generalized function composition for readable pointfree functions

let o be the function composition function, and . the corresponding infix binary operator, i.e.:

o g f := g . f := \x. g (f x)

let f^n be the n-th repitition of the function f, i.e.:

f^0    := id
f^(Sn) := f . f^n

let f_n be the n-th shift of the function f, i.e.:

f_0     := id
f_(S n) := o^n f

observe

1. repeating composition increases bracket width

o^0 = id          = \a b c d e f g. a (b) c d e f g
o^1 = o           = \a b c d e f g. a (b c) d e f g
o^2 = o.o         = \a b c d e f g. a (b c d) e f g
o^3 = o.o.o       = \a b c d e f g. a (b c d e) f g
o^4 = o.o.o.o     = \a b c d e f g. a (b c d e f) g

2. nesting composition increases bracket offset

o^0 o = o               = \a b c d e f g. a (b c) d e f g
o^1 o = o o             = \a b c d e f g. a b (c d) e f g
o^2 o = o (o o)         = \a b c d e f g. a b c (d e) f g
o^3 o = o (o (o o))     = \a b c d e f g. a b c d (e f) g
o^4 o = o (o (o (o o))) = \a b c d e f g. a b c d (e f) g

therefore o^x o^w is an arbitrary bracket with offset x and width w, for example:

o^2 o^3 = at place 2, take 3 arguments
        = \a b c d e f g. a b c (d e f) g

if we need multiple brackets, we can join them with o… for example, we might want to write the compositon of multiple binary functions in pointfree

\f g h x y z. (f x) (g y) (h z)  = o^4 o . o^2 o
                                 = o^2 o . o^3 o

I played with this using http://pointfree.io/.