A set of canonical names (see Feel.Name) that tells a name from the start of one.

The parser makes a name one token at a time, from the tokens it reads, and has to know when to stop. A run of name tokens can be as long as the expression (x + x + x + … is all name tokens, since + can be a part of a name), so it cannot try every length of it. What it asks of the names is whether what it has made is one, only the start of one, or neither (probe/2): when it is neither, no longer name made from it is one either, since each is the start of the next, and the work for a name is the number of tokens that it has in common with a known name, not how long the run is and not how long the known names are (D-177, D-177).

The names are kept in order, so that a string and the names that start with it are together, and the first name that is not before the string answers for all of them. Names are added one at a time, as the parser binds the parameters, iterators and keys that an expression introduces, and the set is a value: adding a name gives a set and leaves the one it was made from as it was.