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?

And do you agree that what I describe above is a property that is weaker than (and so, in particular different from) for example the property "this fold-like function is foldl or foldr".

2015-10-24 19:55 GMT+02:00 Kim-Ee Yeoh <ky3@atamo.com>:

On Sun, Oct 25, 2015 at 12:42 AM, Matteo Acerbi <matteo.acerbi@gmail.com> wrote:
For what concerns question 3, I didn't understand the idea of calling a function "associatively".

This. Associativity is a property of binary operators. It's not a property of the catamorphism 'calling' on a given binary operator.

Also, when Charles writes: "Then it goes on to use f in "thisFold f [0,1,2]" like "f (1 (f 0 2))""

commutativity appears to raise its head.

-- Kim-Ee