&&, _lazy_and

“short circuit and” of Boolean expressions

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b1 && b2 && …
_lazy_and(b1, b2, …)


b1 && b2 && ... evaluates the Boolean expression b1 and b2 and ... by “short circuit evaluation”.

b1 && b2 && ... produces the same result as bool(b1 and b2 and ...), provided the latter call does not throw an error. The difference between these calls is as follows. The call bool(b1 and b2 and ...) evaluates all Boolean expressions before combining them logically via and.

_lazy_and(b1, b2, ...) is equal to b1 && b2 && ....

Note that the result is FALSE if one of b1, b2, and so on evaluates to FALSE. “short circuit evaluation” is based on this fact: b1 && b2 && ... evaluates the arguments from left to right. The evaluation stops immediately if one argument evaluates to FALSE. In this case, _lazy_and returns FALSE without evaluating the remaining Boolean expressions. If none of the expressions b1, b2, and so on evaluates to FALSE, then all arguments are evaluated and the corresponding result (TRUE or UNKNOWN) is returned.

_lazy_and is also called “conditional and”.

If any of the considered Boolean expressions b1, b2, and so on cannot be evaluated to TRUE, FALSE, or UNKNOWN, then _lazy_and throws an error.

_lazy_and is used internally by the if, repeat, and while statements. For example, the statement if b1 and b2 then ... is equivalent to if b1 && b2 then ....

_lazy_and() returns TRUE.


Example 1

This example show the difference between short circuit and complete evaluation of Boolean conditions. For x = 0, the evaluation of leads to an error:

x := 0:
bool(x <> 0 and sin(1/x) = 0)
Error: Division by zero. [_invert]

With “short circuit evaluation”, the expression is not evaluated. This avoids the previous error:

x <> 0 && sin(1/x) = 0

delete x

Example 2

The following statements do no lead to an error because if uses short circuit evaluation internally:

for x in [0, PI, 1/PI] do
  if x <> 0 and sin(1/x) = 0 then

delete x

Example 3

_lazy_and can be called without parameters:



b1, b2, …

Boolean expressions

Return Values


Overloaded By

b1, b2

See Also

MuPAD Functions