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