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### 11.3 Lists as Sets

These functions perform operations on lists which represent sets of elements.

— Function: member* item list `&key :test :test-not :key`

> This function searches list for an element matching item. If a match is found, it returns the cons cell whose `car` was the matching element. Otherwise, it returns `nil`. Elements are compared by `eql` by default; you can use the `:test`, `:test-not`, and `:key` arguments to modify this behavior. See Sequences.

> Note that this function's name is suffixed by ‘`*`’ to avoid the incompatible `member` function defined in Emacs. (That function uses `equal` for comparisons; it is equivalent to `(member*` item list `:test 'equal)`.)

The `member-if` and `member-if-not` functions analogously search for elements which satisfy a given predicate.

— Function: tailp sublist list

> This function returns `t` if sublist is a sublist of list, i.e., if sublist is `eql` to list or to any of its `cdr`s.

— Function: adjoin item list `&key :test :test-not :key`

> This function conses item onto the front of list, like `(cons` item list`)`, but only if item is not already present on the list (as determined by `member*`). If a `:key` argument is specified, it is applied to item as well as to the elements of list during the search, on the reasoning that item is “about” to become part of the list.

— Function: union list1 list2 `&key :test :test-not :key`

> This function combines two lists which represent sets of items, returning a list that represents the union of those two sets. The result list will contain all items which appear in list1 or list2, and no others. If an item appears in both list1 and list2 it will be copied only once. If an item is duplicated in list1 or list2, it is undefined whether or not that duplication will survive in the result list. The order of elements in the result list is also undefined.

— Function: nunion list1 list2 `&key :test :test-not :key`

> This is a destructive version of `union`; rather than copying, it tries to reuse the storage of the argument lists if possible.

— Function: intersection list1 list2 `&key :test :test-not :key`

> This function computes the intersection of the sets represented by list1 and list2. It returns the list of items which appear in both list1 and list2.

— Function: nintersection list1 list2 `&key :test :test-not :key`

> This is a destructive version of `intersection`. It tries to reuse storage of list1 rather than copying. It does not reuse the storage of list2.

— Function: set-difference list1 list2 `&key :test :test-not :key`

> This function computes the “set difference” of list1 and list2, i.e., the set of elements that appear in list1 but not in list2.

— Function: nset-difference list1 list2 `&key :test :test-not :key`

> This is a destructive `set-difference`, which will try to reuse list1 if possible.

— Function: set-exclusive-or list1 list2 `&key :test :test-not :key`

> This function computes the “set exclusive or” of list1 and list2, i.e., the set of elements that appear in exactly one of list1 and list2.

— Function: nset-exclusive-or list1 list2 `&key :test :test-not :key`

> This is a destructive `set-exclusive-or`, which will try to reuse list1 and list2 if possible.

— Function: subsetp list1 list2 `&key :test :test-not :key`

> This function checks whether list1 represents a subset of list2, i.e., whether every element of list1 also appears in list2.