Iota and Jot
|Paradigms||Formal language, Turing tarpit, esoteric|
|Designed by||Chris Barker|
2001 / 2001
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.
Note that this article uses Backus-Naur form to describe syntax.
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,
From this, one can recover the usual SKI expressions, thus:
Because of its minimalism, it has influenced research concerning Chaitin's constant.
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 .
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 satisfies for arbitrary SKI terms and . For example,
Jot is connected to Iota by the fact that and by using the same identities on SKI terms for obtaining the basic combinators and .
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.
- ^ Barker, Chris. "Zot". The Esoteric Programming Languages Webring. Archived from the original on 12 March 2016. Retrieved 4 October 2016.
- ^ Stay, Michael (August 2005). "Very Simple Chaitin Machines for Concrete AIT". Fundamenta Informaticae. IOS Press. 68 (3): 231–247. arXiv:cs/0508056. Bibcode:2005cs........8056S. Retrieved 20 February 2011.
- Official website
- Barker, Chris. "Iota and Jot: the simplest languages?". The Esoteric Programming Languages Webring. Archived from the original on 7 May 2016. Retrieved 13 August 2004.