Operator, please dial the number

Darius J Chuck



The grammar of TAO includes the following rule (in BNF):

<operator>   ::= "`" <any>

Where any is any printable Unicode character.

The operator is a very simple, yet very versatile concept, which captures the essence of many syntactical constructs. It has 2 basic roles in TAO:

  1. Escape mechanism for the 3 meta symbols of the grammar, i.e. [, ], and ` (the operator symbol itself).

  2. Extension mechanism for future notations based on TAO as well as for custom ad-hoc notations – either community-built notations that might become standard or limited-use internal notations. There is thus a risk associated with abuse of this mechanism. In the spirit of TAO, the use of operators should be kept to a minimum.

Furthermore, an important property of the operator is that a single operator meta symbol ` introduces two annotation insertion points at the same depth in the syntax tree – on either side of the operator. This enables slightly more compact notations than could be achieved otherwise.

The property is also where operator gets its name from. It is however a more primitive and lower-level construct than a programming language operator – a programming language built on top of TAO could use it to represent operators.


What follows from the grammar definition, but is perhaps worth noting, is that operators are always single-character. A possible way to model a multi-character high-level operators could be to use a low-level operator for “quoting” these, e.g.


Here `. is the low-level quoting operator and <=> is the high-level multicharacter quoted operator.

A less generic, but a more compact way could be (colored for clarity):


Here `< could be a low-level operator that introduces a class of high-level operators. The annotation that follows it – => – determines a specific high level operator (<=>). What follows is a tree that contains the right-hand-side argument to the high-level operator.

Better practice

A programming language built in the true spirit of TAO however would avoid both of the above solutions. A better one would not use operators in this case at all, e.g.:


But that’s a story for another time.