MIBBLLII

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MIBBLLII Isn't brainfuck But Looks Like It Is is a programming language made by Nathan van Doorn. It is based on the wikipedia:B,C,K,W system. It maps input (expressed as a church list of church booleans corresponding to the bits of the input, ending with an infinite stream of church trues) to output (expressed as a similar list, presumably finite).

Combinators

Expression Evaluates as
+ a b c a [ b c ]
- a b c a c b
. a b a
, a b a b b
> a a
< a b c a c [ b c ]

[ and ] are used to group combinators for evaluation order.

Proof of Turing Completeness

SKI combinator calculus is Turing-complete, and all the operators in SKI exist in MIBBLLII as <, ., and >. It is still Turing-complete without < or >, as the following shows.

<       +[+,][++-]
>       ,.

See also