Written Assignment #1
=====================

Due 2/1 at 11:59pm

In either LaTeX or in a .txt file: 

1) Prove preservation and progress for STLC, making sure 
   to do a clean proof of the substitution-preserves-typing
   lemma. 

2) Extend your proof from 1) to support sums and products. 

3) Extend your proof from 1) to support references. 

Read L. Lamport's "How to Write a 21st Century Proof" if you
want guidance on writing well-structured paper proofs. 

4) Consider the following big-step operational semantics 
   of STLC: 

     ------------------------
     |         e || v       |  "e big-steps to v"
     ------------------------


     --------------------------------------- [BStep-Val]
     v || v


     e1||(\x:t. e)   e2||v2    e[x:=v2]||v
     --------------------------------------- [BStep-App]     
     (e1 e2) || v

   Prove that:

     \forall e v. e -->* v ==> e || v 

   recalling that -->* is the reflexive, transitive closure
   of the small-step --> relation for STLC that we saw 
   in class.