Binding Strength

For two entities X and Y that are adjacent in an expression (that is, X Y), the binding strength between them and the result of the bind is shown in this table:

    Y
    A F H MOP DOP DOT IDX
X A
6 A
3 AF
3 AF
4 F
   
7 REF
4 A
F
2 A
1 F
4 F
4 F
   
   
4 F
H
   
1 F
4 F
4 F
   
   
4 H
AF
2 A
1 F
   
   
   
   
   
MOP
   
   
4 ERR
   
   
   
   
DOP
5 MOP
5 MOP
5 MOP
   
   
   
   
JOT
5 MOP
5 MOP
5 MOP
4 F
   
   
   
DOT
6 ERR
5 MOP
5 MOP
   
6 ERR
   
   
REF
7 A
7 F
7 H
7 MOP
7 DOP
   
   
IDX
3 ERR
3 ERR
3 ERR
   
   
   
   
A : *Array, for example, 0 1 2 'hello' ⍺ ⍵
F : *Function (primitive/defined/derived/system), for example, + - +.× myfn ⎕CR {⍺ ⍵}
H : *Hybrid function/operator, that is, / ⌿ \ ⍀
AF : Bound left argument, for example, 2+
MOP : *Monadic operator, for example, ¨ ⍨ &
DOP : Dyadic operator, for example, ⍣ ⍠ ⍤ ⌸
JOT : Jot, that is, compose/null operand ∘
DOT : Dot, that is, reference/product .
IDX : square-bracketed expression, for example, [⍺+⍳⍵]
ERR : Error

* indicates a "first-class" entity, which can be parenthesised or named

In this table:

For example, in the expression a b.c[d], where a, b, c and d are arrays, the binding proceeds:

      a b . c [d]
       6 7 6 4      ⍝ binding strengths between entities
→     a (b.) c [d]
       0    7 4
→     a (b.c) [d]
       6     4
→     (a(b.c))[d]