Designed by Chris Barker | Developer Chris Barker | |
First appeared 2001; 16 years ago (2001) Last release 2001 / 2001; 16 years ago (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.
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Universal iota
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
Iota is the LL(1) language that prefix orders trees of the aforementioned Universal iota ι combinator leafs, consed by function application ε,
so that for example 7004110110000000000♠0011011 denotes
Jot
Jot is the total regular language,
where the
Zot
The Zot and Positive Zot languages command Iota computations, from inputs to outputs by continuation-passing style, in syntax resembling Jot,
where 7000100000000000000♠1 produces the continuation