Operator precedence

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Task
Operator precedence
You are encouraged to solve this task according to the task description, using any language you may know.
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.

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'
'LESS' 'NOT LESS'
'GREATER' 'NOT GREATER'
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 pre-defined ones may be overloaded and their priorities may be changed.

Array, Procedure, Dereference, Selection and Generator operations[edit]

priority Operation +Algol68Rev0 +Algol68G
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" +Algol68Rev0&1 +Algol68C,G +Algol68Rev0
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" +Algol68Rev0&1 +Algol68C,G +Algol68Rev0
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" +Algol68Rev0&1 +Algol68C +Algol68Rev0
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 68Rev0 indicates Algol 68 Final Report (Essentially Revision 0)
  • ALGOL 68Rev0&1 indicates Algol 68 Revised Report (Essentially Revision 1)
  • ALGOL 68C indicates Cambridge University Algol 68[1].
  • ALGOL 68G 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: gawk-Reference

 
# 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
Works with: GNU bc
 ! 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 right-associative.

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:[email protected]+? 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:? >%@2 ?x assigns 4 to x
# Accept only a number a:#*?x assigns a to x and matches 1 with #
/ Accept only a non-integer 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) Left-to-right
2 ++ Suffix increment
-- Suffix decrement
() Function call
[] Array subscripting
. Element selection by reference
-> Element selection through pointer
typeid() Run-time 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 Right-to-left
-- Prefix decrement
+ Unary plus
- Unary minus
! Logical NOT
~ Bitwise NOT
(type) Type cast
* Indirection (dereference)
& Address-of
sizeof Size-of
new, new[] Dynamic memory allocation (C++ only)
delete, delete[] Dynamic memory deallocation (C++ only)
4 .* Pointer to member (C++ only) Left-to-right
->* 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 ?:) Right-to-left
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 Left-to-right

For quick reference, see also this equivalent, color-coded 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 S-Expressions 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 thread-first macro and the thread-last 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 B-NOT Negation
B-AND Conjunction
B-XOR Exclusive disjunction
Lowest B-OR 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 S-expressions with a prefixed polish notation. In result all of the code is parenthesized and the code is evaluated from the innermost S-expression to the outermost S-expression.

D[edit]

A copy from the D wiki.

Priority Description Operators Comments
15 Template instantiation  ! Top-level ',' 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 top-level ',' in rhs expression specially and require balanced ) or ] in order to be completed
13 Power operator ^^ Right-associative
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 && Short-circuit
4 Logical OR || Short-circuit
3 Conditional operator  ?: Right-associative
2 Assignment operators = -= += <<= >>= >>>= = *= %= ^= ^^= ~= Right-associative
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 non-object 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 Right-to-left
9 * Multiplication Left-to-right
/ Division
// Integer division
\\ Integer remainder (modulo)
8 + Addition Left-to-right
- 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) Left-to-right
and then Conjunctive Boolean operator (semistrict — short-circuit)
4 or Disjunctive Boolean operator (strict) Left-to-right
or else Disjunctive Boolean operator (semistrict — short-circuit)
xor Exclusive disjunctive Boolean operator
3 implies Implicative Boolean operator (( a implies b ) = ( not a or else b )) Left-to-right
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]

MSDN documentation

Factor[edit]

Because Factor uses postfix notation and relies entirely on fixed-argument function composition, all operators have the same precedence. Think of using a calculator that uses reverse-polish notation. Instead of writing (3+5)*2, you'd write 3 5 + 2 *. There is no need for parentheses to clarify the order of operations.

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 co-expression 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                          # non-null
        = 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                     # co-expression creation
        every expr1 [do expr2]          # iterate over generated values
        fail                            # failure of procedure
        if expr1 then exp2 [else exp3]  # if-then-else
        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]          # until-loop
        while expr1 [do expr2]          # while-loop

Haskell[edit]

Precedence Operator Description Associativity
9

highest

. Function composition Right
8 ^,^^,** Power Right
7 *,/,`quot`,`rem`,`div`,`mod` Left
6 +,- Left
5 : Append to list Right
4 ==,/=,<,<=,>=,> Compare-operators
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 well-documented on the Oracle website.

JavaScript[edit]

Mozilla Developer Network have a nice list of this at JavaScript Reference:Expressions and operators:Operator Precedence

jq[edit]

The order of precedence of jq operators is shown in the following table, which also shows operator associativity:

  1. "%right" and %left" mean respectively right and left-associative;
  2. "%nonassoc" means it is a syntax error to find the operator twice in a row;
  3. "(none)" means that that no associativity is defined.

The associativity rules can be summarized:

  1. Operators with one of the characters "=", "<", or ">" in them are non-associative;
  2. "," and "//" are right-associative;
  3. All others are or behave as left-associative operators.


Precedence Operator Associativity Description
lowest |  %right pipe
,  %left generator
//  %right specialized "or" for detecting empty streams
= |= += -= *= /= %= //=  %nonassoc set component
or  %left short-circuit "or"
and  %left short-circuit "and"
 != == < > <= >=  %nonassoc boolean tests
+ -  %left polymorphic plus and minus
* / %  %left polymorphic multiply, divide; mod
highest  ? (none) post-fix operator for suppressing errors (see note [1] below)

Notes:

  1. 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'.
  2. Parentheses alter the order of evaluation in the usual way.
  3. Control structures such as if ... then ... else ... end and reduce ... as VAR (...; ...) determine the boundaries of subexpressions.

Julia[edit]

Julia Operators in Order of Preference
--------------------------------------------
Syntax 				. followed by ::
Exponentiation			^
Fractions			//
Multiplication			* / % & \
Bitshifts			<< >> >>>
Addition			+ - | ⊻
Syntax				: .. followed by |>
Comparisons			> < >= <= == === != !== <:
Control flow			&& followed by || followed by ?
Assignments			= += -= *= /= //= \= ^= ÷= %= |= &= ⊻= <<= >>= >>>=

Operator precedence can be checked within Julia with the Base.operator_precedence function:

julia> Base.operator_precedence(:>=), Base.operator_precedence(:&&), Base.operator_precedence(:(=))
(6, 4, 1)

Julia Associativity of Operators
---------------------------------------------
Assignment (=, etc.), conditional (a ? b : c), -> arrows, lazy OR/AND (&& ||), 
power operators, and unary operators are right associative. All others are 
left associative.

Kotlin[edit]

This is well-documented 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:

  1. Concatenation and exponentiation are right-associative, all other binary operators are left-associative
  2. 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.
Power-related operators e, e^e, etc.
Multiplication-related operators e, e/e, ee, e e, etc.
Addition-related operators ee, e+e, ee, etc.
Relational operators e==e, ee, ee, etc.
Arrow and vector operators ee, ee, etc.
Logic operators e&&e, ee, ee, 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 (~=)
Element-wise AND (&)
Element-wise OR ( |)
Short-circuit AND (&&)
Lowest Short-circuit 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 user-defined 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 operator-rich 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]

Operator Precedence

PARI/GP[edit]

Unless otherwise stated, operators at a given level are applied left-to-right.

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), selection operator (as in v[1]).
', ~, ! Postfix derivative, transpose, and factorial; prefix negation.
# Prefix cardinality operator (like length()).
^ Infix exponentiation operator, evaluated right-to-left.
+, - (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 component-wise and is stricter than ==.
&&, || Infix shortcut logical AND and OR.
=, +=, -=, *=, %=, /=, \=, \/=, <<=, >>= Infix assignment, evaluated right-to-left.
lowest -> Infix function definition.

There are some exceptions to this standard order:

  • If the short-circuit 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]

Translation of: Common Lisp

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 S-expressions 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
  1. The % operator is also used for string formatting; the same precedence applies.
  2. The power operator ** binds less tightly than an arithmetic or bitwise unary operator on its right, that is, 2**-1 is 0.5.

Racket[edit]

Racket uses S-expr 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 left-associated except exponentiation and Pair creation which are right-associated. Operators of the same scope and precedence will be evaluated from left-to-right. Precedence can be overridden by using parentheses, such that a + b - c <> a + (b - c).

By default, intrinsic types (Integer, String, Double, etc.) are passed by value and complex types (objects, arrays, etc.) are passed by reference. This can be overridden by using the ByVal or ByRef keyword before the parameter name in the method signature.

Operator(s) Arity Description
. (dot) 2 Scope resolution
AddressOf, WeakAddressOf 1 Delegate creation
IsA, Is 2 Compare an object reference to a class or interface name; Compare the operands to determine whether they are references to the same object
^ 2 Exponentiation
- 1 Negation and unary minus
Not 1 Logical not
* / \ Mod 2 Multiplication; floating-point division; integer division; modulo
+, - 2 Addition and string concatenation; subtraction
=, <, >, <>, <=, >= 2 Equal (comparison and assignment); less-than; greater-than; not equal; less-than or equal; greater-than or equal
And 2 Logical and bitwise And
Or, Xor 2 Logical and bitwise Or; logical and bitwise Exclusive-Or
 : 2 Pair (e.g. linked-list) 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 [email protected])
* / % 2 L Y Multiplication, division, modulo (remainder)
+ - 2 L Y Addition (or concatenation), subtraction
<< >> 2 L Y Bitwise shift-left (or append), bitwise shift-right
& 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 flip-flops
 ? : 3 R N Conditional
rescue 2 L N Exception-handling 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

Scheme[edit]

As with Common Lisp and Racket, Scheme uses s-expressions so there is no need for operator precedence.

e.g. an expression like "3 + 4 x 5" must be entered as either (+ 3 (* 4 5)) or (* (+ 3 4) 5)

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, bit-wise NOT, logical NOT.
** Exponentiation. Right-to-left 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.
& Bit-wise AND.
^ Bit-wise exclusive OR.
| Bit-wise OR. Valid for integer operands only.
&& Logical AND. Evaluates its second operand lazily.
|| Logical OR. Evaluates its second operand lazily.
lowest x ? y : z If-then-else, as in C. Evaluates its second and third operands lazily.

TI-83 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) left-to-right.

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 if-then-else If expression

zkl[edit]

All operations of equal precedence are evaluated (associate) left-to-right. 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