One aspect of parsing precedence is associativity. A left-associative operator is one, such as *, with the property that x * y * z is parsed as (x * y) * z. A right-associative operator is one, such as =, with the property that x = y = z is parsed as x = (y = z). These operators are left associative: # #? % & * ** + ++ , - . .. ..< .? / // << @@ ^ ^** ^< ^<= ^> ^>= ^^ _ _< _<= _> _>= | |_ || · (missing documentation) ⊠ (missing documentation) ⧢ (missing documentation) , and these operators are right associative: != %= &= **= *= ++= += -= -> ..<= ..= //= /= : := ; < <- <<= <= <== <=== <==> <==>= = =!= == === ===> ===>= ==> ==>= => > >= >> >>= ? ?? ??= @ @= @@= \ \= \\ \\= ^**= ^= ^^= _= |- |-= |= |_= ||= ·= ⊠= ⧢= and or SPACE xor .
Here are the operators arranged in order of increasing parsing precedence. For example, * has higher parsing precedence than +, and hence 2+3*5 is parsed as though it had been written as 2+(3*5). The symbol SPACE represents the operator that is used when two things are adjacent in program code.
8 ;
10 ,
14 %= &= **= *= ++= += -= -> ..<= ..= //= /= := <- <<= <==>= = ===>= ==>= => >> >>= ??= @= @@= \= \\= ^**= ^= ^^= _= |-= |= |_= ||= ·= ⊠= ⧢=
18 <<
20 |-
22 <=== ===>
24 <==>
26 <== ==>
28 ?? or
30 xor
32 and
34 not
36 != < <= =!= == === > >= ?
38 ||
40 :
42 |
44 ^^
46 &
48 .. ..<
50 + ++ -
52 ·
54 ** ⊠ ⧢
58 % * / // \ \\
60 @
62 SPACE
64 (*)
66 @@
68 ^* ^~ _* _~ ~
70 # #? . .? ^ ^** ^< ^<= ^> ^>= _ _< _<= _> _>= |_
72 ! ^! _!
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The source of this document is in Macaulay2Doc/ov_language.m2:1150:0.