CS 641 lecture -*- Outline -*-

* summary and review

** what to read in the rest of the book
   chapter 16-17, 19, 20-21 are the best for getting an idea of the
   second-order type systems

   might want to reread 1-6 for review

** technical ideas
   Q: what technical ideas did we discuss?
      Lambda calculus, capture, free variables, etc.
      operational semantics: big step vs. little step semantics
      type systems: rules, unique types
		    subtyping, subsumption, variance properties,
		    minimum types, subject reduction, type soundness,
		    second-order (universal, existential types)
      equational logics

** intuitions
   Q: what intuitions did we discuss?
      Objects, fields, methods, dynamic dispatch,
      inheritance: delegation, embedding, traits, classes
      the Curry-Howard isomorphism (formula as types)
      types as sets, subtyping as subset inclusion

** relationships/questions
   Q: what kind of questions did we ask?
      Church-Rosser property of an operational semantics
      The soundness of type systems (subject reduction).
      equivalence of semantics, or translations
      unique typing, minimum typing
      The soundness and completeness of equational logics.

** limits
   Q: what are the limits of the theory that we've studied so far?
      Mostly uses the embedding model,
      doesn't deal with multimethods, concurrency, components, etc.