Operator precedence
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This page uses content from Wikipedia. The original article was at Operators in C and C++. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) 
 Task
Provide a list of precedence and associativity of all the operators and constructs that the language utilizes in descending order of precedence such that an operator which is listed on some row will be evaluated prior to any operator that is listed on a row further below it.
Operators that are in the same cell (there may be several rows of operators listed in a cell) are evaluated with the same level of precedence, in the given direction.
State whether arguments are passed by value or by reference.
Contents
 1 8th
 2 ALGOL 60
 3 ALGOL 68
 4 ALGOL W
 5 AWK
 6 bc
 7 Bracmat
 8 C
 9 C++
 10 Clojure
 11 COBOL
 12 Common Lisp
 13 D
 14 Eiffel
 15 Erlang
 16 F#
 17 Fortran
 18 FutureBasic
 19 Go
 20 Icon and Unicon
 21 Haskell
 22 J
 23 Java
 24 jq
 25 Kotlin
 26 Lua
 27 Mathematica
 28 Matlab
 29 Nim
 30 OCaml
 31 Oforth
 32 Pascal
 33 Perl
 34 Perl 6
 35 Phix
 36 PHP
 37 PARI/GP
 38 PicoLisp
 39 PL/I
 40 Python
 41 Racket
 42 REALbasic
 43 REXX
 44 Ring
 45 Ruby
 46 Scilab
 47 Simula
 48 Seed7
 49 Sidef
 50 Tcl
 51 TI83 BASIC
 52 VBScript
 53 Visual Basic
 54 Visual Basic .NET
 55 XPL0
 56 zkl
8th[edit]
In 8th it's very simple: the currently invoked word has precedence, and items are operated upon in the order they are popped off the stack.
ALGOL 60[edit]
Priority  Description  Operators  Associativity 

highest  
1  power  'POWER' 
left 
2  unary operator (opposite)  +  
left 
3  multiplication & division  * / '/' 
left 
4  addition & subtraction  +  
left 
5  comparison  'EQUAL' 'NOT EQUAL' 
left 
6  logical NOT  'NOT' 
left 
7  logical AND  'AND' 
left 
8  logical OR  'OR' 
left 
9  equivalence  'EQUIV' 
left 
10  implication  'IMPL' 
left 
lowest 
Note: '/' is the Euclidean division
ALGOL 68[edit]
The coder may define new operators and both those and the predefined ones may be overloaded and their priorities may be changed.
Array, Procedure, Dereference, Selection and Generator operations[edit]
priority  Operation  +Algol68^{Rev0}  +Algol68^{G} 

Effectively 12 (Primary) 
dereferencing, deproceduring(~,~), subscripting[~], rowing[~,] & slicing[~:~]  currying(~,), diag, trnsp, row, col  
Effectively 11 (Secondary) 
of (selection), loc & heap (generators)  →  new (generator) 
These are technically not operators, rather they are considered "units associated with names"
Monadic operators[edit]
priority (Tertiary) 
Algol68 "Worthy characters"  +Algol68^{Rev0&1}  +Algol68^{C,G}  +Algol68^{Rev0} 

10  not, up, down, lwb, upb,
, abs, arg, bin, entier, leng, level, odd, repr, round, shorten 
¬, ↑, ↓, ⌊, ⌈  ~, norm, trace, t, det, inv  lws, ups, ⎩, ⎧, btb, ctb 
Standard dyadic operators with associated priorities[edit]
priority (Tertiary) 
Algol68 "Worthy characters"  +Algol68^{Rev0&1}  +Algol68^{C,G}  +Algol68^{Rev0} 

9  +*, i  +×, ⊥  !  
8  shl, shr, **, up, down, lwb, upb  ↑, ↓, ⌊, ⌈  lws, ups, ⎩, ⎧  
7  *, /, %, over, %*, mod, elem  ×, ÷, ÷×, ÷*, %×, □  ÷:  
6  , +  
5  <, lt, <=, le, >=, ge, >, gt  ≤, ≥  
4  =, eq, /=, ne  ≠  ~=  
3  &, and  ∧  /\  
2  or  ∨  \/  
1  minusab, plusab, timesab, divab, overab, modab, plusto,
:=, +:=, *:=, /:=, %:=, %*:=, +=: 
×:=, ÷:=, ÷×:=, ÷*:=, %×:=  minus, plus, div, overb, modb, ÷::=, prus 
Note: Tertiaries include names nil and ○.
Assignation and identity relations etc[edit]
Again, these are technically not operators, rather they are considered "units associated with names"
priority (Quaternaries) 
Algol68 "Worthy characters"  +Algol68^{Rev0&1}  +Algol68^{C}  +Algol68^{Rev0} 

Effectively 0  :=, =:, = , :=:, :/=:, is, isnt, at , @  :≠:, :  :~=:  ct, ::, ctab, ::=, .., is not 
Note: Quaternaries include names skip and ~.
Algol 68 also includes (something like) C's ternary conditions, e.g.:
 case ~ in ~ ouse ~ in ~ out ~ esac or simply "( ~  ~ : ~  ~  ~ )",
 if ~ then ~ elif ~ then ~ else ~ fi or simply "( ~  ~ : ~  ~  ~ )",
And (unlike C's comma operator) the ";" can be used to indicate statements are done sequentially, where as the "," indicates that the statements can be done "collaterally", e.g. in parallel. Or a parallel clause can be used to force statements to be executed in parallel, e.g. par( ~, ~, ... )
Key: The super scripts indicate the following:
 ALGOL 68^{Rev0} indicates Algol 68 Final Report (Essentially Revision 0)
 ALGOL 68^{Rev0&1} indicates Algol 68 Revised Report (Essentially Revision 1)
 ALGOL 68^{C} indicates Cambridge University Algol 68[1].
 ALGOL 68^{G} indicates Algol 68 Genie[2]
ALGOL W[edit]
Priority  Operator  Description  Associativity  Arity 

highest  long short abs  Widen, narrow, absolute value  left  unary 
shl shr **  left shift, right shift, raise to power  left  binary  
* / div rem  multiply, divide, integer division, remainder  left  binary  
+   addition, subtraction  left  unary and binary  
< <= = ¬= >= > is  comparison, "is" checks a reference has a particular type  left  binary  
not  logical or bits negation  left  unary  
and  logical or bits "and"  left  binary  
lowest  or  logical or bits "or"  left  binary 
AWK[edit]
See also: gawkReference
# Operators are shown in decreasing order of precedence.
# A blank line separates groups of operators with equal precedence.
# All operators are left associative except:
# . assignment operators
# . conditional operator
# . exponentiation
# which are right associative.
#
# ( ) grouping
#
# $ field reference
#
# ++ increment (both prefix and postfix)
#  decrement (both prefix and postfix)
#
# ^ exponentiation
# ** exponentiation (not all awk's)
#
# + unary plus
#  unary minus
# ! logical NOT
#
# * multiply
# / divide
# % modulus
#
# + add
#  subtract
#
# string concatenation has no explicit operator
#
# < relational: less than
# <= relational: less than or equal to
# > relational: greater than
# >= relational: greater than or equal to
# != relational: not equal to
# == relational: equal to
# > redirection: output to file
# >> redirection: append output to file
#  redirection: pipe
# & redirection: coprocess (not all awk's)
#
# ~ regular expression: match
# !~ regular expression: negated match
#
# in array membership
#
# && logical AND
#
#  logical OR
#
# ?: conditional expression
#
# = assignment
# += addition assignment
# = subtraction assignment
# *= multiplication assignment
# /= division assignment
# %= modulo assignment
# ^= exponentiation assignment
# **= exponentiation assignment (not all awk's)
bc[edit]
From the POSIX Standard, ordered by decreasing precedence:
Precedence  Operator(s)  Description  Associativity 

Highest  ++,   Prefix/Postfix Increment/Decrement  n/a 
unary   Negation  n/a  
^  Exponentiation  Right to left  
*, /, %  Multiplication, Division, Remainder  Left to right  
+, binary   Addition, Subtraction  Left to right  
=, +=, =, *=, /=, %=, ^=  Assignment  Right to left  
==, <=, >=, !=, <, >  Comparison  None  
!  Logical Not  n/a  
&&  Logical And  Left to right  
Lowest    Logical Or  Left to right 
Bracmat[edit]
Bracmat has 15 binary operators and 12 unary operators, not counting the minus
The binary operators have a simple precedence order and all binary operators are rightassociative.
Precedence  Operator  Description  Example  Note 

Highest  _ 
In pattern: matches any binary operator. Outside pattern: evaluates to last matched operator  a*b:?x_?y & p_q becomes p*q
 
$ 
Function application. Evaluates rhs and then applies function on lhs  put$!x
 
' 
Function application. Applies function on lhs to unevaluated rhs  apply'(?a 13 ?z)
 
\D 
Symbolic differentiation  x\D(x^2) differentiates x^2 to x
 
\L 
Logarithm  e\Ly is the natural logarithm of y
 
^ 
Exponentiation  x^2 is the square of x
 
* 
Multiplication  a*b is the product of a and b 
neutral element: 1
 
+ 
Addition  a+b is the sum of a and b 
neutral element: 0
 
white space  constructs a white space separated list  a b 
neutral element: empty string ""
 
: 
Match subject on the left with pattern on the right  a b c d:? c ?
 
& 
"and then"  1:2 & out$"The end of time is nearing"
 
  "or else"  1:2  out$"Don't think so"
 
, 
constructs a comma separated list  1,2,3
 
. 
constructs a dot separated list or tree in general  (aa.bb).cc.dd
 
Lowest  = 
define  swap=a b.!arg:(?a.?b)&(!b.!a)

Precedence among unary operators is a mixed bag. Unary operators can modify something that is to the right of the unary operator, which can be another unary operator, a string or a binary operator.
Of the unary operators ?
and !
(or !!
), the latter have the higher priority. So 17:?!x
assigns the value 17
to the variable that happens to be the value of x
. (Like *x = 17
in C). (The unary operators !
and !!
cannot be combined and are reduced to !!
)
The negation operator ~
negates the first of the unary operators / # < > % @
that is present. If none of these unary operators is present, the negation operator negates the node (string or expression with binary operator) itself, with the meaning "not equal to". Bang operators !
or !!
turn their operand into a variable that is supposed to have a value. The negation operator operates on the value (direct resp. indirect) of a variable, not on the variable name itself.
The combination ~<>
has to be read in one piece, meaning "not unequal", which is not quite unequal to ~
. It is used for case insensitive matching.
Some combinations of unary operators have currently no meaning and are silently reinterpreted: ~?x
is the same as ?x
and ~?!x
is the same as ?!x
. But ~#?x
is not the same as #?x
.
The [
and `
(grave accent) are outside any considerations of precedence.
If you are wondering what the discussed unary operators are for, see this table:
Operator  Description  Example 

! or !! 
retrieves value  (x=17)&!x becomes 17

? 
(In a pattern) Assigns value. Or is a wildcard.  1 2 3:?x 3 ? & !x becomes 1 2

` 
Cuts corners, like FENCE in SNOBOL4 or ! in Prolog 
1 2 3:? `?x 3 assigns 2 to x , because assigning 1 2 is never tried.

@ 
Accept atomic subjects only  2*a+3*b+c+6*d:?+@+? succeeds, because c is atomic.

% 
Accept anything but neutral element  8 2 3:%?x ? assigns 8 to x

> ( < ) 
Greater (less) than  1 2 3 4:? >[email protected] ?x assigns 4 to x

# 
Accept only a number  a:#*?x assigns a to x and matches 1 with #

/ 
Accept only a noninteger number  1 2 5/2 3:? /?x ? assigns 5/2 to x

~ 
Negate  a:~b (succeeds) 5:~<5 (succeeds)

[ 
Catches position in subject rather than part of the subject itself  a b c d:? [?p&!p gives 4 , the length of the subject in number of elements. a b c d:? [2 ?x assigns c d to x .

C[edit]
Same as C++.
C++[edit]
The following is a table that lists the precedence and associativity of all the operators in the C and C++ languages. An operator's precedence is unaffected by overloading.
Precedence  Operator  Description  Associativity 

1
highest 
::

Scope resolution (C++ only)  Lefttoright 
2  ++

Suffix increment  


Suffix decrement  
()

Function call  
[]

Array subscripting  
.

Element selection by reference  
>

Element selection through pointer  
typeid()

Runtime type information (C++ only) (see typeid)  
const_cast

Type cast (C++ only) (see const cast)  
dynamic_cast

Type cast (C++ only) (see dynamic cast)  
reinterpret_cast

Type cast (C++ only) (see reinterpret cast)  
static_cast

Type cast (C++ only) (see static cast)  
3  ++

Prefix increment  Righttoleft 


Prefix decrement  
+

Unary plus  


Unary minus  
!

Logical NOT  
~

Bitwise NOT  
(type)

Type cast  
*

Indirection (dereference)  
&

Addressof  
sizeof

Sizeof  
new , new[]

Dynamic memory allocation (C++ only)  
delete , delete[]

Dynamic memory deallocation (C++ only)  
4  .*

Pointer to member (C++ only)  Lefttoright 
>*

Pointer to member (C++ only)  
5  *

Multiplication  
/

Division  
%

Modulo (remainder)  
6  +

Addition  


Subtraction  
7  <<

Bitwise left shift  
>>

Bitwise right shift  
8  <

Less than  
<=

Less than or equal to  
>

Greater than  
>=

Greater than or equal to  
9  ==

Equal to  
!=

Not equal to  
10  &

Bitwise AND  
11  ^

Bitwise XOR (exclusive or)  
12  

Bitwise OR (inclusive or)  
13  &&

Logical AND  
14  

Logical OR  
15  ?:

Ternary conditional (see ?:)  Righttoleft 
16  =

Direct assignment  
+=

Assignment by sum  
=

Assignment by difference  
*=

Assignment by product  
/=

Assignment by quotient  
%=

Assignment by remainder  
<<=

Assignment by bitwise left shift  
>>=

Assignment by bitwise right shift  
&=

Assignment by bitwise AND  
^=

Assignment by bitwise XOR  
=

Assignment by bitwise OR  
17  throw

Throw operator (exceptions throwing, C++ only)  
18  ,

Comma  Lefttoright 
For quick reference, see also this equivalent, colorcoded table.
Clojure[edit]
As is the case with LISPs in general, there is no need to worry about operator precedence. This is one of the benefits of SExpressions and prefix notation. All functions evaluate left to right and inside out. The operators in Clojure are just functions, and everything is fully parenthesized.
That being said, there is a macro expansion phase that precedes compilation, and with macros you have great power to change the rules. A couple of the most common macros with respect to ordering are the threadfirst macro and the threadlast macro. These allow you to order expressions as a chain, which in many cases is preferable for readability.
COBOL[edit]
The following data was derived from the 2009 draft COBOL 20XX Standard.
Arithmetic Expressions[edit]
Precedence  Operator(s)  Description 

Highest  +  
Unary plus and minus 
** 
Exponentiation  
* / 
Multiplication and Division  
Lowest  +  
Addition and Subtraction 
Boolean Expressions[edit]
Precedence  Operator  Description 

Highest  BNOT 
Negation 
BAND 
Conjunction  
BXOR 
Exclusive disjunction  
Lowest  BOR 
Inclusive disjunction 
Concatenation Expressions[edit]
The &
operator is the only operator used in concatenation expressions.
Logical Expressions[edit]
Precedence  Operator  Description 

Highest  NOT 
Logical negation 
AND 
Logical conjunction  
Lowest  OR 
Logical inclusive OR 
Common Lisp[edit]
There is no need to worry about operator precedence in Common Lisp and Lisp's in general. Operators (like +  * / ) are normal functions and all of the code is organized as Sexpressions with a prefixed polish notation. In result all of the code is parenthesized and the code is evaluated from the innermost Sexpression to the outermost Sexpression.
D[edit]
Priority  Description  Operators  Comments  

15  Template instantiation  !  Toplevel ',' in rhs expression treated specially. Cannot be chained  
14.5  Lambda abstraction  =>  Not a real operator, occurs twice, this is binding power to the left.  
14  Postfix operators  . ++  ( [  ( and [ treat toplevel ',' in rhs expression specially and require balanced ) or ] in order to be completed  
13  Power operator  ^^  Rightassociative  
12  Unary operators  & ++  * +  ! ~  
11    * / %  
10    +  ~  Binary '~' is the concatenation operator  
9  Bit shift operators  << >> >>>  
6a  Comparison operators  == != > < >= <= !> !< !>= !<= <> !<> <>= !<>= in !in is !is  Unordered with respect to bitwise operators, cannot be chained.  
8b  Bitwise AND  &  Unordered with respect to comparison operators  
7b  Bitwise XOR  ^  Unordered with respect to comparison operators  
6b  Bitwise OR    Unordered with respect to comparison operators  
5  Logical AND  &&  Shortcircuit  
4  Logical OR    Shortcircuit  
3  Conditional operator  ?:  Rightassociative  
2  Assignment operators  = = += <<= >>= >>>= = *= %= ^= ^^= ~=  Rightassociative  
1.5  Lambda abstraction  =>  Not a real operator, occurs twice, this is binding power to the right  
1  Comma operator  ,  Not to be confused with other uses of ',', though their precedence is the same  
0  Range separator  ..  Not a real operator, hardwired into syntax at specific points 
Eiffel[edit]
Official documentation: [[3]], section 8.28.5
Priority  Operator  Description  Associativity 

13
Highest 
.

Dot notation, in qualified and nonobject calls  
12  old

Used in postconditions to denote the value an expression had before routine entry  
not

Unary negation  
+

Unary plus  


Unary minus  
All free unary operators  Custom unary aliases (See note below table)  
11  All free binary operators  Custom binary aliases (See note below table)  
10  ^

Power operator  Righttoleft 
9  *

Multiplication  Lefttoright 
/

Division  
//

Integer division  
\\

Integer remainder (modulo)  
8  +

Addition  Lefttoright 


Subtraction  
7  ..

To define an interval  
6  =

Equality (reference)  
/=

Inequality (reference)  
~

Equality (object, uses x.is_equal(y) assuming x /= Void)  
/~

Inequality (object, uses x.is_equal(y) assuming x /= Void)  
<

Less than  
>

Greater than  
<=

Less than or equal  
>=

Greater than or equal  
5  and

Conjunctive Boolean operator (strict)  Lefttoright 
and then

Conjunctive Boolean operator (semistrict — shortcircuit)  
4  or

Disjunctive Boolean operator (strict)  Lefttoright 
or else

Disjunctive Boolean operator (semistrict — shortcircuit)  
xor

Exclusive disjunctive Boolean operator  
3  implies

Implicative Boolean operator (( a implies b ) = ( not a or else b ))

Lefttoright 
2  [ ]

Manifest tuple delimiter  
1
Lowest 
;

Optional semicolon between an assertion clause and the next 
Any sequence of free operators (that does not already have a defined meaning, such as =
or ?
) can be used as an alias for unary or binary operations.
The set of free operators is:
: \ ? = ~ / ! # $ % & * +  < > @ ^ `  , ' ;
Special binary aliases such as ()
and []
can also be used.
Refer to section 8.32.21 of the aforementioned link for more details.
Erlang[edit]
Official documentation table: [[4]], see "Operator Precedence" towards the end.
F#[edit]
Fortran[edit]
Operators  Details 

Function calls  
** 
Numeric 
* , / 
Numeric 
+ ,  
Unary numeric operators 
+ ,  
Binary numeric operators 
// 
String 
FROM , TO 

.EQ. , .GE. , .GT. , .LE. , .LT. , .NE. , == , >= , > , <= , < , /= 
Relational 
.NOT. , # 
Logical 
.AND. , & 
Logical 
.OR. ,  
Logical 
.EQV. , .NEQV. 
Logical 
, 

(, ) 

Start and End of an expression 
FutureBasic[edit]
When an expression includes more than one operator, the order in which the operations are performed can affect the result. When an operator appears to the left or right of a parenthetical expression, all of the operations within the parentheses are performed first. When several operators all appear within the same matching pair of parentheses (or outside of all parentheses), the order in which their operations are performed is determined by their order of precedence, with "higher precedence" operations being performed before "lower precedence" ones. For example, consider this expression: 4 + 7 * 5 The "*" operator has a higher precedence than the "+" operator (see the table below). So, when this expression is evaluated, first 7 is multiplied by 5 to get 35; then that result is added to 4 to get the final answer of 39. The following table lists the operators in order of their precedence, from highest to lowest. When an expression contains several operators at the same level of precedence (and within the same depth of parentheses), their operations are always performed from left to right.
Precedence  Operators 

Highest  Unary operators: +, , ^, *, /, \, \\, <, <=, >, >=, =, 
==, <>, !=, <<, >>, Not, Mod, And, Or, Xor, Nand, Nor  
1  unary "+", unary "", Not 
2  ^ 
3  *, /, \, \\, Mod 
4  + (addition),  (substraction) 
5  <, <=, >, >=, =, ==, <>, !=, << (strings), >> (strings) 
6  << (shift left), >> (shift right) 
7  And, Or, Xor, Nand, Nor 
Go[edit]
Precedence  Operators 

Highest  Unary operators: +, , !, ^, *, &, < 
5  *, /, %, <<, >>, &, &^ 
4  +, , , ^ 
3  ==, !=, <, <=, >, >= 
2  && 
1   
Binary operators of the same precedence associate from left to right. Associativity has no meaning for unary operators.
Syntactic elements not in the list are not considered operators in Go; if they present ambiguity in order of evaluation, the ambiguity is resolved by other rules specific to those elements.
Icon and Unicon[edit]
Taken from http://www.cs.arizona.edu/icon/refernce/exprlist.htm#expressions (blank lines separate groups of operators with equal precedence):
(expr) # grouping {expr1;expr2;...} # compound x(expr1,expr2,...) # process argument list x{expr1,expr2,...} # process coexpression list [expr1,expr2,...] # list expr.F # field reference expr1[expr2] # subscript expr1[expr2,expr3,...] # multiple subscript expr1[expr2:expr3] # section expr1[expr2+:expr3] # section expr1[expr2:expr3] # section not expr # success/failure reversal  expr # repeated alternation ! expr # element generation * expr # size + expr # numeric value  expr # negative . expr # value (dereference) / expr # null \ expr # nonnull = expr # match and tab ? expr # random value ~ expr # cset complement @ expr # activation ^ expr # refresh expr1 \ expr2 # limitation expr1 @ expr2 # transmission expr1 ! expr2 # invocation expr1 ^ expr2 # power expr1 * expr2 # product expr1 / expr2 # quotient expr1 % expr2 # remainder expr1 ** expr2 # intersection expr1 + expr2 # sum expr1  expr2 # numeric difference expr1 ++ expr2 # union expr1  expr2 # cset or set difference expr1  expr2 # string concatenation expr1  expr2 # list concatenation expr1 < expr2 # numeric comparison expr1 <= expr2 # numeric comparison expr1 = expr2 # numeric comparison expr1 >= expr2 # numeric comparison expr1 > expr2 # numeric comparison expr1 ~= expr2 # numeric comparison expr1 << expr2 # string comparison expr1 <<= expr2 # string comparison expr1 == expr2 # string comparison expr1 >>= expr2 # string comparison expr1 >> expr2 # string comparison expr1 ~== expr2 # string comparison expr1 === expr2 # value comparison expr1 ~=== expr2 # value comparison expr1  expr2 # alternation expr1 to expr2 by expr3 # integer generation expr1 := expr2 # assignment expr1 < expr2 # reversible assignment expr1 :=: expr2 # exchange expr1 <> expr2 # reversible exchange expr1 op:= expr2 # (augmented assignments) expr1 ? expr2 # string scanning expr1 & expr2 # conjunction Low Precedence Expressions break [expr] # break from loop case expr0 of { # case selection expr1:expr2 ... [default:exprn] } create expr # coexpression creation every expr1 [do expr2] # iterate over generated values fail # failure of procedure if expr1 then exp2 [else exp3] # ifthenelse next # go to top of loop repeat expr # loop return expr # return from procedure suspend expr1 [do expr2] # suspension of procedure until expr1 [do expr2] # untilloop while expr1 [do expr2] # whileloop
Haskell[edit]
Precedence  Operator  Description  Associativity 

9
highest 
.

Function combination  Right 
8  ^,^^,**

Power  Right 
7  *,/,`quot`,`rem`,`div`,`mod`

Left  
6  +,

Left  
5  :

Append to list  Right 
4  ==,/=,<,<=,>=,>

Compareoperators  
3  &&

Logical AND  Right 
2  

Logical OR  Right 
1  >>,>>=

Left  
1  =<<

Right  
0  $,$!,`seq`

Right 
J[edit]
Precedence  Grammatical classification  Associativity 

highest  conjunctions  long left scope 
adverbs  
lowest  verbs  long right scope 
See http://www.jsoftware.com/help/dictionary/partsofspeech.htm for tokens in each grammatical class.
Note that other parts of speech do not have any precedence, because they are not "operators".
Note that this is an imprecise statement of the grammatical rules. For a complete treatment, see http://www.jsoftware.com/help/dictionary/dicte.htm
Here's an informal treatment of the grammar:
Conjunctions require a left and right argument, either of which may be a noun or a verb. If one argument is omitted the conjunction is curried with the remaining argument, forming an adverb (if the right argument is omitted, the precedence of the conjunction is treated as lower than the precedence of a verb).
Adverbs require a single left argument, which may be a noun or a verb.
Verbs require a right argument which must be a noun and may accept an optional left argument (which must also be a noun). Unless we're working with a dangling (rightmost) conjunction, verbs have lower precedence than adverbs and conjunctions. (A conjunction on the far right without a right argument is treated as having lower precedence than verbs.) That said, note that the form verb verb verb
is legal  this creates a derived verb whose arguments are given to the left and right verb and their results will be the argument for the middle verb. Longer trains are treated by using this mechanism on the rightmost three verbs. A shorter train is also given special treatment (the right verb gets the right argument, the left verb gets a left argument and the result of the right verb).
Nouns are not operators and accept no arguments.
The result of a verb must be a noun.
The result of an adverb or a conjunction can have any one of these grammatical classifications, and verb results are typical (and, thus, the result of an adverb or a conjunction may accept further arguments). Adverbs and conjunctions serve a role analogous to that of macros in other languages.
Java[edit]
This is welldocumented on the Oracle website.
jq[edit]
The order of precedence of jq operators is shown in the following table, which also shows operator associativity:
 "%right" and %left" mean respectively right and leftassociative;
 "%nonassoc" means it is a syntax error to find the operator twice in a row;
 "(none)" means that that no associativity is defined.
The associativity rules can be summarized:
 Operators with one of the characters "=", "<", or ">" in them are nonassociative;
 "," and "//" are rightassociative;
 All others are or behave as leftassociative operators.
Precedence  Operator  Associativity  Description 

lowest    %right  pipe 
,  %left  generator  
//  %right  specialized "or" for detecting empty streams  
= = += = *= /= %= //=  %nonassoc  set component  
or  %left  shortcircuit "or"  
and  %left  shortcircuit "and"  
!= == < > <= >=  %nonassoc  boolean tests  
+   %left  polymorphic plus and minus  
* / %  %left  polymorphic multiply, divide; mod  
highest  ?  (none)  postfix operator for suppressing errors (see note [1] below) 
Notes:
 If the expression immediately to the left of "?" raises an error, "?" suppresses it and emits nothings at all. E.g. 'error("bye")?' is equivalent to the expression 'empty'.
 Parentheses alter the order of evaluation in the usual way.
 Control structures such as if ... then ... else ... end and reduce ... as VAR (...; ...) determine the boundaries of subexpressions.
Kotlin[edit]
This is welldocumented on the Kotlin language website.
Lua[edit]
Table available here. That table does not contain all operators, however.
Precedence  Operator  Description 

lowest  or  Boolean OR 
and  Boolean AND  
<, <=, >, >=, ~=, ==  Comparisons  
..  Concatenation [1]  
+,   Addition and subtraction  
*, /, %  Multiplication, division, modulo  
not, , #  Boolean NOT, negation, length  
^  Exponentiation [1]  
highest  x[index], x.index, x(arguments...), x:m(arguments...)  Generic index, string index, function call, method index+call [2] 
Notes:
 Concatenation and exponentiation are rightassociative, all other binary operators are leftassociative
 Binding is done at the call site; therefore, method lookup is syntactically part of the call
Mathematica[edit]
Here is an outline:
Precedence  Class  Examples 

highest  Extensions of symbol names  x_, #2 , e::s, etc. 
Function application variants  e[e], e@@e, etc.  
Powerrelated operators  √e, e^e, etc.  
Multiplicationrelated operators  ∇e, e/e, e⊗e, e e, etc.  
Additionrelated operators  e⊕e, e+e, e⋃e, etc.  
Relational operators  e==e, e∼e, e∈e, etc.  
Arrow and vector operators  e↗e, e⇌e, etc.  
Logic operators  e&&e, e∨e, e⊢e, etc.  
Pattern and rule operators  e, e>e, e/.e, etc.  
Pure function operator  e&  
Assignment operators  e=e, e:=e, etc.  
lowest  Compound expression  e;e 
There is a table of precedence of all operators on the page tutorial/OperatorInputForms in Mathematica help.
Matlab[edit]
Here is an outline:
Precedence  Class  

highest  Parenthesis ()  
Transpose (.'), power (.^), complex conjugate transpose ('), matrix power (^)  
Unary plus (+), unary minus (), logical negation (~)  
Multiplication (.*), right division (./), left division (.\), matrix multiplication (*), matrix right division (/), matrix left division (\)  
Addition (+), subtraction ()  
Colon operator (:)  
Less than (<), less than or equal to (<=), greater than (>), greater than or equal to (>=), equal to (==), not equal to (~=)  
Elementwise AND (&)  
Elementwise OR (  )
 
Shortcircuit AND (&&)  
Lowest  Shortcircuit OR (  )

There is a table of precedence of all operators on the page [6]
Nim[edit]
Precedence  Operators  Relevant character 

9 (highest)  $ , ^
 
8  * , / , div , mod , shl , shr , %

* , % , \ , /

7  + , 


6  &

&

5  ..

.

4  == , <= , < , >= , > , != , in , notin , is , isnot , not , of

= , < , > , !

3  and


2  or , xor


1  @ , : , ?
 
0 (lowest)  assignment operator (like += , *= )

OCaml[edit]
This table contains the precedence and associativity of operators and other expression constructs in OCaml, including userdefined operators.
Oforth[edit]
Oforth uses RPN notation. There are not different operator precedences. Everything is evaluated left to right.
Pascal[edit]
This table contains the precedence and associativity of operators:
Priority  Description  Operators  Associativity 

highest  
1  unary operators  not @ 
left to right 
2  mult operators  * / div mod and shl shr as << >> 
left to right 
3  add operators  +  or xor 
left to right 
4  relations  = <> < > <= >= in is 
left to right 
lowest 
Example::
The expression ( a>n and b<n )
is equivalent to :
( ( a > (n and b) ) < n )
, so, it is invalid !
we must code:
(a>n) and (b<n)
Perl[edit]
See the relevant documentation for a table of Perl 5 operators ordered by precedence level.
Perl 6[edit]
See this table for a list of the precedence levels. Perl 6 is an operatorrich language (and users may define more operators at will), so instead of listing all the operators in the table, representative operators are listed for some of the precedence levels; see later in the same file for a more complete list of predefined operators at each precedence level.
Phix[edit]
Precedence  Operators 

highest  parenthesis/function/type calls/ternary operator 
subscripts/slices  
unary unary+ not  
* /  
+   
&  
< > <= >= = !=  
and or xor  
lowest  { , , , } 
Parenthesis is required to mix and/or/xor in an expression.
PHP[edit]
PARI/GP[edit]
Unless otherwise stated, operators at a given level are applied lefttoright.
Precedence  Operator  Description 

highest  :

Type information for gp2c . Ignored by gp.

()

Postfix function call notation.  
++ , 

Postfix increment or decrement operators. (Note that these work like the prefix ++ and  operators in C.)
 
.

Member operator (as in m.mod ).
 
' , ~ , !

Postfix derivative, transpose, and factorial; prefix negation.  
#

Prefix cardinality operator (like length() ).
 
^

Infix exponentiation operator, evaluated righttoleft.  
+ ,  (unary)

Prefix sign operators.  
* , / , % , \ , \/ , << , >>

Infix multiplication, division, modulus, integer division, rounded quotient, left shift, and right shift.  
+ , 

Infix addition and subtraction.  
< , <= , > , >= , != or <> , == , ===

Infix comparison operators. === tests whether two objects are identical componentwise and is stricter than == .
 
&& , 

Infix shortcut logical AND and OR.  
= , += , = , *= , %= , /= , \= , \/= , <<= , >>=

Infix assignment, evaluated righttoleft.  
lowest  >

Infix function definition. 
There are some exceptions to this standard order:
 If the shortcircuit operator `&&` is used and the left expression is falsy (`0`, `[]`, etc.) then the right expression is not evaluated. Similarly, with `` is the left is truthy then the right expression is not evaluated.
 Assignment and all of the compound assignment operators need an lvalue on the left; if there is an expression where the rightmost part is an lvalue, assignment happens first. So `1 + n = 4 + 1` first adds 4 to 1, then assigns 5 to n, then adds 1 to 5.
See the User's Guide to PARI/GP in the documentation, section 2.4, "GP operators".
PicoLisp[edit]
There is no need to worry about operator precedence in PicoLisp and Lisp's in general. All operators are normal functions and all of the code is organized as Sexpressions with a prefixed polish notation.
PL/I[edit]
Priority  Description  Operators  Associativity 

highest  
1  exponentiation  **  from right to left 
1  unary operators   +  from right to left 
1  logical NOT  ¬  from right to left 
2  arithmetic * /  * /  from left to right 
3  arithmetic +   +   from left to right 
4  concatenation    from left to right 
5  comparison  = ¬= > < >= <=  from left to right 
6  logical AND  &  from left to right 
7  logical OR    from left to right 
lowest 
Python[edit]
See this table and the whole page for details on Python version 3.x An excerpt of which is this table:
Precedence  Operator  Description 

lowest  lambda  Lambda expression 
if – else  Conditional expression  
or  Boolean OR  
and  Boolean AND  
not x  Boolean NOT  
in, not in, is, is not, <, <=, >, >=, !=, ==  Comparisons, including membership tests and identity tests,  
  Bitwise OR  
^  Bitwise XOR  
&  Bitwise AND  
<<, >>  Shifts  
+,   Addition and subtraction  
*, /, //, %  Multiplication, division, remainder [1]  
+x, x, ~x  Positive, negative, bitwise NOT  
**  Exponentiation [2]  
x[index], x[index:index], x(arguments...), x.attribute  Subscription, slicing, call, attribute reference  
highest  (expressions...), [expressions...], {key:datum...}, {expressions...}  Binding or tuple display, list display, dictionary display, set display 
 Footnotes
 The
%
operator is also used for string formatting; the same precedence applies.  The power operator
**
binds less tightly than an arithmetic or bitwise unary operator on its right, that is,2**1
is0.5
.
Racket[edit]
Racket uses Sexpr for its syntax, operators and functions show no precedences as all code is written as:
(function arguments ...)
function being any function or operator (language or user defined) and arguments are the arguments passed to it.
REALbasic[edit]
All operators are leftassociated except exponentiation and Pair creation which are rightassociated. Operators of the same scope and precedence will be evaluated from lefttoright. Precedence can be overridden by using parentheses, such that a + b  c <> a + (b  c).
Operator(s)  Description 

. (dot)  Object or namespace member access 
AddressOf, WeakAddressOf  Delegate creation 
IsA, Is  Compare an object reference to a class or interface name; Compare the operands to determine whether they are references to the same object 
^  Exponentiation 
  Negation and unary minus 
Not  Logical not 
* / \ Mod  Multiplication; floatingpoint division; integer division; modulo 
+,   Addition and string concatenation; subtraction 
=, <, >, <>, <=, >=  Equal (comparison and assignment); lessthan; greaterthan; not equal; lessthan or equal; greaterthan or equal 
And  Logical and bitwise And 
Or, Xor  Logical and bitwise Or; logical and bitwise ExclusiveOr 
:  Pair (e.g. linkedlist) creation 
REXX[edit]
Arguments are passed by value.
╔══════════════════════════════════════════════════════════════════════╗ ║ ║ ║ The following is a table that lists the precedence and associativity ║ ║ of all the operators in the (classic) REXX language. ║ ║ ║ ║ 1 is the highest precedence. ║ ║ ║ ╠══════════╤════════╤══════════════════════════════════════════════════╣ ║ │ │ ║ ║precedence│operator│ description ║ ║ │ │ ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 1 │  │ unary minus ║ ║ │ + │ unary plus ║ ║ │ \ │ logical not ║ ║ │ ├──(the following aren't supported by all REXXes)──╢ ║ │ ¬ │ logical not ║ ║ │ ~ │ logical not ║ ║ │ ^ │ logical not ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 2 │ ** │ exponentiation (integer power) ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 3 │ * │ multiplication ║ ║ │ / │ division ║ ║ │ % │ integer division ║ ║ │ // │ modulus (remainder division, sign of dividend)║ ║ │ / / │ modulus (any 2 or 3 character operators may ║ ║ │ │ have whitespace between characters.) ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 4 │ + │ addition ║ ║ │  │ subtraction ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 5 │  │ concatenation ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 6 │ & │ logical AND ║ ║ │  │ logical OR (inclusive OR) ║ ║ │ && │ logical XOR (exclusive OR) ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 7 │[blank] │ concatenation ║ ║ │abuttal │ concatenation ║ ╟──────────┼────────┼──────────────────────────────────────────────────╢ ║ 8 │ = │ equal to ║ ║ │ == │ exactly equal to (also, strictly equal to) ║ ║ │ \= │ not equal to ║ ║ │ <> │ not equal to (also, less than or greater than) ║ ║ │ >< │ not equal to (also, greater than or less than) ║ ║ │ > │ greater than ║ ║ │ >= │ greater than or equal to ║ ║ │ < │ less than ║ ║ │ <= │ less than or equal to ║ ║ │ >> │ exactly greater than ║ ║ │ << │ exactly less than ║ ║ │ <<= │ exactly less than or equal to ║ ║ │ >>= │ exactly greater than or equal to ║ ║ │ ├──(the following aren't supported by all REXXes)──╢ ║ │ /= │ not equal to ║ ║ │ ¬= │ not equal to ║ ║ │ ~= │ not equal to ║ ║ │ ^= │ not equal to ║ ║ │ /== │ not exactly equal to ║ ║ │ \== │ not exactly equal to ║ ║ │ ¬== │ not exactly equal to ║ ║ │ ~== │ not exactly equal to ║ ║ │ ^== │ not exactly equal to ║ ║ │ /< │ not less than ║ ║ │ ~< │ not less than ║ ║ │ ¬< │ not less than ║ ║ │ ^< │ not less than ║ ║ │ /> │ not greater than ║ ║ │ ¬> │ not greater than ║ ║ │ ~> │ not greater than ║ ║ │ ^> │ not greater than ║ ║ │ /<= │ not less than or equal to ║ ║ │ ¬<= │ not less than or equal to ║ ║ │ ~<= │ not less than or equal to ║ ║ │ ^<= │ not less than or equal to ║ ║ │ />= │ not greater than or equal to ║ ║ │ ¬>= │ not greater than or equal to ║ ║ │ ~>= │ not greater than or equal to ║ ║ │ ^>= │ not greater than or equal to ║ ║ │ \>> │ not exactly greater than ║ ║ │ ¬>> │ not exactly greater than ║ ║ │ ~>> │ not exactly greater than ║ ║ │ ^>> │ not exactly greater than ║ ║ │ \<< │ not exactly less than ║ ║ │ ¬<< │ not exactly less than ║ ║ │ ~<< │ not exactly less than ║ ║ │ ^<< │ not exactly less than ║ ╚══════════╧════════╧══════════════════════════════════════════════════╝
Ring[edit]
The next table present operators from higher precedence (Evaluated first) to lower precedence.
Operator
. [] () {}
 ~ :Literal [list items]
++  
Start:End
* / %
+ 
<< >>
&
 ^
< > <= >=
= !=
not
and or
Assignment = += = *= /= %=>>= <<= &= ^= =
Example:
See 3+5*4 # prints 23
Ruby[edit]
Ruby operators, by precedence (high to low), with arity (N), associativity (A), and definability (D)
Operator(s)  N  A  D  Operation 

! ~ +  1  R  Y  Boolean NOT, bitwise complement, unary plus 
**  2  R  Y  Exponentiation 
  1  R  Y  Unary minus (define with @) 
* / %  2  L  Y  Multiplication, division, modulo (remainder) 
+   2  L  Y  Addition (or concatenation), subtraction 
<< >>  2  L  Y  Bitwise shiftleft (or append), bitwise shiftright 
&  2  L  Y  Bitwise AND 
 ^  2  L  Y  Bitwise OR, bitwise XOR 
< <= >= >  2  L  Y  Ordering 
== === != =~ !~ <=>  2  N  Y  Equality, pattern matching, comparison 
&&  2  L  N  Boolean AND 
  2  L  N  Boolean OR 
.. ...  2  N  N  Range creation and Boolean flipflops 
? :  3  R  N  Conditional 
rescue  2  L  N  Exceptionhandling modifier 
= **= *= / = %= += = <<= >>= &&= &= ^=  2  R  N  Assignment 
defined?  1  N  N  Test variable definition and type 
not  1  R  N  Boolean NOT (low precedence) 
and or  2  L  N  Boolean AND, Boolean OR (low precedence) 
if unless while until  2  N  N  Conditional and loop modifiers 
Scilab[edit]
Priority  Description  Operators  Associativity 

highest  
1  transpose  ' 

2  power  ** ^ 
right 
3  multiplication & division  * / \ 
left 
4  unary operator (opposite)  +  
left 
5  addition & subtraction  +  
left 
6  comparison  == ~= > < >= <= 
left 
7  logical NOT  ~ 
left 
8  logical AND  and 
left 
9  logical OR  or xor 
left 
lowest 
Simula[edit]
Modern Simula syntax:
Priority  Description  Operators  Associativity 

highest  
1  power  ** 
left 
2  unary operator (opposite)  +  
left 
3  multiplication & division  * / // 
left 
4  addition & subtraction  +  
left 
5  comparison  = <> < <= > >= 
left 
6  logical NOT  NOT 
left 
7  logical AND  AND 
left 
8  logical OR  OR 
left 
9  equivalence  EQUIV 
left 
10  implication  IMPL 
left 
lowest 
Note: // is the Euclidean division
Seed7[edit]
Seed7 supports user defined operators with priority and associativity. This includes user defined operator symbols. Priority and associativity are defined with the Seed7 Structured Syntax Description (S7SSD) A S7SSD statement like
$ syntax expr: .(). + .() is > 7;
specifies the syntax of the +
operator.
The right arrow >
describes the associativity:
Binding of operands from left to right. With 7
the priority
of the +
operator is defined. The syntax pattern
.(). + .()
is introduced and delimited with dots (.
). Without dots the pattern is
() + ()
The symbol ()
is a nonterminal symbol and +
is a terminal symbol.
The S7SSD does not distinguish between different nonterminal symbols.
Instead it only knows one nonterminal symbol: ()
.
The include file syntax.s7i contains the syntax of the predefined operators. The table below is extracted from syntax.s7i:
Priority  infix/prefix  Left associative  Right associative  Not associative 

1  infix  conv varConv cast value parse  
1  prefix  {  getfunc getobj [  
2  infix  . [ ^ >  
3  prefix  &  
4  infix  !  **  
4  prefix  !  
5  prefix  +  conj  
6  infix  * / div rem mdiv mod  
7  infix  +   
8  infix  mult find  times  
9  infix  << >>  
10  infix  &  
11  infix  
12  infix  = <> < > <= >= in not in  
13  prefix  new sub  not subtype subrange set array hash  
14  infix  and  
15  infix  or  
16  infix  val radix RADIX digits sci  
17  infix  exp lpad rpad lpad0  
18  infix  <&  
20  infix  := +:= := *:= /:= <<:= >>:= &:= @:= 
Sidef[edit]
All operators in Sidef have the same precedence, which is controlled by lack of whitespace between the operands.
For example:
1+2 * 3+4 # means: (1+2) * (3+4)
See also the documentation on the precedence of operators.
Tcl[edit]
Tcl only supports operators within an expression context (such as the expr
command, which lists the operators with more detail):
Precedence  Operator  Description 

highest   + ~ !  Unary minus, unary plus, bitwise NOT, logical NOT. 
**  Exponentiation. Righttoleft associative.  
* / %  Multiply, divide, remainder.  
+   Add and subtract.  
<< >>  Left and right shift.  
< > <= >=  Boolean less, greater, less than or equal, and greater than or equal.  
== !=  Boolean equal and not equal.  
eq ne  Boolean string equal and string not equal.  
in ni  List containment and negated list containment.  
&  Bitwise AND.  
^  Bitwise exclusive OR.  
  Bitwise OR. Valid for integer operands only.  
&&  Logical AND. Evaluates its second operand lazily.  
  Logical OR. Evaluates its second operand lazily.  
lowest  x ? y : z  Ifthenelse, as in C. Evaluates its second and third operands lazily. 
TI83 BASIC[edit]
Priority  Description  Operators  Associativity 

highest  
1  function  √( e^( 10^( sin( ...  
2  unary right operator  ² !  left to right 
3  exponentiation  ^  left to right 
4  unary left operator  ()  right to left 
5  permutation combination  nPr nCr  left to right 
6  arithmetic * /  × ÷  left to right 
7  arithmetic +   +   left to right 
8  relation  = ≠ > < ≥ ≤  left to right 
9  logical AND  and  left to right 
10  logical OR  or xor  left to right 
11  conversion  ►Frac ►Dec ...  left to right 
lowest 
note: no operator between 2 symbols means an implied multiplication, so priority 6
and left to right associativity
note: NOT is not an operator, it is a function: not()
Examples:
2^2=(2^2)=4 2^3^2=(2^3)^2=64 4/2π=(4/2)π=2π=6.283185307 B/2A=((B/2)*A)=(B/2)*A
VBScript[edit]
Priority  Description  Operators  Associativity 

highest  
1  unary operator (opposite)  +  
left 
2  power  ^ 
left 
3  multiplication & division  * / 
left 
4  integer division  \ 
left 
5  modulus  mod 
left 
6  addition & subtraction  +  
left 
7  concatenation  & 
left 
8  comparison  = <> < <= > >= Is 
left 
9  logical NOT  Not 
left 
10  logical AND  And 
left 
11  logical OR  Or 
left 
12  logical exclusion  Xor 
left 
13  equivalence  Eqv 
left 
14  implication  Imp 
left 
lowest 
Let's not the difference with Visual Basic on unary operator priority.
Example:
2^2=(2)^2=4 2^3^2=(2^3)^2=64
Visual Basic[edit]
Priority  Description  Operators  Associativity 

highest  
1  power  ^ 
left 
2  unary operator (opposite)  +  
left 
3  multiplication & division  * / 
left 
4  integer division  \ 
left 
5  modulus  mod 
left 
6  addition & subtraction  +  
left 
7  concatenation  & 
left 
8  bit shift  << >> 
left 
9  comparison  = <> < <= > >= Is IsNot Like 
left 
10  logical NOT  Not 
left 
11  logical AND  And AndAlso 
left 
12  logical OR  Or OrElse 
left 
13  logical XOR  Xor 
left 
lowest 
Visual Basic .NET[edit]
See Visual Basic
Note: the Imp and Eqv VB6 operators were been removed from Visual Basic .NET.
XPL0[edit]
All operations of equal precedence are evaluated (associate) lefttoright.
Precedence  Operator  Description 

highest  () ,  Grouping, comma separator (constructs) 
 + addr @  Unary minus, unary plus, address of a variable  
<< >> >>  Left and right logical shifts, arithmetic shift right  
* /  Multiply and divide  
+   Add and subtract  
= # < <= > >=  Comparisons: equal, not equal, less than, etc.  
~ not  Bitwise NOT  
& and  Bitwise AND  
! or  xor  Bitwise OR and exclusive OR  
lowest  ifthenelse  If expression 
zkl[edit]
All operations of equal precedence are evaluated (associate) lefttoright. If shared with C it has the same precedence except for logical and/or, which have the same precedence.
Precedence  Operator  Description 

highest  () .(dot) [],  Grouping/function call, .resolve, subscripting 
 not  Unary minus, logical not  
* / %  Multiply, divide and modulo  
+   Add and subtract  
< <= > >=  Comparisons: equal, not equal, less than, etc.  
== !=  Comparisons: equal, not equal  
and or  logical AND and logical OR  
:  compose (nest expressions)  
lowest  := =  Assignment 
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