CS 641 units -*- Outline -*-

  History
	in 1990 the course focused on denotational semantics and type theory.
	in 1992, we used the book Essentials of Programming Languages,
		and worked with lambda prolog and type inference.
	in 1994 the emphasis is on axiomatic sematics

* introduction
	problems and techniques of semantics

* ML

** standard-ml
	core language, modules, large programs,static semantics of modules
	(used in 1990)
** type-reconstruction
	type system, reconstruction algorithms
	(used in 1990)


* Type Theory

** typed-lambda-calculus
	type frames, subtyping, partial homomorphisms, cccs
	(used in 1990)

** fixpoints
	fixed points and recursion (denotational semantics), full abstraction
	(used in 1990)

** subtyping-cardelli
	records, variants, and function subtyping a la Cardelli
	(at a later date, could do subtyping for higher order types)
	(used in 1990)

** higher-order-types
	implicit type systems (with recursive types, intersection types),
	explicit systems: second order types (F2, \2),
	stratified systems (F-omega, \-omega), propositions as types (\P),
	the calculus of constructions
	(used in 1990)

* Specification

** spec-overview
	the correctness problem, relation to sematics and verification,
	notion of an implementation as semantics of specification
	(used in 1990)

** equational-spec
	examples, review of equational deduction, algebras,
	free algebra, initial algebra, parameterization,
	with some emphasis on category theory.
	Institutions, specification building operations, Extended ML.
	(planned for, but not realized in 1990)

** interface-spec
	mutable types, relation to equational specifications, Larch or Specs
	(planned for, but not realized in 1990)

** refinement-of-specs
	incompleteness and sufficient completeness, refinement notions,
	Schoett's work, Extended ML's notions of refinement.
	(planned for, but not realized in 1990)

* Verification

** verification-overviews
	methods based on denotational semantics,
	pre and postconditions, the language Euclid, Hoare logics
	weakest preconditions, etc.
	(planned for, but not realized in 1990)

** axiomatic-semantics
	definition of programming languages by axioms in a logic,
	Dijkstra's language, the lambda calculus (?).
	(planned for, but not realized in 1990)

** transformational-implementation
	reasoning about functional programs, higher-order programs,
	applications to ML.
	(planned for, but not realized in 1990)

** refinement-and-verification
	overview (Liskov-Guttag style verification),
	Hoare's rep invariants and abstraction functions,
	Verification in Extended ML.
	Use of subtypes in object-oriented programs.
	(planned for, but not realized in 1990)

** recursive-function-verification
	Problems of verification with recursive functions,
	Verifications with recursive functions and subtypes!
	(planned for, but not realized in 1990)