PHP is famous for its type-juggling. I must admit it puzzles me, and I'm having a hard time to find out basic logical/fundamental things in comparisons.
For example: If $a > $b
is true and $b > $c
is true, must it mean that $a > $c
is always true too?
Following basic logic, I would say yes however I'm that puzzled I do not really trust PHP in this. Maybe someone can provide an example where this is not the case?
Also I'm wondering with the strict lesser-than and strict greater-than operators (as their meaning is described as strictly which I only knew in the past from the equality comparisons) if it makes any difference if left and right operands are swapped with strictly unequal values:
# Precondition:
if ($a === $b) {
throw new Exception(
'Both are strictly equal - can not compare strictly for greater or smaller'
);
}
($a > $b) !== ($b > $a)
For most of all type comparison combinations these greater / lesser comparison operators are not documented, so reading the manual was not really helpful in this case.
($a > $b) !== ($b < $a)
?
PHP's comparison operators deviate from the computer-scientific definitions in several ways:
In order to constitute an equivalence relation ==
has to be reflexive, symmetric and transitive:
PHP's == operator is not reflexive, i.e. $a == $a is not always true: var_dump(NAN == NAN); // bool(false) Note: The fact that any comparison involving NAN is always false is not specific to PHP. It is mandated by the IEEE 754 Standard for Floating-Point Arithmetic (more info).
PHP's == operator is symmetric, i.e. $a == $b and $b == $a are always the same.
PHP's == operator is not transitive, i.e. from $a == $b and $b == $c does not follows $a == $c: var_dump(true == "a"); // bool(true) var_dump("a" == 0); // bool(true) var_dump(true == 0); // bool(false)
In order to constitute a partial order <=
/>=
has to be reflexive, anti-symmetric and transitive:
PHP's <= operator is not reflexive, i.e. $a <= $a is not always true (Example same as for ==).
PHP's <= operator is not anti-symmetric, i.e. from $a <= $b and $b <= $a does not follow $a == $b: var_dump(NAN <= "foo"); // bool(true) var_dump("foo" <= NAN); // bool(true) var_dump(NAN == "foo"); // bool(false)
PHP's <= operator is not transitive, i.e. from $a <= $b and $b <= $c does not follow $a <= $c (Example same as for ==).
Extra: PHP's <= operator is not total, i.e. both $a <= $b and $b <= $a can be false: var_dump(new stdClass <= new DateTime); // bool(false) var_dump(new DateTime <= new stdClass); // bool(false)
In order to constitute a strict partial order <
/>
has to be irreflexive, asymmetric and transitive:
PHP's < operator is irreflexive, i.e. $a < $a is never true. Note that this is true only as of PHP 5.4. Previously INF < INF evaluated to true.
PHP's < operator is not asymmetric, i.e. from $a < $b does not follow !($b < $a) (Example same as for <= not being anti-symmetric).
PHP's < operator is not transitive, i.e. from $a < $b and $b < $c does not follow $a < $c: var_dump(-INF < 0); // bool(true) var_dump(0 < TRUE); // bool(true) var_dump(-INF < TRUE); // bool(false)
Extra: PHP's < operator is not trichotomous, i.e. all of $a < $b, $b < $a and $a == $b can be false (Example same as for <= not being total).
Extra: PHP's < operator can be circular, i.e. it is possible that $a < $b, $b < $c and $c < $a: var_dump(INF < []); // bool(true) var_dump([] < new stdClass); // bool(true) var_dump(new stdClass < INF); // bool(true) Note: The above example throws a "Object of class stdClass could not be converted to double" notice.
You can find a few nice graphs for PHP's comparison operators on PHP Sadness 52 - Comparison operators.
As a last note, I want to point out that there are two equalities that PHP does guarantee (unlike pretty much everything else). These two always hold, simply because the compiler reduces one to the other:
($a > $b) == ($b < $a)
($a >= $b) == ($b <= $a)
There are no strict identical comparison operators (>==
or <==
) in PHP (by PHP 5.6.14 at least), but there are a few ways to enforce a strict type check before checking Greater/Lower:
Check both variable types with if (gettype($a) === gettype($b)) Force your needed type-cast eg. if ((string)$a === (string)$b) Force your needed type-juggle eg. if (($a . '') === ($b . ''))
Take note that:
Floating point precision is limited
INF and NAN are of type float under ieee754
Some Infinity equals some other Infinity (since PHP 5.4)
Scientific notation e is always of type float, and never integer even if the number is small
Integers going over PHP_INT_MAX get automatically converted to float
Floats over system's boundaries get the INF value
Undefined variables are of type and value NULL
Integers preceded by 0 are converted from octal to decimal (by convention)
Converting Strings containing an integer with a leading 0 to integer strips the leading 0
List of some exotic comparisons:
Very strange: $a VS. $b $a>$b $a<$b $a<=$b $a>=$b $a==$b $a===$b float(NAN) float(-INF) false false false false false false float(NAN) float(0) false false false false false false float(NAN) float(1) false false false false false false float(NAN) float(INF) false false false false false false float(NAN) float(NAN) false false false false false false float(NAN) int(-1) false false false false false false float(NAN) int(0) false false false false false false float(NAN) int(1) false false false false false false
Equal but not identical:
$a VS. $b $a>$b $a<$b $a<=$b $a>=$b $a==$b $a===$b
NULL(NULL) array() false false true true true false NULL(NULL) bool(false) false false true true true false NULL(NULL) float(0) false false true true true false NULL(NULL) int(0) false false true true true false NULL(NULL) str('') false false true true true false array() bool(false) false false true true true false bool(false) float(0) false false true true true false bool(false) int(0) false false true true true false str('') bool(false) false false true true true false bool(false) str('0') false false true true true false float(-INF) bool(true) false false true true true false bool(true) float(1) false false true true true false float(INF) bool(true) false false true true true false float(NAN) bool(true) false false true true true false bool(true) int(-1) false false true true true false bool(true) int(1) false false true true true false bool(true) str("\0") false false true true true false bool(true) str('+') false false true true true false bool(true) str('-') false false true true true false bool(true) str('01') false false true true true false bool(true) str('1') false false true true true false bool(true) str('false') false false true true true false str('text') bool(true) false false true true true false str('true') bool(true) false false true true true false int(0) float(0) false false true true true false str("\0") float(0) false false true true true false str('') float(0) false false true true true false str('+') float(0) false false true true true false str('-') float(0) false false true true true false str('0') float(0) false false true true true false str('false') float(0) false false true true true false str('text') float(0) false false true true true false str('true') float(0) false false true true true false int(1) float(1) false false true true true false float(1) str('01') false false true true true false float(1) str('1') false false true true true false str("\0") int(0) false false true true true false str('') int(0) false false true true true false str('+') int(0) false false true true true false str('-') int(0) false false true true true false int(0) str('0') false false true true true false str('false') int(0) false false true true true false str('text') int(0) false false true true true false str('true') int(0) false false true true true false int(1) str('01') false false true true true false int(1) str('1') false false true true true false str('1') str('01') false false true true true false
Lower and Greater at the same time?
$a VS. $b $a>$b $a<$b $a<=$b $a>=$b $a==$b $a===$b float(NAN) str("\0") true true true true false false float(NAN) str('') true true true true false false float(NAN) str('+') true true true true false false float(NAN) str('-') true true true true false false float(NAN) str('0') true true true true false false float(NAN) str('01') true true true true false false float(NAN) str('1') true true true true false false float(NAN) str('false') true true true true false false float(NAN) str('text') true true true true false false float(NAN) str('true') true true true true false false
Equal AND identical:
$a VS. $b $a>$b $a<$b $a<=$b $a>=$b $a==$b $a===$b NULL(NULL) NULL(NULL) false false true true true true float(-INF) float(-INF) false false true true true true float(INF) float(INF) false false true true true true
Lower or Greater:
$a VS. $b $a>$b $a<$b $a<=$b $a>=$b $a==$b $a===$b
NULL(NULL) bool(true) false true true false false false float(-INF) NULL(NULL) true false false true false false NULL(NULL) float(1) false true true false false false float(INF) NULL(NULL) true false false true false false float(NAN) NULL(NULL) true false false true false false NULL(NULL) int(-1) false true true false false false NULL(NULL) int(1) false true true false false false NULL(NULL) str("\0") false true true false false false NULL(NULL) str('+') false true true false false false NULL(NULL) str('-') false true true false false false NULL(NULL) str('0') false true true false false false NULL(NULL) str('01') false true true false false false NULL(NULL) str('1') false true true false false false NULL(NULL) str('false') false true true false false false NULL(NULL) str('text') false true true false false false NULL(NULL) str('true') false true true false false false array() bool(true) false true true false false false float(-INF) array() false true true false false false array() float(0) true false false true false false array() float(1) true false false true false false float(INF) array() false true true false false false float(NAN) array() false true true false false false array() int(-1) true false false true false false array() int(0) true false false true false false array() int(1) true false false true false false array() str("\0") true false false true false false str('') array() false true true false false false array() str('+') true false false true false false array() str('-') true false false true false false array() str('0') true false false true false false array() str('01') true false false true false false array() str('1') true false false true false false array() str('false') true false false true false false array() str('text') true false false true false false array() str('true') true false false true false false bool(true) bool(false) true false false true false false float(-INF) bool(false) true false false true false false float(1) bool(false) true false false true false false float(INF) bool(false) true false false true false false float(NAN) bool(false) true false false true false false bool(false) int(-1) false true true false false false int(1) bool(false) true false false true false false bool(false) str("\0") false true true false false false bool(false) str('+') false true true false false false bool(false) str('-') false true true false false false bool(false) str('01') false true true false false false str('1') bool(false) true false false true false false bool(false) str('false') false true true false false false str('text') bool(false) true false false true false false str('true') bool(false) true false false true false false bool(true) float(0) true false false true false false bool(true) int(0) true false false true false false str('') bool(true) false true true false false false bool(true) str('0') true false false true false false float(-INF) float(0) false true true false false false float(-INF) float(1) false true true false false false float(INF) float(-INF) true false false true false false float(-INF) int(-1) false true true false false false float(-INF) int(0) false true true false false false float(-INF) int(1) false true true false false false float(-INF) str("\0") false true true false false false float(-INF) str('') false true true false false false float(-INF) str('+') false true true false false false float(-INF) str('-') false true true false false false float(-INF) str('0') false true true false false false float(-INF) str('01') false true true false false false float(-INF) str('1') false true true false false false float(-INF) str('false') false true true false false false float(-INF) str('text') false true true false false false float(-INF) str('true') false true true false false false float(1) float(0) true false false true false false float(INF) float(0) true false false true false false float(0) int(-1) true false false true false false int(1) float(0) true false false true false false float(0) str('01') false true true false false false str('1') float(0) true false false true false false float(INF) float(1) true false false true false false float(1) int(-1) true false false true false false float(1) int(0) true false false true false false float(1) str("\0") true false false true false false str('') float(1) false true true false false false float(1) str('+') true false false true false false float(1) str('-') true false false true false false float(1) str('0') true false false true false false float(1) str('false') true false false true false false str('text') float(1) false true true false false false str('true') float(1) false true true false false false float(INF) int(-1) true false false true false false float(INF) int(0) true false false true false false float(INF) int(1) true false false true false false float(INF) str("\0") true false false true false false float(INF) str('') true false false true false false float(INF) str('+') true false false true false false float(INF) str('-') true false false true false false float(INF) str('0') true false false true false false float(INF) str('01') true false false true false false float(INF) str('1') true false false true false false float(INF) str('false') true false false true false false float(INF) str('text') true false false true false false float(INF) str('true') true false false true false false int(0) int(-1) true false false true false false int(1) int(-1) true false false true false false str("\0") int(-1) true false false true false false str('') int(-1) true false false true false false str('+') int(-1) true false false true false false str('-') int(-1) true false false true false false str('0') int(-1) true false false true false false int(-1) str('01') false true true false false false str('1') int(-1) true false false true false false str('false') int(-1) true false false true false false str('text') int(-1) true false false true false false str('true') int(-1) true false false true false false int(1) int(0) true false false true false false int(0) str('01') false true true false false false str('1') int(0) true false false true false false int(1) str("\0") true false false true false false str('') int(1) false true true false false false int(1) str('+') true false false true false false int(1) str('-') true false false true false false int(1) str('0') true false false true false false int(1) str('false') true false false true false false str('text') int(1) false true true false false false str('true') int(1) false true true false false false str('') str("\0") false true true false false false str('+') str("\0") true false false true false false str('-') str("\0") true false false true false false str("\0") str('0') false true true false false false str("\0") str('01') false true true false false false str('1') str("\0") true false false true false false str('false') str("\0") true false false true false false str('text') str("\0") true false false true false false str('true') str("\0") true false false true false false str('') str('+') false true true false false false str('') str('-') false true true false false false str('') str('0') false true true false false false str('') str('01') false true true false false false str('') str('1') false true true false false false str('') str('false') false true true false false false str('') str('text') false true true false false false str('') str('true') false true true false false false str('-') str('+') true false false true false false str('+') str('0') false true true false false false str('+') str('01') false true true false false false str('1') str('+') true false false true false false str('false') str('+') true false false true false false str('text') str('+') true false false true false false str('true') str('+') true false false true false false str('-') str('0') false true true false false false str('-') str('01') false true true false false false str('1') str('-') true false false true false false str('false') str('-') true false false true false false str('text') str('-') true false false true false false str('true') str('-') true false false true false false str('0') str('01') false true true false false false str('1') str('0') true false false true false false str('false') str('0') true false false true false false str('text') str('0') true false false true false false str('true') str('0') true false false true false false str('false') str('01') true false false true false false str('text') str('01') true false false true false false str('true') str('01') true false false true false false str('1') str('false') false true true false false false str('text') str('1') true false false true false false str('true') str('1') true false false true false false str('text') str('false') true false false true false false str('true') str('false') true false false true false false str('true') str('text') true false false true false false
$a > $b > $c
Conundrum when: $a
is not greater than $c
.
A<C : float(NAN) > str('a') > str('') A<C : float(NAN) > str('a') > str('1') A<C : float(NAN) > str('a') > str('A') A<C : float(NAN) > str('a') > str('0') A<C : float(NAN) > str('1') > str('') A<C : float(NAN) > str('1') > str('0') A<C : float(NAN) > str('A') > str('') A<C : float(NAN) > str('A') > str('1') A<C : float(NAN) > str('A') > str('0') A<C : float(NAN) > str('0') > str('') A<C : str('') > float(NAN) > str('a') A<C : str('') > float(NAN) > str('1') A<C : str('') > float(NAN) > str('A') A<C : str('') > float(NAN) > str('0') A<C : str('a') > str('') > float(NAN) A<C : str('a') > str('1') > float(NAN) A<C : str('a') > str('A') > float(NAN) A<C : str('a') > str('0') > float(NAN) A<C : str('0') > str('') > float(NAN) A==C : bool(true) > str('') > float(NAN) A==C : bool(true) > str('') > float(-INF) A==C : bool(true) > str('') > int(-1) A==C : bool(true) > str('') > float(-1) A==C : bool(true) > array() > float(NAN) A==C : bool(true) > array() > float(INF) A==C : bool(true) > array() > float(-INF) A==C : bool(true) > array() > str('a') A==C : bool(true) > array() > int(1) A==C : bool(true) > array() > float(1) A==C : bool(true) > array() > str('1') A==C : bool(true) > array() > str('A') A==C : bool(true) > array() > int(-1) A==C : bool(true) > array() > float(-1) A==C : bool(true) > int(0) > float(-INF) A==C : bool(true) > int(0) > int(-1) A==C : bool(true) > int(0) > float(-1) A==C : bool(true) > str('0') > float(NAN) A==C : bool(true) > str('0') > float(-INF) A==C : bool(true) > str('0') > int(-1) A==C : bool(true) > str('0') > float(-1) A==C : bool(true) > float(0) > float(-INF) A==C : bool(true) > float(0) > int(-1) A==C : bool(true) > float(0) > float(-1) A==C : int(1) > str('a') > str('1') A==C : int(1) > str('A') > str('1') A==C : float(1) > str('a') > str('1') A==C : float(1) > str('A') > str('1') A==C : str('a') > str('1') > int(0) A==C : str('a') > str('1') > float(0) A==C : str('') > float(-INF) > NULL(NULL) A==C : str('') > float(-INF) > bool(false) A==C : str('') > int(-1) > NULL(NULL) A==C : str('') > int(-1) > bool(false) A==C : str('') > float(-1) > NULL(NULL) A==C : str('') > float(-1) > bool(false) A==C : array() > float(NAN) > NULL(NULL) A==C : array() > float(NAN) > bool(false) A==C : array() > float(INF) > NULL(NULL) A==C : array() > float(INF) > bool(false) A==C : array() > float(-INF) > NULL(NULL) A==C : array() > float(-INF) > bool(false) A==C : array() > str('a') > NULL(NULL) A==C : array() > str('a') > bool(false) A==C : array() > int(1) > NULL(NULL) A==C : array() > int(1) > bool(false) A==C : array() > float(1) > NULL(NULL) A==C : array() > float(1) > bool(false) A==C : array() > str('1') > NULL(NULL) A==C : array() > str('1') > bool(false) A==C : array() > str('A') > NULL(NULL) A==C : array() > str('A') > bool(false) A==C : array() > str('0') > NULL(NULL) A==C : array() > int(-1) > NULL(NULL) A==C : array() > int(-1) > bool(false) A==C : array() > float(-1) > NULL(NULL) A==C : array() > float(-1) > bool(false) A==C : str('') > float(NAN) > bool(false) A==C : str('') > float(NAN) > NULL(NULL) A==C : str('A') > str('1') > int(0) A==C : str('A') > str('1') > float(0) A==C : int(0) > float(-INF) > NULL(NULL) A==C : int(0) > float(-INF) > bool(false) A==C : int(0) > int(-1) > NULL(NULL) A==C : int(0) > int(-1) > bool(false) A==C : int(0) > float(-1) > NULL(NULL) A==C : int(0) > float(-1) > bool(false) A==C : str('0') > float(NAN) > bool(false) A==C : str('0') > float(-INF) > bool(false) A==C : str('0') > int(-1) > bool(false) A==C : str('0') > float(-1) > bool(false) A==C : float(0) > float(-INF) > NULL(NULL) A==C : float(0) > float(-INF) > bool(false) A==C : float(0) > int(-1) > NULL(NULL) A==C : float(0) > int(-1) > bool(false) A==C : float(0) > float(-1) > NULL(NULL) A==C : float(0) > float(-1) > bool(false) A===C : str('0') > float(NAN) > str('0') A===C : str('') > float(NAN) > str('') A===C : str('a') > float(NAN) > str('a') A===C : str('1') > float(NAN) > str('1') A===C : str('A') > float(NAN) > str('A')
Fun string comparison: 'Queen' >
'King' >
'Jack' >
'Ace'
Also check out PHP type comparison tables covering pairs:
isset() and is_null()
if() and empty()
boolean == vs. ===
Check the differences between PHP versions live at. http://3v4l.org/MAfDu.
if ( (string)$a===(string)$b )
but isn't this exactly the same as if ( (string)$a==(string)$b )
?
(string)1==(string)'01'
-> bool(true)
and for type-juggle (1 . '')=='01'
-> bool(true)
not exactly the same as ===
when you would get bool(false)
on both accounts
INFINITY is equal to INFINITY which is mathematically incorrect!
is a decidedly debatable statement. Also note that NaN
is by convention not greater than, less than or equal to anything in any programming language that I know of.
After your correction of the second part of your question, I leave the answer to that part to the others. I just want to give the most surprising answer to the first part of your question, i.e., whether there is an example of the <
and >
operators being intransitive. Here it is.
These are all true
:
"10" < "1a"
"1a" < "2"
"10" > "2"
If <
were transitive ($a < $b
∧ $b < $c
⇒ $a < $c
), the last line would be
"10" < "2"
but PHP tries to be kind (?!) and interpret strings as numbers whenever it can.
It turns out that, because of the above intransitivity, sort()
can sort the same elements into a different order depending on their input order, even when no two elements are ==
(and no element is NAN). I pointed this out in a comment to sort(), the essence of which is:
sort(array("10", "1a", "2" )) => array("10", "1a", "2" )
sort(array("10", "2", "1a")) => array("1a", "2", "10")
sort(array("1a", "10", "2" )) => array("2", "10", "1a")
sort(array("1a", "2", "10")) => array("1a", "2", "10")
sort(array("2", "10", "1a")) => array("2", "10", "1a")
sort(array("2", "1a", "10")) => array("10", "1a", "2" )
sort()
table, picked it as well for the practical implications when writing the related blog post The Greatest PHP Value. Thanks again for your answer.
usort
whenever possible?
usort($arr, 'strcmp')
. This works (for strings, of course), but it's best to use sort($arr, SORT_STRING)
.
Success story sharing
($a > $b) and ($b > $c)
with$a > $c
even though the documentation says those<
/>
operators say they are strict?$a == $b
is the same as(type) $a === (type) $b
. A simple example of this is that"15" == "0xf"
, but(int) "15" !== (int) "0xf"
. And both comparison and casting rules in PHP are totally crazy ^^(int)"0xf"
evaluates to integer0
, so of course0 !== 15
. Comparison in this example behaves exactly as expected. It's the casting that's confusing here. I'll admit,(INF < INF) === true
was a genuine comparison problem, but it was a special case, and it's been resolved as you pointed out. Great answer.. +1