Conditions in the OPM Query Language are used to restrict the possible instantiations of variables in a SELECT, DELETE or UPDATE query. Conditions are formed using conjunctions and disjunctions of various atomic comparisons of expressions.
<conditions> ::= <atomic condition>
| ( <conditions> )
| <conditions> AND <conditions>
| <conditions> OR <conditions>
;
<atomic condition> ::= <expression> <is null op>
| <expression> <bin op> <expression>
| <expression> <comp op> ALL <variable>
| <expression> <match op> <string>
;
<is null op> ::= IS NULL
| IS NOT NULL
;
<bin op> ::= <comp op>
| <in op>
| <contains op>
;
<comp op> ::= '=' | '!=' | '>' | '>=' | '<' | '<='
;
<contains op> ::= CONTAINS | NOT CONTAINS
;
<in op> ::= IN | NOT IN
;
<match op> ::= MATCH | NOT MATCH
;
An atomic condition is said to be satisfied by a particular instantiation of variables if, for that instantiation of variables, the values of the expressions involved in the condition make the condition true. More precisely:
,
while e IS NOT NULL is satisfied if the value of e is not
equal to Null ;
, where
is one of =, !=, <, >,
<= or >=, is satisfied if the values associated with 
and 
are both not equal to Null , and the binary relationship
associated with 
holds between 
and 
. (e.g.,
= 
is satisfied if the values of 
and 
are equal and not equal to Null , while 
!= 
is
satisfied if the values associated with 
and 
are not equal,
and neither value is equal to Null .)
ALL v, where e is an expression and v
a variable, is satisfied by a particular instantiation iff for any
valid variable instantiation which is equal to the current instantiation on all
variables other than v (and possibly on v as well), the condition
is satisfied;
CONTAINS 
is satisfied iff the value
of 
is a set and the value of 
occurs in 
.
NOT CONTAINS 
is satisfied if the value of 
is a set,
the value of 
is not equal to Null , and the value of 
does not occur
in the value of 
;
IN 
is satisfied iff the value
of 
is a set and the value of 
occurs in 
.
NOT IN 
is satisfied if the value of 
is a set,
the value of 
is not equal to Null , and the value of 
does not occur
in the value of 
;
MATCH 
is satisfied if the values of
and 
are strings, and the value of 
, treated as a regular expression matches the value of 
.
NOT MATCH 
is satisfied if the values of 
and 
are strings, and the value of 
does not match the value of 
.
For example suppose we have a variable instantiation which is valid for the FROM statement
FROM X IN PERSON, Y IN X.owns[FRAGMENT]Then the condition
Y IS NULL would be satisfied iff the owns
attribute of X is the empty set.
Note: this semantics of comparison operators with respect to Nulls appears to be reasonable and necessary because of the use of Null to represent empty set-valued attributes. For example, if we wished to ask a query ``what are the names of people who own a Fragment owned by John'', we could write
SELECT X.name
FROM X IN PERSON, J IN PERSON,
XF IN X.owns[FRAGMENT], JF IN J.owns[FRAGMENT]
WHERE J.name = "John"
AND XF = JF
;
If we made the condition XF = JF true when both XF and
JF were equal to Null , and if the owns attribute of John
was the empty set, then this query would return the names of any
People that do not own any Fragments.