2.17 Implicit quantification

The rule for implicit quantification in Mercury is not the same as the usual one in mathematical logic. In Mercury, variables that do not occur in the head of a clause are implicitly existentially quantified around their closest enclosing scope (in a sense to be made precise in the following paragraphs). This allows most existential quantifiers to be omitted, and leads to more concise code.

An occurrence of a variable is in a negated context if it is in a negation, in a universal quantification, in the condition of an if-then-else, in an inequality, or in a lambda expression.

Two goals are parallel if they are different disjuncts of the same disjunction, or if one is the “else” part of an if-then-else and the other goal is either the “then” part or the condition of the if-then-else, or if they are the goals of disjoint (distinct and non-overlapping) lambda expressions.

If a variable occurs in a negated context and does not occur outside of that negated context other than in parallel goals (and in the case of a variable in the condition of an if-then-else, other than in the “then” part of the if-then-else), then that variable is implicitly existentially quantified inside the negation.