Maps.

Maps form a subclass of sets.

1. A map is a set that is either empty or whose elements are all ordered pairs. An ordered pair is a tuple whose first two components and no others are defined.

2. There are two special operators for evaluating a map at a point in its domain. Suppose that
   F
   is a map.

   1. F(EXPR)
      will evaluate to the value of the second component of the ordered pair whose first component is the value of
      EXPR
      , provided there is exactly one such ordered pair in
      F
      ; otherwise, it evaluates to
      OM
      .

   2. F{EXPR}
      will evaluate to the set of all values of second components of ordered pairs in
      F
      whose first component is the value of
      EXPR
      . If there are none such, its value is the empty set.

3. A map in which no value appears more than once as the first component of an ordered pair is called a single-valued map or smap; otherwise, the map is called a multi-valued map or mmap.