CSE 360 Homework 2

1. Below is a fragment of a module that you should use to start this problem.

   module hw2p1.
   import lists.
   
   type one_element           list A -> o.
   type two_or_more_elements  list A -> o.
   type three_elements        list A -> o.
   type palindrome            list A -> o.
   type common_sub_seq        list A -> list A -> list A -> o.
   type sub_seq               list A -> list A -> o.
   type example               int -> list int -> o.
   
   
      Place code for these predicates here.  If you need to add
      other predicates and type declarations, please do.  Use
      This module fragment as a guide only.
   
   
   example 0 nil.
   example 1 (1::nil).
   example 2 (1::3::nil).
   example 3 (1::3::1::nil).
   example 4 (1::3::5::8::nil).
   example 5 (2::3::1::4::5::6::7::2::3::nil).
   example 6 (2::3::6::5::5::6::5::2::3::4::5::6::nil).
   example 7 (2::3::6::5::5::6::6::5::5::6::3::2::nil).
   

   You should be able to have a session with Elp similar to this one.
2. Below is a fragment of a module that you should use to start this problem.

   module hw2p2.
   
   kind nat     type.
   type z       nat.
   type s       nat -> nat.
   
   type even    nat -> o.
   type odd     nat -> o.
   type half    nat -> nat -> o.
   type mod3    nat -> nat -> o.
   
        
      Place code for these predicates here.  If you need to add
      other predicates and type declarations, please do.  Use
      This module fragment as a guide only.
   
   type number   string -> nat -> o.
   
   number "zero" z.
   number "one"  (s z).
   number "two" (s (s z)).
   number "three" (s (s (s z))).
   number "four"  (s (s (s (s z)))).
   number "five"  (s (s (s (s (s z))))).
   

   You should be able to have a session with Elp similar to this one.