4.2.5 Relational expressions

Relational expressions (<rel_expr>s) compare two arithmetic expressions (see Arithmetic expressions) or test an arithmetic expression for a property. A relational expression can be either true or false.

coNCePTuaL supports a variety of relational expressions. The following is the language's order of operations from highest to lowest precedence:

In addition, as in most programming languages, parentheses can be used to group subexpressions.

The unary relation IS EVEN is true if a given arithmetic expression represents an even number and the unary relation IS ODD is true if a given arithmetic expression represents an odd number. For example, ‘456 IS EVEN’ is true and ‘64 MOD 6 IS ODD’ is false.

The coNCePTuaL operators ‘=’, ‘<’, ‘>’, ‘<=’, ‘>=’, and ‘<>’ represent, respectively, the mathematical relations =, <, >, <=, >=, and <> (i.e., not equal). These are all binary relations that operate on arithmetic expressions (see Arithmetic expressions). For example, ‘2+2 = 4’ is true and ‘2**3 > 2**4’ is false. The DIVIDES relation is true if the first expression evenly divides the second, i.e., that e2 = 0 (mod e1). Hence, ‘2 DIVIDES 1234’ (equivalent to ‘1234 MOD 2 = 0’ ) is true while ‘2 DIVIDES 4321’ (equivalent to ‘4321 MOD 2 = 0’ ) is false.

The ternary relation IS IN has the form ‘<expr> IS IN [<expr>, <expr>]’. The relational expression ‘x IS IN [a, b] ’ is true if x lies within the closed interval [a, b] and false otherwise. The interval bounds a and b can be specified in any order. Hence, ‘x IS IN [a, b]’ can be more precisely described as “(a <= x <= b) or (b <= x <= a)”. To provide a few examples, ‘4 IS IN [3,5] ’ and ‘4 IS IN [5,3]’ are both true; ‘5 IS IN [3,5]’ is true; however, ‘6 IS IN [3,5]’ is false. The complementary operation to IS IN is the ternary relation IS NOT IN. Hence, ‘4 IS NOT IN [3,5] ’ is false while ‘6 IS NOT IN [3,5] ’ is true.

Conjunction (“and”) and disjunction (“or”) combine multiple relational expressions. <rel_expr> ‘/\’ <rel_expr> is true if and only if both <rel_expr>s are true, and <rel_expr> ‘\/’ <rel_expr> is true if and only if either <rel_expr> is true. For example, ‘456 IS EVEN \/ 2**3 > 2**4’ is true and ‘456 IS EVEN /\ 2**3 > 2**4’ is false. Conjunction and disjunction are both short-circuiting operations. Evaluation proceeds left-to-right. Expressions such as ‘x<>0 /\ 1/x=1’ will therefore not result in a divide-by-zero error.

coNCePTuaL does not currently have a logical negation operator.

• Formal grammar for relational expressions: EBNF version of the preceding prose