Iota and Jot
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.
|Paradigms||Formal language, Turing tarpit, esoteric|
|Designed by||Chris Barker|
2001 / 2001
From this, one can recover the usual SKI expressions, thus:
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 .
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.