It has already been established in this thread what Charles meant by 3.

He meant that a fold-function that has the property he is after would guarantee that it:

a) takes all the content elements from a data structure, say x1,...,xn,

b) builds an application tree with the to-be-folded, binary operation f in the internal nodes of a binary tree, whose leafs, read from left to right, form exactly the sequence x1,...,xn,

c) evaluates that application tree.

Do you agree that what I describe above is a property of a given fold-like function, not of the f handed to that fold-like function?