Operator precedence

Operator precedence is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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)

The following contains tables of precedence and associativity of all the operators various languages. Operators are listed top to bottom, in descending precedence. Descending precedence refers to the priority of evaluation. Considering an expression, 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 precedence, in the given direction.

ALGOL 68

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

priority	Operation	+Algol68FR	+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

priority (Tertiary)	Algol68 "Worthy characters"	+Algol68RR	+Algol68C,G	+Algol68FR
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

priority (Tertiary)	Algol68 "Worthy characters"	+Algol68RR	+Algol68C,G	+Algol68FR
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

Again, these are technically not operators, rather they are considered "units associated with names"

priority (Quaternaries)	Algol68 "Worthy characters"	+Algol68RR	+Algol68C	+Algol68FR
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^FR indicates Algol 68 Final Report (Essentially Revision 0)
• ALGOL 68^RR 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]

C++

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

J

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.

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

This is well-documented on the Oracle website.

OCaml

This table contains the precedence and associativity of operators and other expression constructs in OCaml, including user-defined operators.

Perl 6

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, representatives operators are listed; see later in the same file for a more complete list of predefined operators at each precedence level.

PHP

Operator Precedence

Python

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.

Tcl

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.