Proof, order of operations and functional languages
ajuc: w sf x sf2 y sf3 z
is equivalent to
sf3(sf2(sf(w,x),y),z)
assuming left to right evaluation (and equal priorities of operations).Trees of operations:  w sf x sf2 y sf3 z

  w-sf1-sf2-sf3
     |   |   |
     x   y   z

  sf(w,sf2(x,sf3(y,z)))

    sf1-sf2-sf3-z
     |   |   |
     w   x   y

You can permutate w,x,y,z in these trees - I was sure this will give the same expressions, but now I'm not.Interesting question.Edit: oh, so you wanted to permutate functions, not arguments. Then it won't give the same expressions.