
|
||||
|
||||
```sh
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$ cat rev.Blc - | ./tromp
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Hello, world!
|
||||
^D
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||||
!dlrow ,olleH
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$ cat rev.Blc - | ./tromp
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Hello, world!
|
||||
^D
|
||||
!dlrow ,olleH
|
||||
```
|
||||
|
||||
### Symbolic Lambda Calculus reduction
|
||||
@@ -387,24 +385,24 @@ BLC8 program `symbolic.Blc` shows individual reduction steps on symbolic lambda
|
||||
Here it is used to show the calculation of 2^3 in Church numerals:
|
||||
|
||||
```sh
|
||||
$ echo "(\f\x f (f (f x))) (\f\x f (f x))" > threetwo
|
||||
$ cat parse.Blc threetwo | ./tromp > threetwo.blc
|
||||
$ cat symbolic.Blc threetwo.blc | ./tromp
|
||||
(\a \b a (a (a b))) (\a \b a (a b))
|
||||
\a (\b \c b (b c)) ((\b \c b (b c)) ((\b \c b (b c)) a))
|
||||
\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)
|
||||
\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)
|
||||
\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))
|
||||
\a \b (\c a (a c)) ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b))
|
||||
\a \b a (a ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
|
||||
\a \b a (a ((\c a (a c)) ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
|
||||
\a \b a (a (a (a ((\c \d c (c d)) ((\c \d c (c d)) a) b))))
|
||||
\a \b a (a (a (a ((\c (\d \e d (d e)) a ((\d \e d (d e)) a c)) b))))
|
||||
\a \b a (a (a (a ((\c \d c (c d)) a ((\c \d c (c d)) a b)))))
|
||||
\a \b a (a (a (a ((\c a (a c)) ((\c \d c (c d)) a b)))))
|
||||
\a \b a (a (a (a (a (a ((\c \d c (c d)) a b))))))
|
||||
\a \b a (a (a (a (a (a ((\c a (a c)) b))))))
|
||||
\a \b a (a (a (a (a (a (a (a b)))))))
|
||||
$ echo "(\f\x f (f (f x))) (\f\x f (f x))" > threetwo
|
||||
$ cat parse.Blc threetwo | ./tromp > threetwo.blc
|
||||
$ cat symbolic.Blc threetwo.blc | ./tromp
|
||||
(\a \b a (a (a b))) (\a \b a (a b))
|
||||
\a (\b \c b (b c)) ((\b \c b (b c)) ((\b \c b (b c)) a))
|
||||
\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)
|
||||
\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)
|
||||
\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))
|
||||
\a \b (\c a (a c)) ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b))
|
||||
\a \b a (a ((\c \d c (c d)) a ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
|
||||
\a \b a (a ((\c a (a c)) ((\c \d c (c d)) ((\c \d c (c d)) a) b)))
|
||||
\a \b a (a (a (a ((\c \d c (c d)) ((\c \d c (c d)) a) b))))
|
||||
\a \b a (a (a (a ((\c (\d \e d (d e)) a ((\d \e d (d e)) a c)) b))))
|
||||
\a \b a (a (a (a ((\c \d c (c d)) a ((\c \d c (c d)) a b)))))
|
||||
\a \b a (a (a (a ((\c a (a c)) ((\c \d c (c d)) a b)))))
|
||||
\a \b a (a (a (a (a (a ((\c \d c (c d)) a b))))))
|
||||
\a \b a (a (a (a (a (a ((\c a (a c)) b))))))
|
||||
\a \b a (a (a (a (a (a (a (a b)))))))
|
||||
```
|
||||
|
||||
As expected, the resulting normal form is [Church
|
||||
@@ -415,8 +413,8 @@ exact inverse of the above assembler. The prime number sieve disassembles as
|
||||
follows:
|
||||
|
||||
```sh
|
||||
$ cat symbolic.Blc primes.blc | ./tromp | head -1
|
||||
\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)
|
||||
$ cat symbolic.Blc primes.blc | ./tromp | head -1
|
||||
\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)
|
||||
```
|
||||
|
||||
Hardly any less obfuscated...
|
||||
@@ -424,13 +422,13 @@ Hardly any less obfuscated...
|
||||
The last line of
|
||||
|
||||
```sh
|
||||
cat symbolic.Blc primes.blc | ./tromp | head -16
|
||||
cat symbolic.Blc primes.blc | ./tromp | head -16
|
||||
```
|
||||
|
||||
starts out as
|
||||
|
||||
```
|
||||
\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
|
||||
\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
|
||||
```
|
||||
|
||||
The `\a` is for ignoring the rest of the input (to which the universal machine
|
||||
@@ -462,16 +460,16 @@ under the interpreter perform much worse than that same program written in Haske
|
||||
Our interpreter copes well with extra levels of interpretation:
|
||||
|
||||
```sh
|
||||
$ time cat primes.blc | ./tromp -b | head -c 210 > /dev/null
|
||||
real 0m0.043s
|
||||
$ time cat uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
|
||||
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
|
||||
$ time cat primes.blc | ./tromp -b | head -c 210 > /dev/null
|
||||
real 0m0.043s
|
||||
$ time cat uni.blc primes.blc | ./tromp -b | head -c 210 > /dev/null
|
||||
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
|
||||
```
|
||||
|
||||
### Obfuscation
|
||||
@@ -495,15 +493,15 @@ 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
|
||||
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,
|
||||
|
||||
+23
-23
@@ -133,10 +133,10 @@ continuations (see the 3rd reference for details).</p>
|
||||
<p>The term space holds <a href="https://en.wikipedia.org/wiki/Lambda_calculus">lambda
|
||||
calculus</a> terms in the following
|
||||
format. 0 denotes some form of I/O; the only four occurrences are at:</p>
|
||||
<pre><code> C=13: recognizes end of a byte
|
||||
C=20: recognize output of 0 bit
|
||||
C=21: recognize output of 1 bit
|
||||
C=end: input list, expanded lazily</code></pre>
|
||||
<pre><code> C=13: recognizes end of a byte
|
||||
C=20: recognize output of 0 bit
|
||||
C=21: recognize output of 1 bit
|
||||
C=end: input list, expanded lazily</code></pre>
|
||||
<p><code>1</code> denotes a variable, with the next entry its <a href="https://en.wikipedia.org/wiki/De_Bruijn_index">de Bruijn
|
||||
index</a>.</p>
|
||||
<p><code>2</code> denotes application with the next entry the size of the term being applied.</p>
|
||||
@@ -150,26 +150,26 @@ free list.</li>
|
||||
<li>lambda term (index in term space).</li>
|
||||
</ol>
|
||||
<p>Here’s what each variable does:</p>
|
||||
<pre><code>L Lambda term space
|
||||
m mode: 0 for bits and 7 for bytes
|
||||
b bits remaining unread in I, -1 on EOF
|
||||
D Desirable temporary
|
||||
c continuation context
|
||||
a active environment pointer
|
||||
C Current term index
|
||||
U Ultimate term pointer
|
||||
u utility entry
|
||||
B Born to be free-list of closures
|
||||
I Input character
|
||||
O Output character
|
||||
e entry of current term</code></pre>
|
||||
<pre><code> L Lambda term space
|
||||
m mode: 0 for bits and 7 for bytes
|
||||
b bits remaining unread in I, -1 on EOF
|
||||
D Desirable temporary
|
||||
c continuation context
|
||||
a active environment pointer
|
||||
C Current term index
|
||||
U Ultimate term pointer
|
||||
u utility entry
|
||||
B Born to be free-list of closures
|
||||
I Input character
|
||||
O Output character
|
||||
e entry of current term</code></pre>
|
||||
<p>Here’s what each of the 6 auxiliary functions do:</p>
|
||||
<pre><code>s variable lookup in active environment with de Bruijn index u
|
||||
S gets one bit of input, setting b to -1 on EOF or to remaining number of bits in current byte
|
||||
k copy fragment from string literal holding lambda terms xor 46 into current end of term space
|
||||
x expand input, adding 11 (resp. 99) entries to term space for bit (resp. byte) mode
|
||||
p parses BLC-encoded lambda term using S(), stores results in term space and returns length
|
||||
d decrease reference counter, add record to free list on reaching zero</code></pre>
|
||||
<pre><code> s variable lookup in active environment with de Bruijn index u
|
||||
S gets one bit of input, setting b to -1 on EOF or to remaining number of bits in current byte
|
||||
k copy fragment from string literal holding lambda terms xor 46 into current end of term space
|
||||
x expand input, adding 11 (resp. 99) entries to term space for bit (resp. byte) mode
|
||||
p parses BLC-encoded lambda term using S(), stores results in term space and returns length
|
||||
d decrease reference counter, add record to free list on reaching zero</code></pre>
|
||||
<!--
|
||||
|
||||
Copyright © 1984-2024 by Landon Curt Noll. All Rights Reserved.
|
||||
|
||||
+23
-23
@@ -13,10 +13,10 @@ calculus](https://en.wikipedia.org/wiki/Lambda_calculus) terms in the following
|
||||
format. 0 denotes some form of I/O; the only four occurrences are at:
|
||||
|
||||
```
|
||||
C=13: recognizes end of a byte
|
||||
C=20: recognize output of 0 bit
|
||||
C=21: recognize output of 1 bit
|
||||
C=end: input list, expanded lazily
|
||||
C=13: recognizes end of a byte
|
||||
C=20: recognize output of 0 bit
|
||||
C=21: recognize output of 1 bit
|
||||
C=end: input list, expanded lazily
|
||||
```
|
||||
|
||||
`1` denotes a variable, with the next entry its [de Bruijn
|
||||
@@ -38,30 +38,30 @@ free list.
|
||||
Here's what each variable does:
|
||||
|
||||
```
|
||||
L Lambda term space
|
||||
m mode: 0 for bits and 7 for bytes
|
||||
b bits remaining unread in I, -1 on EOF
|
||||
D Desirable temporary
|
||||
c continuation context
|
||||
a active environment pointer
|
||||
C Current term index
|
||||
U Ultimate term pointer
|
||||
u utility entry
|
||||
B Born to be free-list of closures
|
||||
I Input character
|
||||
O Output character
|
||||
e entry of current term
|
||||
L Lambda term space
|
||||
m mode: 0 for bits and 7 for bytes
|
||||
b bits remaining unread in I, -1 on EOF
|
||||
D Desirable temporary
|
||||
c continuation context
|
||||
a active environment pointer
|
||||
C Current term index
|
||||
U Ultimate term pointer
|
||||
u utility entry
|
||||
B Born to be free-list of closures
|
||||
I Input character
|
||||
O Output character
|
||||
e entry of current term
|
||||
```
|
||||
|
||||
Here's what each of the 6 auxiliary functions do:
|
||||
|
||||
```
|
||||
s variable lookup in active environment with de Bruijn index u
|
||||
S gets one bit of input, setting b to -1 on EOF or to remaining number of bits in current byte
|
||||
k copy fragment from string literal holding lambda terms xor 46 into current end of term space
|
||||
x expand input, adding 11 (resp. 99) entries to term space for bit (resp. byte) mode
|
||||
p parses BLC-encoded lambda term using S(), stores results in term space and returns length
|
||||
d decrease reference counter, add record to free list on reaching zero
|
||||
s variable lookup in active environment with de Bruijn index u
|
||||
S gets one bit of input, setting b to -1 on EOF or to remaining number of bits in current byte
|
||||
k copy fragment from string literal holding lambda terms xor 46 into current end of term space
|
||||
x expand input, adding 11 (resp. 99) entries to term space for bit (resp. byte) mode
|
||||
p parses BLC-encoded lambda term using S(), stores results in term space and returns length
|
||||
d decrease reference counter, add record to free list on reaching zero
|
||||
```
|
||||
|
||||
|
||||
|
||||
+124
-125
@@ -132,8 +132,7 @@
|
||||
<h2 id="author"><a name="author"></a>Author:</h2>
|
||||
<ul>
|
||||
<li>Name: <a href="../../authors.html#John_Tromp">John Tromp</a><br>
|
||||
Location: <a href="../../location.html#US">US</a> - <em>United States of America</em> (<em>United States</em>)
|
||||
<br><br></li>
|
||||
Location: <a href="../../location.html#US">US</a> - <em>United States of America</em> (<em>United States</em>)</li>
|
||||
</ul>
|
||||
|
||||
<!-- END: next line ends content generated by: bin/output-index-author.sh -->
|
||||
@@ -142,21 +141,21 @@ Location: <a href="../../location.html#US">US</a> - <em>United States of America
|
||||
<!-- START: this line starts content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
|
||||
|
||||
<h2 id="to-build">To build:</h2>
|
||||
<div class="sourceCode" id="cb1"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> all <span class="co"># On a 64-bit machine (default)</span></span>
|
||||
<div class="sourceCode" id="cb1"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">make</span> all <span class="co"># On a 64-bit machine (default)</span></span>
|
||||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> tromp32 <span class="co"># On a 32-bit machine</span></span></code></pre></div>
|
||||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">make</span> tromp32 <span class="co"># On a 32-bit machine</span></span></code></pre></div>
|
||||
<h3 id="bugs-and-misfeatures">Bugs and (Mis)features:</h3>
|
||||
<p>The current status of this entry is:</p>
|
||||
<pre><code>STATUS: INABIAF - please **DO NOT** fix</code></pre>
|
||||
<pre><code> STATUS: INABIAF - please **DO NOT** fix</code></pre>
|
||||
<p>For more detailed information see <a href="../../bugs.html#2012_tromp">2012 tromp bugs</a>.</p>
|
||||
<h2 id="to-use">To use:</h2>
|
||||
<div class="sourceCode" id="cb3"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./tromp</span> <span class="pp">[-</span><span class="ss">b</span><span class="pp">]</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb3"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">./tromp</span> <span class="pp">[-</span><span class="ss">b</span><span class="pp">]</span></span></code></pre></div>
|
||||
<p>Use <code>./tromp32</code> as you would <code>./tromp</code> if on a 32-bit machine.</p>
|
||||
<h2 id="to-use-1">To use:</h2>
|
||||
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> ascii-prog.blc data <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span></span>
|
||||
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> binary-prog.Blc data <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> ascii-prog.blc data <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span></span>
|
||||
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> binary-prog.Blc data <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<h2 id="try">Try:</h2>
|
||||
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./try.sh</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">./try.sh</span></span></code></pre></div>
|
||||
<h2 id="judges-remarks">Judges’ remarks:</h2>
|
||||
<p>The judges dare to say that the data files this entry is processing
|
||||
are more obfuscated than the entry itself.</p>
|
||||
@@ -196,10 +195,10 @@ under 6K in size.</p>
|
||||
With one (arbitrary) argument, it runs in bit mode, using only the least significant
|
||||
bit of input, and using characters <code>0</code> and <code>1</code> for output.</p>
|
||||
<p>The program uses the following exit codes:</p>
|
||||
<pre><code>0: OK; result is a finite list
|
||||
5: Out of term space
|
||||
6: Out of memory
|
||||
1,2,3,4,8,9: result not in list form</code></pre>
|
||||
<pre><code> 0: OK; result is a finite list
|
||||
5: Out of term space
|
||||
6: Out of memory
|
||||
1,2,3,4,8,9: result not in list form</code></pre>
|
||||
<p>The size of the term space is fixed at compile time with <code>-DA</code>.</p>
|
||||
<h3 id="a-half-byte-cat">A half byte <code>cat</code></h3>
|
||||
<p>The shortest (closed) lambda calculus term is <code>\x x (\ 1</code> in <a href="https://en.wikipedia.org/wiki/De_Bruijn_notation">De Bruijn
|
||||
@@ -207,23 +206,23 @@ notation</a>) which is the
|
||||
identity function. When its encoding <code>0010</code> is fed into the universal machine,
|
||||
it will simply copy the input to the output (well, not that simply, since each
|
||||
byte is smashed to bits and rebuilt from scratch). Voila: a half byte cat:</p>
|
||||
<div class="sourceCode" id="cb7"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">" Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb7"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">" Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world</span></code></pre></div>
|
||||
<p>Since the least significant 4 bits of the first byte are just arbitrary padding
|
||||
that is ignored by the program, any character from ASCII 32 (space) through 47
|
||||
(<code>/</code>) will do, e.g.:</p>
|
||||
<div class="sourceCode" id="cb8"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">"*Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb8"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">"*Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world</span></code></pre></div>
|
||||
<h3 id="bad-programs">Bad programs</h3>
|
||||
<p>If the input doesn’t start with a valid program, that is,
|
||||
if the interpreter reaches end-of-file during program parsing,
|
||||
it will crash in some way. E.g. the following might dump core:</p>
|
||||
<div class="sourceCode" id="cb9"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="at">-n</span> <span class="st">"U"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb9"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"U"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<p>Furthermore, the interpreter requires the initial encoded lambda term to be
|
||||
closed, that is, variable <code>n</code> can only appear within at least <code>n</code> enclosing
|
||||
lambdas. For instance, here the term <code>\ 5</code> is not closed, causing the
|
||||
interpreter to crash when looking into a null-pointer environment:</p>
|
||||
<div class="sourceCode" id="cb10"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="st">">Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb10"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="st">">Hello, world"</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
|
||||
<p>will likely dump core.</p>
|
||||
<p>Since these properties can be checked when creating
|
||||
<a href="https://tromp.github.io/cl/Binary_lambda_calculus.html">BLC</a> programs,
|
||||
@@ -266,8 +265,8 @@ as a self interpreter in BLC it is downright minuscule at 232 bits (29 bytes):</
|
||||
0b7fb 00cf6
|
||||
7bb03 91a1a
|
||||
</code></pre>
|
||||
<div class="sourceCode" id="cb13"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> uni8.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="st">" Ni hao"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Ni</span> hao</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb13"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> uni8.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="st">" Ni hao"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Ni</span> hao</span></code></pre></div>
|
||||
<h3 id="a-prime-number-sieve">A prime number sieve</h3>
|
||||
<p>Even shorter than the self-interpreter is this prime number sieve in 167 bits
|
||||
(under 21 bytes):</p>
|
||||
@@ -282,14 +281,14 @@ as a self interpreter in BLC it is downright minuscule at 232 bits (29 bytes):</
|
||||
0000110110
|
||||
</code></pre>
|
||||
<p>The <code>n</code>th bit in the output indicates whether n is prime:</p>
|
||||
<div class="sourceCode" id="cb15"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 70</span>
|
||||
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="ex">0011010100010100010100010000010100000100010100010000010000010100000100</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb15"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 70</span>
|
||||
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">0011010100010100010100010000010100000100010100010000010000010100000100</span></span></code></pre></div>
|
||||
<p>For those who prefer to digest their primes in decimal, there is <code>oddindices.Blc</code>,
|
||||
which will print the indices of all odd characters (with
|
||||
<a href="https://en.wikipedia.org/wiki/Bit_numbering">LSB</a> = 1)
|
||||
separated by a given character:</p>
|
||||
<pre><code>$ (cat oddindices.Blc; echo -n " "; cat primes.blc | ./tromp -b) | ./tromp | head -c 70
|
||||
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</code></pre>
|
||||
<pre><code> $ (cat oddindices.Blc; echo -n " "; cat primes.blc | ./tromp -b) | ./tromp | head -c 70
|
||||
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</code></pre>
|
||||
<h3 id="a-space-filling-program">A Space filling program</h3>
|
||||
<p>The program <code>hilbert.Blc</code>, at 143 bytes, is a very twisty “one-liner” (shown in hexadecimal):</p>
|
||||
<pre><code> 1818181 8111154 6806041 55ff041
|
||||
@@ -309,120 +308,120 @@ separated by a given character:</p>
|
||||
60 8191a00167fb cbcfdf65f7c0 a20</code></pre>
|
||||
<p>It expects <code>n</code> arbitrary characters of input, and draws a space filling <a href="https://en.wikipedia.org/wiki/Hilbert_curve">Hilbert
|
||||
curve</a> of order <code>n</code>:</p>
|
||||
<div class="sourceCode" id="cb18"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"1"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span></span>
|
||||
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<div class="sourceCode" id="cb18"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"1"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span></span>
|
||||
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"12"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _</span>
|
||||
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"12"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _</span>
|
||||
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-10"><a href="#cb18-10" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"123"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _</span>
|
||||
<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
|
||||
<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-18"><a href="#cb18-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
|
||||
<span id="cb18-19"><a href="#cb18-19" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"123"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _</span>
|
||||
<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
|
||||
<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-18"><a href="#cb18-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
|
||||
<span id="cb18-19"><a href="#cb18-19" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-20"><a href="#cb18-20" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb18-21"><a href="#cb18-21" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"1234"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-22"><a href="#cb18-22" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _ _ _ _ _</span>
|
||||
<span id="cb18-23"><a href="#cb18-23" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-24"><a href="#cb18-24" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-25"><a href="#cb18-25" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-26"><a href="#cb18-26" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
|
||||
<span id="cb18-27"><a href="#cb18-27" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-28"><a href="#cb18-28" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> _ <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
|
||||
<span id="cb18-29"><a href="#cb18-29" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-30"><a href="#cb18-30" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> ___ ___ ___ ___ _<span class="kw">|</span></span>
|
||||
<span id="cb18-31"><a href="#cb18-31" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-32"><a href="#cb18-32" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-33"><a href="#cb18-33" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-34"><a href="#cb18-34" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="ex">_</span> _</span>
|
||||
<span id="cb18-35"><a href="#cb18-35" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-36"><a href="#cb18-36" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-37"><a href="#cb18-37" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span></code></pre></div>
|
||||
<span id="cb18-21"><a href="#cb18-21" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">"1234"</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb18-22"><a href="#cb18-22" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _ _ _ _ _</span>
|
||||
<span id="cb18-23"><a href="#cb18-23" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-24"><a href="#cb18-24" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-25"><a href="#cb18-25" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-26"><a href="#cb18-26" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
|
||||
<span id="cb18-27"><a href="#cb18-27" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-28"><a href="#cb18-28" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> _ <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
|
||||
<span id="cb18-29"><a href="#cb18-29" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-30"><a href="#cb18-30" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> ___ ___ ___ ___ _<span class="kw">|</span></span>
|
||||
<span id="cb18-31"><a href="#cb18-31" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
|
||||
<span id="cb18-32"><a href="#cb18-32" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-33"><a href="#cb18-33" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
|
||||
<span id="cb18-34"><a href="#cb18-34" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="ex">_</span> _</span>
|
||||
<span id="cb18-35"><a href="#cb18-35" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
|
||||
<span id="cb18-36"><a href="#cb18-36" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
|
||||
<span id="cb18-37"><a href="#cb18-37" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span></code></pre></div>
|
||||
<h3 id="a-brainfuck-interpreter">A <a href="https://en.wikipedia.org/wiki/Brainfuck">Brainfuck</a> interpreter</h3>
|
||||
<p>The smallest known BF interpreter is written in… you guessed it,
|
||||
<a href="https://tromp.github.io/cl/Binary_lambda_calculus.html">BLC</a>,
|
||||
coming in at 112 bytes (including 3 bits of padding):</p>
|
||||
<pre><code>$ od -t x4 bf.Blc
|
||||
0000000 01a15144 02d55584 223070b7 00f032ff
|
||||
0000020 7f85f9bf 956fe15e c0ee7d7f 006854e5
|
||||
0000040 fbfd5558 fd5745e0 b6f0fbeb 07d62ff0
|
||||
0000060 d7736fe1 c0bc14f1 1f2eff0b 17666fa1
|
||||
0000100 2fef5be8 ff13ffcf 2034cae1 0bd0c80a
|
||||
0000120 e51fee99 6a5a7fff ff0fff1f d0049d87
|
||||
0000140 db0500ab 3bb74023 b0c0cc28 10740e6c
|
||||
0000160</code></pre>
|
||||
<pre><code> $ od -t x4 bf.Blc
|
||||
0000000 01a15144 02d55584 223070b7 00f032ff
|
||||
0000020 7f85f9bf 956fe15e c0ee7d7f 006854e5
|
||||
0000040 fbfd5558 fd5745e0 b6f0fbeb 07d62ff0
|
||||
0000060 d7736fe1 c0bc14f1 1f2eff0b 17666fa1
|
||||
0000100 2fef5be8 ff13ffcf 2034cae1 0bd0c80a
|
||||
0000120 e51fee99 6a5a7fff ff0fff1f d0049d87
|
||||
0000140 db0500ab 3bb74023 b0c0cc28 10740e6c
|
||||
0000160</code></pre>
|
||||
<p>It expects its input to consist of a
|
||||
<a href="https://en.wikipedia.org/wiki/Brainfuck">Brainfuck</a> program
|
||||
(looking only at bits <code>0</code>, <code>1</code> and <code>4</code> to distinguish among <code>,-.+<>][</code>)
|
||||
followed by a <code>]</code>, followed by the input for the Brainfuck program.</p>
|
||||
<pre><code>$ more hw.bf
|
||||
++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.>.]
|
||||
$ cat bf.Blc hw.bf | ./tromp
|
||||
Hello World!</code></pre>
|
||||
<pre><code> $ more hw.bf
|
||||
++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.>.]
|
||||
$ cat bf.Blc hw.bf | ./tromp
|
||||
Hello World!</code></pre>
|
||||
<p>Curiously, the interpreter <code>bf.Blc</code> is the exact same size as <code>hw.bf</code>.</p>
|
||||
<h3 id="a-blc-assembler">A BLC assembler</h3>
|
||||
<p>Writing BLC programs can be made slightly less painful with this parser that
|
||||
translates single-letter-variable lambda calculus into BLC:</p>
|
||||
<div class="sourceCode" id="cb21"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">"\f\x f (f (f x))"</span> <span class="op">></span> three</span>
|
||||
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat parse.Blc three <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a><span class="ex">000001110011100111010</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb21"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">"\f\x f (f (f x))"</span> <span class="op">></span> three</span>
|
||||
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat parse.Blc three <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">000001110011100111010</span></span></code></pre></div>
|
||||
<h3 id="converting-between-bits-and-bytes">Converting between bits and bytes</h3>
|
||||
<p>The program <code>inflate.Blc</code> and its inverse <code>deflate.Blc</code> allow us to translate between
|
||||
BLC and BLC8. If you assemble a byte oriented program, you’ll need to compact it
|
||||
into BLC8:</p>
|
||||
<p>So we could assemble an input reversing program as</p>
|
||||
<div class="sourceCode" id="cb22"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="st">"\a a ((\b b b) (\b \c \d \e d (b b) (\f f c e))) (\b \c c)"</span> <span class="op">></span> reverse</span>
|
||||
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> parse.Blc reverse <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> reverse.blc</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb22"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="st">"\a a ((\b b b) (\b \c \d \e d (b b) (\f f c e))) (\b \c c)"</span> <span class="op">></span> reverse</span>
|
||||
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> parse.Blc reverse <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> reverse.blc</span></code></pre></div>
|
||||
<p>and change it to BLC8 with</p>
|
||||
<div class="sourceCode" id="cb23"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat deflate.Blc reverse.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> rev.Blc</span>
|
||||
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> wc rev.Blc</span>
|
||||
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">0</span> 1 9 rev.Blc</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb23"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat deflate.Blc reverse.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> rev.Blc</span>
|
||||
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> wc rev.Blc</span>
|
||||
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">0</span> 1 9 rev.Blc</span></code></pre></div>
|
||||
<p>and then try it out with:</p>
|
||||
<div class="sourceCode" id="cb24"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat rev.Blc <span class="at">-</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world!</span>
|
||||
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a><span class="ex">^D</span></span>
|
||||
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a><span class="ex">!dlrow</span> ,olleH</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb24"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat rev.Blc <span class="at">-</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world!</span>
|
||||
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">^D</span></span>
|
||||
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a> <span class="ex">!dlrow</span> ,olleH</span></code></pre></div>
|
||||
<h3 id="symbolic-lambda-calculus-reduction">Symbolic Lambda Calculus reduction</h3>
|
||||
<p>BLC8 program <code>symbolic.Blc</code> shows individual reduction steps on symbolic lambda terms.
|
||||
Here it is used to show the calculation of 2^3 in Church numerals:</p>
|
||||
<div class="sourceCode" id="cb25"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">"(\f\x f (f (f x))) (\f\x f (f x))"</span> <span class="op">></span> threetwo</span>
|
||||
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat parse.Blc threetwo <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> threetwo.blc</span>
|
||||
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat symbolic.Blc threetwo.blc <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a><span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))</span> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> b<span class="kw">))</span></span>
|
||||
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="ex">a</span><span class="kw">))</span></span>
|
||||
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
|
||||
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
|
||||
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
|
||||
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
|
||||
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
|
||||
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
|
||||
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))))</span></span>
|
||||
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))</span></span>
|
||||
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
|
||||
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
|
||||
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">))))))</span></span>
|
||||
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))))</span></span>
|
||||
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))))))</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb25"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">"(\f\x f (f (f x))) (\f\x f (f x))"</span> <span class="op">></span> threetwo</span>
|
||||
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat parse.Blc threetwo <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">></span> threetwo.blc</span>
|
||||
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat symbolic.Blc threetwo.blc <span class="kw">|</span> <span class="ex">./tromp</span></span>
|
||||
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))</span> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> b<span class="kw">))</span></span>
|
||||
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="ex">a</span><span class="kw">))</span></span>
|
||||
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
|
||||
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
|
||||
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
|
||||
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
|
||||
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
|
||||
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
|
||||
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))))</span></span>
|
||||
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))</span></span>
|
||||
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
|
||||
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
|
||||
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">))))))</span></span>
|
||||
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))))</span></span>
|
||||
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))))))</span></span></code></pre></div>
|
||||
<p>As expected, the resulting normal form is <a href="https://en.wikipedia.org/wiki/Church_encoding">Church
|
||||
numeral</a> 8.</p>
|
||||
<p>Taking only the first line of output gives us a sort of BLC disassembler, an
|
||||
exact inverse of the above assembler. The prime number sieve disassembles as
|
||||
follows:</p>
|
||||
<div class="sourceCode" id="cb26"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-1</span></span>
|
||||
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> b <span class="er">(</span><span class="ex">b</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> c c<span class="kw">)</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> e <span class="er">(</span><span class="ex">\f</span> <span class="dt">\g</span> g<span class="kw">)</span> <span class="kw">((</span><span class="ex">\f</span> c c f <span class="er">(</span><span class="kw">(</span><span class="ex">\g</span> g g<span class="kw">)</span> <span class="kw">(</span><span class="ex">\g</span> f <span class="er">(</span><span class="ex">g</span> g<span class="kw">))))</span> <span class="kw">(</span><span class="ex">\f</span> <span class="dt">\g</span> <span class="dt">\h</span> <span class="dt">\i</span> i g <span class="er">(</span><span class="ex">h</span> <span class="er">(</span><span class="ex">d</span> f<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> b <span class="er">(</span><span class="ex">e</span> c<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\b</span> <span class="dt">\c</span> c <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d<span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb26"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-1</span></span>
|
||||
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> b <span class="er">(</span><span class="ex">b</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> c c<span class="kw">)</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> e <span class="er">(</span><span class="ex">\f</span> <span class="dt">\g</span> g<span class="kw">)</span> <span class="kw">((</span><span class="ex">\f</span> c c f <span class="er">(</span><span class="kw">(</span><span class="ex">\g</span> g g<span class="kw">)</span> <span class="kw">(</span><span class="ex">\g</span> f <span class="er">(</span><span class="ex">g</span> g<span class="kw">))))</span> <span class="kw">(</span><span class="ex">\f</span> <span class="dt">\g</span> <span class="dt">\h</span> <span class="dt">\i</span> i g <span class="er">(</span><span class="ex">h</span> <span class="er">(</span><span class="ex">d</span> f<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> b <span class="er">(</span><span class="ex">e</span> c<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\b</span> <span class="dt">\c</span> c <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d<span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span></code></pre></div>
|
||||
<p>Hardly any less obfuscated…</p>
|
||||
<p>The last line of</p>
|
||||
<div class="sourceCode" id="cb27"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-16</span></span></code></pre></div>
|
||||
<div class="sourceCode" id="cb27"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-16</span></span></code></pre></div>
|
||||
<p>starts out as</p>
|
||||
<pre><code>\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</code></pre>
|
||||
<pre><code> \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</code></pre>
|
||||
<p>The <code>\a</code> is for ignoring the rest of the input (to which the universal machine
|
||||
applies the decoded lambda term). The <code>\b b (..) (...)</code> is the list constructor,
|
||||
usually called <code>cons</code>, applied to a head (a list element) and a tail (another list).
|
||||
@@ -445,16 +444,16 @@ Syntax</a> which relies on the highly optimized
|
||||
Haskell runtime system for evaluation. Of course individual BLC programs running
|
||||
under the interpreter perform much worse than that same program written in Haskell.</p>
|
||||
<p>Our interpreter copes well with extra levels of interpretation:</p>
|
||||
<div class="sourceCode" id="cb29"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m0.043s</span>
|
||||
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m0.191s</span>
|
||||
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m1.919s</span>
|
||||
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m23.514s</span>
|
||||
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 4m52.700s</span></code></pre></div>
|
||||
<div class="sourceCode" id="cb29"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m0.043s</span>
|
||||
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m0.191s</span>
|
||||
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m1.919s</span>
|
||||
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m23.514s</span>
|
||||
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">></span> /dev/null</span>
|
||||
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 4m52.700s</span></code></pre></div>
|
||||
<h3 id="obfuscation">Obfuscation</h3>
|
||||
<p>Obfuscation is due entirely to conciseness. Some questions to ponder:</p>
|
||||
<p>Which of the term space codes <code>0</code>, <code>1</code>, <code>2</code>, <code>3</code> serve multiple purposes?</p>
|
||||
@@ -465,15 +464,15 @@ under the interpreter perform much worse than that same program written in Haske
|
||||
<h3 id="portability">Portability</h3>
|
||||
<p>The program freely (without casting) converts between <code>int</code> and <code>int *</code>, causing
|
||||
many warnings;</p>
|
||||
<pre><code> 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</code></pre>
|
||||
<pre><code> 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</code></pre>
|
||||
<p>Avoiding these would make the program substantially longer,
|
||||
and detract from its single minded focus on conciseness.</p>
|
||||
<p>It implicitly declares functions <code>read(2)</code>, <code>write(2)</code>, <code>exit(3)</code> and
|
||||
|
||||
Reference in new issue
Block a user