Term Grouping

Grouping happens following tokenization and is when tokens are organized hierarchically by parenthetical level.

This is accomplished by a simple LL(1) recursive descent parser. Tokens are organized into terms, of which there are several kinds.

Group terms

Group terms are the representation of a parenthetical group and all of the terms inside of it. For example, given the string "1 + (2 - (3 / 4))", there are three group terms:

1. The term containing the 3 term, the / term, and the 4 term
2. The term containing the 2 term, the - term, and group term #1
3. The overall "root" group term containing the 1 term, the + term, and group term #2.

Function term

A function term is a specialized group term. Like the group term, it can have "subterms", but it also has a property denoting the name of the function. For example, if we have the string "sin($x) + $x", the function term will be the term containing the first $x variable, plus the name of the function ("sin").

Number term

A number term is a term representing a numeric literal.

Variable term

A variable term is a term representing a variable.

Operator term

An operator term is a term representing one of the built-in operators.

During tokenization, we created operator tokens for opening and closing parentheses. An operator term does not represent those particular tokens, since parentheses are represented with group terms and function terms.