MIBBLLII

MIBBLLII Isn't brainfuck But Looks Like It Is is a programming language made by Nathan van Doorn. It is based on the 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
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. <      +[+,][++-] >       ,.