The type satisfies provides a mechanism for embedding arbitrary predicates in Maple's type system. It enables you to define a structured type corresponding to an arbitrary predicate without having to pollute the type namespace. This is helpful when used in conjunction with the few Maple facilities (such as the two-argument form of indets) that accept types, but not arbitrary predicates.

An expression expr is of type satisfies(P1, P2, ...) if all Pk(expr) evaluate to true, or to And, Or, Xor, Implies, Not constructions that, when converted to their corresponding boolean operators (and, or, xor, implies, not; see convert/boolean_operator), evaluate to true. Also all Pk(expr) are expected to evaluate to either true or false, or to And, Or, Xor, Implies, Not constructions with those meanings.

Type satisfies is always used as a structured type with at least one parameter. The function type(expr, 'satisfies'(P)) evaluates to true if the expression expr satisfies the predicate P. More than one predicate P1, P2, ... can be supplied, in which case the expression expr must satisfy all of the predicates P1, P2, ....

Type satisfies evaluates the Pk(expr) in the order supplied until an expression evaluates to false. Then the type(expr, 'satisfies'(P1, P2, ...) call returns false. If no predicate returns false, then the value true is returned.

Predicates are expected to return normally, without raising exceptions. You can use the ordered evaluation of the predicates to test that any preconditions for error-free evaluations are met. See Example 3.