Do all of the following.

1. The alphabet for all these examples is {y,z,a}
   1. 1 or more y followed by one or more of ( either ( z followed by zero or one of z ) or ( a followed by y followed by z ) ) followed by exactly 4 a's followed by exactly 5 z's
   2. all strings that do not contain the substring azza
   3. starts with 2 or more zyz's, ends with 1 or more aa's, and does not contain the substring za.

2. For the next questions, use the following signature

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