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.