[Turing_Machine]

"Branchs/trees are a superset of pairs/lists"

No, they aren't. A tree is acyclic by definition. Cons cells allow circular structures.

[Turing_Machine]

To take a familiar example, the Web is not a tree. While you might argue that each page has unique children (outlinks), there is no unique parent -- a page can have an arbitrarily large number of incoming links, and the page can link back to those pages in turn, producing cyclic structures of immense complexity.

For some interesting discussion on the limits of tree structures with respect to urban planning see A City is Not a Tree by Christopher Alexander (who is also the inspiration for the Design Patterns movement in software engineering). http://www.rudi.net/node/317

[Deestan]

All good, just a nitpick: You don't need a unique parent to have a tree. You don't even need directed edges. :)

The purest definition of a tree graph is "a graph with no cycles".

[sesqu]

We use different definitions. My trees are acyclic connected graphs with one root.

[omaranto]

The structures described are called trees in the post, but are actually just sets of named objects, which can be used to describe cyclic structures in the same way conses can.

[chalst]

And this is useful: you can represent the transitions of a state machine in this way, for instance.

[Confusion]

The structure he calls a 'tree' allows cycles and is a generalization of a list. Whether he uses the correct word isn't really interesting: it doesn't detract anything from the post.