Binding Strength

Table

The rules for how Variables, Functions, Operators, Hyperators and other syntactic elements combine are covered in the following table:

#	Category	Description	Example
12:	Brackets left	Brackets to what is on their left	"? […]"
11:	Specification left	Left arrow to what is on its left	"? ←"
10:	Right hyperand, right operand	Dyadic hyperator to its right hyperand	"HYP ?"
9:	Right hyperand, left operand	Dyadic hyperator to its right hyperand	"HYP ?"
8:	Left hyperand, right operand	Hyperator to its left hyperand	"? HYP"
7:	Left hyperand, left operand	Hyperator to its left hyperand	"? HYP"
6:	Right operand	Dyadic operator to its right operand	"DOP ?"
5:	Vector notation	Array to an array	"A A"
4:	Left operand	Operator to its left operand	"? MOP"
4:	Trains to right paren		"… F)"
3:	Left paren to Trains		"(F …"
3:	Left argument	Function to its left argument	"A F"
2:	Right argument	Function to its right argument	"F A"
1:	Specification right	Left arrow to what is on its right	"← ?"
0:	Brackets right	Brackets to what is on their right	"[…] ?"

One way to look at these rules is that if you are given three names and/or symbols, you can always tell whether the middle object binds to the left or right object.

Vector Notation

As the above table indicates, Vector Notation has a lower Binding Strength than both a right operand to its operator and either hyperand to its hyperator. One consequence of this is a change introduced in NARS2000 Version 0.5.10 w.r.t. Numeric Strands. In particular,

• A dyadic operator written as … dop 1 2 3 is interpreted as having a right operand (short right scope) of 1 and a right argument of 2 3.
• A hyperator written as 1 2 3 mhmo is interpreted as having a left hyperand (short left scope) of 3 and a left operand (long left scope) of 1 2.
• A dyadic hyperator written as … dhmo 1 2 3 is interpreted as having a right hyperand (short right scope) of 1 and a right argument of 2 3.
• A dyadic hyperator written as … dhdo 1 2 3 is interpreted as having a right hyperand (short right scope) of 1, a right operand (short right scope) of 2, and a right argument of 3.

To reduce confusion, use parentheses such as (LO (LH dhdo 1) 2) 3.