Empty List

[] (which represents emptiness) acts like an identity element for an operation that chooses between alternatives, when a List of possible choices is returned. This is a common, standard idiom.

Empty is not an “error” or a “failure”, but a signal to stop, prune, backtrack and delete the empty, now cyclic path.

Considered as an identity element for an operation of a choice between alternatives: if [] then try the next one.

This is a standard idiom in parsing - the current parser sees nothing (returns an empty result) - try the next one.

This is idiom is applicable for an ordinary Monadic composition, or for composition of partial (non-total) functions.

This generalizes the pattern of selection in the process of systematic exploration or a complete traversal of a tree-like (acyclic) structure.

This is at the core of universal backtracking search, which either abandons the path on a contradiction or a dead-end or an expected base-case.

Such kind of a search is complete.

A recursive traversal with stops at an expected base case ([]) is also a special case of a backtracking search process.

[] (but not null) is a legitimate signal and is an identity for concatenation. so is the "" (the empty string).

Again, being an identity element for concatenation operation is what makes them leigitimate. A general NULL is not an identity and is a huge and embarrassing theoretical mistake (by math-illiterates).

Maybe is just this empty/non-empty (Nothing or Something) aspect of a list being redefined with a different pair of constructors.

A recursive traversal of a tree stops (and recursion backtracks) at every expected Leaf.