mirror of
https://github.com/urbit/shrub.git
synced 2024-12-02 21:34:04 +03:00
72 lines
1.6 KiB
Plaintext
72 lines
1.6 KiB
Plaintext
Author: Curtis Yarvin (curtis.yarvin@gmail.com)
|
|
Date: 3/8/2008
|
|
Version: 0.13
|
|
|
|
1. Manifest
|
|
|
|
This file defines one Turing-complete function, "nock."
|
|
|
|
nock is in the public domain. So far as I know, it is
|
|
neither patentable nor patented. Use it at your own risk.
|
|
|
|
2. Data
|
|
|
|
Both the domain and range of nock are "nouns."
|
|
|
|
A "noun" is either an "atom" or a "cell." An "atom" is an unsigned
|
|
integer of any size. A "cell" is an ordered pair of any two nouns,
|
|
the "head" and "tail."
|
|
|
|
3. Pseudocode
|
|
|
|
nock is defined in a pattern-matching pseudocode.
|
|
|
|
Match precedence is top-down. Operators are prefix. Parens
|
|
denote cells, and group right: (a b c) is (a (b c)).
|
|
|
|
4. Definition
|
|
|
|
4.1 Transformations
|
|
|
|
*(a 0 b c) => *(*(a b) c)
|
|
*(a 0 b) => /(b a)
|
|
*(a 1 b) => (b)
|
|
*(a 2 b) => **(a b)
|
|
*(a 3 b) => &*(a b)
|
|
*(a 4 b) => ^*(a b)
|
|
*(a 5 b) => =*(a b)
|
|
*(a 6 b c d) => *(a 2 (0 1) 2 (1 c d) (1 0) 2 (1 2 3) (1 0) 4 4 b)
|
|
*(a b c) => (*(a b) *(a c))
|
|
*(a) => *(a)
|
|
|
|
4.2 Operators
|
|
|
|
4.2.1 Goto (*)
|
|
|
|
*(a) -> nock(a)
|
|
|
|
4.2.2 Deep (&)
|
|
|
|
&(a b) -> 0
|
|
&(a) -> 1
|
|
|
|
4.2.3 Bump (^)
|
|
|
|
^(a b) -> ^(a b)
|
|
^(a) -> a + 1
|
|
|
|
4.2.4 Same (=)
|
|
|
|
=(a a) -> 0
|
|
=(a b) -> 1
|
|
=(a) -> =(a)
|
|
|
|
4.2.5 Snip (/)
|
|
|
|
/(1 a) -> a
|
|
/(2 a b) -> a
|
|
/(3 a b) -> b
|
|
/((a + a) b) -> /(2 /(a b))
|
|
/((a + a + 1) b) -> /(3 /(a b))
|
|
/(a) -> /(a)
|