Observational equivalence for Godel's T and System F
====================================================

* Read / internalize chapter 49 of Harper. 

* Write out the full proof of theorem 49.10, Reflexivity of Logical
  Equivalence.  (Try to do this without peeking at Harper's proof.)

* Prove rule 49.9 in section 49.4.2.

* Read chapter 51 of Harper. 

* Extend the development in chapter 51 of Harper to include a product type
  constructor with pairing and projection term constructors.  Write out the
  new cases for all [and only!] the interesting proofs.  Use your own
  judgement about what counts as interesting.

* Prove the following:

    THEOREM: Let  

        e  :  All t. t->t->t

     be an arbitrary term of the type of Church booleans.  Then either

        e =~ tru
     or
        e =~ fls

     where =~ is observational equivalence and tru and fls are the Church
     booleans (tru = /\t. \x:t. y:t. x and fls = /\t. \x:t. y:t. y).