GFR Wrote:(priority to the right ... whenever necessary) :
b[3]<h>x = b^...^b^b^x
b[2]<h>x = b*...b*b*b*x ,
b[1]<h>x = b+...b+b+b+x,
... (and I stop here, for ... avoiding problems ...)
Thats exactly the proposal I was waiting for as we still needed an ASCII notation for \( f^{\circ n} \). This perfectly fits with this proposal:
\( f^{\circ n}(x) \)=f<n>(x)
In your above example we can directly interpret the function as f=b[k] which also is used in Haskell (I think) where you write (a*) for the function x->a*x and (*a) for the function x->x*a, where * is an arbitrary binary operation.
So when writing b[k]<n> we just let out the parens in (b[k])<n> for simplification.