- make-product-comparator comparator ...procedure
Returns a comparator which compares values satisfying the type tests of all of the given comparators by comparing them with each of the given comparators in turn, left to right, and returning the result of the first non-equal comparison. If all the given comparators consider two values equal, the product comparator also considers them equal.
The product comparator is formally defined as follows. The domain of the product comparator is the intersection of the domains of all the given comparators. The product comparator is then a comparator whose
- type test returns #t if all of the comparators’ type tests are satisfied by the given value, otherwise returning #f;
- equality predicate returns #t if the given values are equal according to the equality predicates of all the comparators, otherwise returning #f;
- ordering predicate, given two arguments a b, compares them using each of the comparators from left to right thus:
- if the current comparator’s ordering predicate returns true, the ordering predicate of the product comparator returns #t;
- if the current comparator’s equality predicate returns true, the next comparator is checked; or
- if there are no more comparators left, the ordering predicate of the product comparator returns #f;
- and whose hash function hashes together the results of applying each of the comparators’ hash functions to the given value in an implementation-defined way.
If the ordering predicate or the hash function of any of the given comparators does not exist, the corresponding procedure in the product comparator will also not exist.
If there are no comparators given, this procedure returns the comparator-one, or a new comparator with identical behaviour to it.
Note: This procedure actually creates comparators which are more general than a comparator over a product type – for example, because each comparator has its own type test, it can be used to combine a comparator for one type with that of a subtype; or if more than one comparator looks at the same component of a type. However, in most cases it is expected that this procedure will be used together with make-wrapper-comparator to create comparators over record types, i.e. product types, hence the name.