Do all of the following.

1. The alphabet for all these examples is {w,x,y}
   1. 4 or more w followed by one or more of ( either ( x followed by zero or one of x ) or ( y followed by w followed by x ) ) followed by exactly 3 y's followed by exactly 1 x's
   2. all strings that do not contain the substring wwyy
   3. starts with 2 or more xwx's, ends with 6 or more yy's, and does not contain the substring xy.

2. For the next questions, use the following signature

   signature lab02 = sig
    type `a set
    create `a set
    pull `a set -> `a
    push `a * `a set -> `a set
    dup `a set -> `a set
    zilch `a set -> bool
end
   1. What is the type of
      1. dup
      2. zilch(create)
      3. pull (create)
      4. pull (dup )
      5. pull (push )
      6. push (dup (push (1, lab02.create)),lab02.create)
      7. push (zilch(create)), create)

      where the lab02.xxx notation means that a new instance of the module is used every time -- in other words, the `a are independent

   2. What is the value (if any) of
      1. push (2, push (3, create))
      2. zilch(create)