Jump to content

Iota and Jot

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by IM Serious (talk | contribs) at 14:41, 1 January 2017 (Zot). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Chris Bark's Iota and Jot (from Greek iota ι, Hebrew yodh י, the smallest letters in those two alphabets) are extremely minimalist formal systems, designed to be even simpler than other more popular alternatives, such as the lambda calculus and SKI combinator calculus. They can therefore also be considered minimalist computer programming languages, or Turing tarpits, esoteric programming languages that are designed to be as small as possible but still Turing-complete. Both systems use only two symbols and involve only two operations. Zot is a successor to Iota that includes input and output.[1]

Chris Bark's universal ι combinator has a very simple structure (defined here using denotational semantics in terms of the lambda calculus):

From this, one can recover the usual SKI basis combinators as follows:

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

Iota

Iota is the LL(1) language prefix ordering trees of the aforementioned combinator leafs consed by function application

  iota = "1" | "0" iota iota

so that for example denotes , whereas denotes .

Jot

Jot is the regular language

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

where the denote whereas the denote and the reduce to yielding a Gödel numbering of all algorithms.

Zot

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

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

where produces the continuation and produces the continuation and consumes the final input digit continuing through continuation .

See also

References

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