Leonine relations on nodes

[Edward K. Ream]

In mathematics, a binary relation on a set X is just a set of 2-tuples X × X.

Let us define a Leonine relation to be a set of tuples N × N, where N is the set of all Leo nodes. Informally, a Leonine relation R(n) gives, for any particular Leo node n, the (list of) all Leo nodes associated with node n.

Aha 1: Within Leo, we can represent a Leonine relation in two ways:

- explicitly: as an organizer node containing any number of clones.

- implicitly: as a Leonine script.

Aha 2: c.cloneFindByPredicate forms the basis of all possible Leonine relations.

Indeed, c.cloneFindByPredicate(predicate) produces an organizer node containing clones of nodes that match the predicate, which is just the explicit form of a relation.

Why does this matter?

A frequently-requested feature: associate one or more nodes with other nodes. Examples:

- Associate a function with its unit tests.

- Associate a function with its documentation nodes.

- Associate an issue with nodes related to it.

Leonistas can create such associations in two ways:

1. Explicitly, laboriously: Manually create "permanent" organizer nodes containing a node (the first child) and its "related" nodes (the cloned children of the organizer node).

2. Automagically: Use an @command script based on c.cloneFindByPredicate.

The predicate (@command script) can be anything we like!  The predicate can match:

- patterns in headlines or body text,

- relations between nodes,

- uAs or tags,

- anything else!

Aha 3: Leonine relations can express the meaning of programs, functions, data, or anything else.

Proof:  Everything in mathematics is a relation, so if something has mathematical meaning, that meaning must be equivalent to a Leonine relation.

A detail: meaning is not necessarily limited to relationships between nodes, but neither are predicates, so the proof appears sound.

Edward