Total BF is a WIP total (fully defined, always terminating) version of brainfuck abandoned by User:Tailcalled. It will obviously not be Turing-complete.
Total BF will have some sort of effect system, which will limit the programs that can be written.
Current ideas for effects documented (hopefully self-expanatory):
+ :: [$#n+1] - :: [$#n+255] > :: [$n, #n] < :: [#n, $n] . :: [$#n] , :: [$#m] -- note, m, not n
A loop will then require an instruction along the lines of any of the following:
a :: [$#n+x] where x != 0
b :: [$n+x, #n] where x != 0
or possibly others.