On Thu, Jun 4, 2009 at 9:13 AM, wren ng thornton <wren@freegeek.org> wrote:

The Visitor pattern isn't a functor, it's a collection of things. The type being visited is the functor[1], the set of methods on that type for accepting a visitor is a catamorphism[2], and the visitor itself is an algebra for the functor[3].


[1] Or rather, the coproduct of all related classes that can chain a visitor forms a type, and that type is a functor.


[2] For the recursive Visitor pattern I use most often, that is. For the non-recursive version it's usually fmap. This is the part where the pattern gets a bit shaky because there are actually many different patterns all called "Visitor". The main points of interest are whether it's recursive or not, and whether it applies the visitor to itself, to its children, or both.

non-recursive + itself == ($)

non-recursive + children == fmap (under open-recursion interpretation of the type, aka all nodes are elements)

recursive + children == fmap (under closed-recursion interpretation, aka only fringe nodes are elements)

recursive + both == cata (usually, though it depends how you aggregate)

recursive + itself == This is actually a variant of the Iterator pattern