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In formal language theory and computer science, Iota and Jot (from Greek iota ι, Hebrew yodh י, the smallest letters in those two alphabets) are languages, extremely minimalist formal systems, designed to be even simpler than other more popular alternatives, such as the lambda calculus and SKI combinator calculus. Thus, they can also be considered minimalist computer programming languages, or Turing tarpits, esoteric programming languages designed to be as small as possible but still Turing-complete. Both systems use only two symbols and involve only two operations. Both were created by professor of linguistics Chris Barker in 2001. Zot (2002) is a successor to Iota that supports input and output.[1]

Iota, Jot, Zot
ParadigmsFormal language, Turing tarpit, esoteric
Designed byChris Barker
DeveloperChris Barker
First appeared2001; 18 years ago (2001)
Final release
2001 / 2001; 18 years ago (2001)
Implementation languageScheme, JavaScript
PlatformScheme interpreter, Web browser (JavaScript)
LicensePublic domain
Websitewww.nyu.edu/projects/barker
Influenced
Zot

Universal iotaEdit

Chris Barker's universal iota combinator ι has the very simple λf.fSK structure defined here, using denotational semantics in terms of the lambda calculus,

 

 

 

 

 

(1)

From this, one can recover the usual SKI expressions, thus:

 

 

 

 

 

(2)

Because of its minimalism, it has influenced research concerning Chaitin's constant.[2]

IotaEdit

Iota is the LL(1) language that prefix orders trees of the aforementioned Universal iota ι combinator leafs, consed by function application ε,

iota = "1" | "0" iota iota

so that for example 0011011 denotes  , whereas 0101011 denotes  .

JotEdit

Jot is the regular language consisting of all sequences of 0 and 1,

jot = "" | jot "0" | jot "1"

The semantics is given by translation to SKI expressions. The empty string denotes  ,   denotes  , where   is the translation of  , and   denotes  .

The point of the   case is that the translation satisifes   for arbitrary SKI terms   and  . For example,

 
holds for arbitrary strings  . Similarly,
 
holds as well. These two examples are the base cases of the translation of arbitrary SKI terms to Jot given by Barker, making Jot a natural Gödel numbering of all algorithms.

Jot is connected to Iota by the fact that   and by using the same identities on SKI terms for obtaining the basic combinators   and  .

ZotEdit

The Zot and Positive Zot languages command Iota computations, from inputs to outputs by continuation-passing style, in syntax resembling Jot,

zot = pot | ""
pot = iot | pot iot
iot = "0" | "1"

where 1 produces the continuation  , and 0 produces the continuation  , and wi consumes the final input digit i by continuing through the continuation w.

See alsoEdit

ReferencesEdit

  1. ^ Barker, Chris. "Zot". The Esoteric Programming Languages Webring. Archived from the original on 12 March 2016. Retrieved 4 October 2016. Cite uses deprecated parameter |deadurl= (help)
  2. ^ Stay, Michael (August 2005). "Very Simple Chaitin Machines for Concrete AIT". Fundamenta Informaticae. IOS Press. 68 (3): 231–247. Retrieved 20 February 2011.

External linksEdit