Common operator notation: Difference between revisions

Revision as of 22:03, 30 January 2008

Revision as of 22:00, 2 April 2008

Line 5:

and associativities is just one way. However, it is not the most

general way: this model cannot give an operator

more precedence when competing with '-−' than it can when competing

with '+', while still giving '+' and '-−' equivalent precedences and

associativities. <!-- speculation... Can it be demonstrated that this is the only sensible way? I do not know, but any such demonstration would be

welcome. --> A generalized version of this model (in which each

Line 26:

higher precedences lower numbers. In cases in which two operators

of different precedences compete for the same operand, the operator

with the higher precedence wins. For example, '*×' has a higher

precedence than '+', so 3+4*54×5 = (3+(4*54×5)), not ((3+4)*5×5).

[[Operator position]] indicates where, in the sequence, the operator appears. In terms of operator position, an operator may be prefix, postfix, or infix. A prefix operator immediately precedes its operand, as in "-x−x". A postfix operator immediately succeeds its operand, as in "x!". An infix operator exists between its left and right operands, as in "A + B".

[[Operator associativity]], loosely speaking, describes what operators

Line 39:

or postfix operator can be either associative or non-associative.

If an operator is left-associative, the operators are applied in

left-to-right order. The arithmetic operators '+', '-−', '*×', and

'/÷', for example, are all left-associative. That is,

3+4+5-6-7 = ((((3+4)+5)-6)-7).

If an operator is right-associative, the

operators are applied in right-to-left order. In the [[Java (programming language)|Java programming language]], the assignment operator "<tt>=</tt>" is

right-associative. That is, the Java statement "<tt>a = b = c;</tt>" is

equivalent to "<tt>(a = (b = c));</tt>". It first assigns the value of c to

b, then assigns the value of b to a. An operator which is

non-associative cannot compete for operands with operators of equal

precedence. For example, in [[Prolog]], the infix operator '"<tt>:-'</tt>" is

non-associative, so constructs such as "<tt>a :- b :- c</tt>" constitute

syntax errors. There may nonetheless be a use for such

constructs as "<tt>a =|> b =|> c</tt>".

A prefix or postfix operator is associative if and only if it may

compete for operands with operators of equal precedence. The unary

prefix operators '+', '-−', and 'sin', for example, are all

associative prefix operators. The unary postfix operator '!' and,

in the [[C (programming language)|C]] language, the post-increment and post-decrement operators

"<tt>++</tt>" and "<tt>--</tt>" are examples of associative postfix operators. When

more than one associative prefix or postfix operator of equal

precedence precedes or succeeds an operand, the operators closer to

the operand associate first. For example, -sin−sin x = -−(sin(x)) and, in [[C (programming language)|C]],

the expression "<tt>x++--</tt>" is equivalent to "<tt>(x++)--</tt>". When prefix and postfix operators of equal precedence coexist,

the order of association is undefined.

Line 68:

do not necessarily have higher precedence than all infix operators.

For example, if the prefix operator 'sin' is given a precedence

between that of '+' and '*×',

sin 4*34×3+2 = ((sin(4*34×3)) + 2), not (((sin 4) *× 3) + 2) or sin(((4*34×3)+2)).

The rules for expression evaluation are simple:

Line 77:

# Among operators of equal precedence, associate operands with operators according to the associativity of the operators.

Note that an infix operator need not be binary. [[C (programming language)|C]], for example, has a ternary infix operator "<tt>[[?:]]</tt>". <!-- speculation Would

it, then, be accurate to call parenthisizationparenthesization an n-ary bifix

operation? :) -->