Lecture 2: Static and Dynamic Semantics

• Small-step semantics
• Big-step semantics immediately reduces an expression to a value; small-step semantics evaluates programs one tiny step at a time.
• Small-step semantics has two kinds of rules. "Reduction" or "substantative" rules actually do something, and "compatibility" rules do bookkeeping.
• Homework 1 - prove that a derivation in the big-step rules implies a derivation in the small-step rules for the natural number addition language.
• Types: nats and bools
• "Stuckness" - undefined behavior is bad!
• Safety: if e : t and e ->* e', then either e' -> e'' or else e' value
  • Progress: if e : t then e' -> e'' or else e' value
  • Preservation: if e : t and e -> e' then e' : t