Pseudoholomorphic curve: Difference between revisions

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{{Unreferenced|date=April 2009}}
The author is known as Irwin Wunder but it's not the most masucline name out there. Supervising is my occupation. Years ago we moved to North Dakota and I adore every day living here. One of the issues she enjoys most is to read comics and she'll be starting some thing else alongside with it.<br><br>My web-site [http://gcjcteam.org/index.php?mid=etc_video&document_srl=655020&sort_index=regdate&order_type=desc at home std testing]
 
'''Binary combinatory logic''' ('''BCL''') is a formulation of [[combinatory logic]] using only the symbols 0 and 1. BCL has applications in the theory of program-size complexity ([[Kolmogorov complexity]]).
 
==Definition==
===Syntax===
[[Backus-Naur form|Backus&ndash;Naur form]]:
* <tt> <term> ::= 00 | 01 | 1 <term> <term>  </tt>
===Semantics===
The [[denotational semantics]] of BCL may be specified as follows:
* <tt>[ 00 ] == ''K''</tt>
* <tt>[ 01 ] == ''S''</tt>
* <tt>[ 1 <term1> <term2> ] == ''('' [<term1>] [<term2>] '')'' </tt> 
where "<tt>[...]</tt>" abbreviates "the meaning of <tt>...</tt>".  Here <tt>''K''</tt> and <tt>''S''</tt> are the ''KS''-basis combinators, and <tt>''( )''</tt> is the ''application'' operation, of [[combinatory logic]]. (The prefix <tt>1</tt> corresponds to a left parenthesis, right parentheses being unnecessary for disambiguation.)
 
Thus there are four equivalent formulations of BCL, depending on the manner of encoding the triplet (K,&nbsp;S,&nbsp;left parenthesis). These are <tt>(00,&nbsp;01,&nbsp;1)</tt> (as in the present version), <tt>(01,&nbsp;00,&nbsp;1)</tt>, <tt>(10,&nbsp;11,&nbsp;0)</tt>, and <tt>(11,&nbsp;10,&nbsp;0)</tt>.
 
The [[operational semantics]] of BCL, apart from eta-reduction (which is not required for [[Turing-complete|Turing completeness]]), may be very compactly specified by the following [[rewriting]] rules for subterms of a given term, [[parsing]] from the left:
* <tt> &nbsp;1100xy&nbsp;&nbsp;<math>\rightarrow</math> x  </tt>
* <tt> 11101xyz&nbsp;<math>\rightarrow</math>&nbsp;11xz1yz  </tt>
where <tt>x</tt>, <tt>y</tt>, and <tt>z</tt> are arbitrary subterms. (Note, for example, that because parsing is from the left, <tt>10000</tt> is not a subterm of <tt>11010000</tt>.)
 
==See also==
* [[Iota and Jot]]
* [[Binary lambda calculus]]
 
==External links==
* [http://homepages.cwi.nl/~tromp/cl/cl.html John's Lambda Calculus and Combinatory Logic Playground]
 
[[Category:Algorithmic information theory]]
[[Category:Combinatory logic]]

Latest revision as of 01:21, 17 November 2014

The author is known as Irwin Wunder but it's not the most masucline name out there. Supervising is my occupation. Years ago we moved to North Dakota and I adore every day living here. One of the issues she enjoys most is to read comics and she'll be starting some thing else alongside with it.

My web-site at home std testing