Major Section: ACL2-BUILT-INS
General Forms: (union$ l1 l2 ... lk) (union$ l1 l2 ... lk :test 'eql) ; same as above (union$ l1 l2 ... lk :test 'eq) ; same, but eq is equality test (union$ l1 l2 ... lk :test 'equal) ; same, but equal is equality test
(Union$ x y) equals a list that contains both the members of x and
the members of y. More precisely, the resulting list is the same as one
would get by first deleting the members of y from x, and then
concatenating the result to the front of y. The optional keyword,
:TEST, has no effect logically, but provides the test (default eql)
used for comparing members of the two lists.
Union$ need not take exactly two arguments: (union$) is nil,
(union$ x) is x, (union$ x y z ... :test test) is
(union$ x (union$ y z ... :test test) :test test), and if :TEST is
not supplied, then (union$ x y z ...) is (union$ x (union$ y z ...)).
For the discussion below we restrict ourselves, then, to the cases
(union$ x y) and (union$ x y :test test).
The guard for a call of union$ (in the two cases just above) depends
on the test. In all cases, both arguments must satisfy true-listp. If
the test is eql, then one of the arguments must satisfy
eqlable-listp. If the test is eq, then one of the arguments must
satisfy symbol-listp.
See equality-variants for a discussion of the relation between
union$ and its variants:
(union-eq x lst)is equivalent to(union$ x lst :test 'eq);
(union-equal x lst)is equivalent to(union$ x lst :test 'equal).
In particular, reasoning about any of these primitives reduces to reasoning
about the function union-equal.
Note that union-eq can take any number of arguments, in analogy to
union$; indeed, (union-eq ...) expands to (union$ ... :test 'eq).
However, union-equal is a function, not a macro, and takes exactly two
arguments.
Union$ is similar to the Common Lisp primitive union. However,
Common Lisp does not specify the order of elements in the result of a call of
union.
