CS 641 lecture -*- Outline -*-

* summary and review

** what to read in the rest of the book
   part 2 gives semantics of statements, including statements as games (14)
   part 3 treats recursion and looping
   part 4 treats other tpics, including specification statements

   might want to reread chapter 1 for review

** technical ideas
   Q: what technical ideas did we discuss?
      contracts, agents, specification, correctness, refinement,
      posets, lattices,
      HOL
       Q: What did we learn about HOL?
          logic encompassing the lambda calculus
          the analogy between lattices and logic; boolean lattices, etc.
       Q: What did we learn by learning to do proofs in HOL?
     Predicates are isomorphic to sets, relations to predicates
     Properties of variables, substitution property,
          multiple assignment, parameter passing, blocks
     Relational semantics, coercion operators, relational assignment,
         different kinds of relational semantics
     Predicate transformer semantics, relational updates, duality,
     Predicate transformers are also a boolean lattice
     
** intuitions
   Q: what intuitions did we discuss?
      specifications, contracts, wide-spectrum langauges
      lattices, homomorphisms, categories
      proofs that go "over and back" (algebra)
      deductive systems,
      modeling of states
      pointwise extension, isomorphic views of predicates and sets
      blocks as a state extension, computation, retraction
      different kinds of semantics (angelic and demonic) for nondeterminism
      hierarchy of semantic domains
      inheritance of properties from codomain in function construction
      being able to work at more abstract levels of lattices in a proof

** relationships/questions
   Q: what kind of questions did we ask?
      Lattice (order) properties, category (function, composition) properties
      Relationships between expressions and semantics

** limits
   Q: what are the limits of the theory that we've studied so far?
      Doesn't deal with OO, concurrency, components, etc.