CMSC 654,  Program Verification


Instructor: 	Howard E. Motteler
Office: 	TF 111
Phone: 		455-2590
Office hours: 	before class


Text: 	David A. Schmidt, Denotational Semantics

In addition, lecture notes will be provided, including a review of
mathematical logic, material on the lambda calculus, and a chapter on
axiomatic semantics, by John Gannon, of UMCP.  Copies of recommended
outside readings will be placed on reserve in the library.


			Course Outline

Introduction							1 week

	Topics in Program Verification
	Review of Mathematical Logic

Axiomatic Semantics						3-4 weeks

	Hoare's Axiomatic Method
	Proofs of partial and total correctness
	Dijkstra's Method of Weakest Preconditions
	Program derivation and logic programming

Denotational Semantics  					11-12 weeks

	Review: syntax, sets, functions and domains
	Functions as "first class" objects
	Lambda Calculus and Combinators
	Church-Rosser Theorem
	Syntactic fixpoint operators
	Models of the lambda and combinator calculus.
	Domain Theory, recursive definitions and fixed point operators
	Denotational definitions and imperative languages
	(This section will cover material from the Schmidt text, 
	 lecture notes, and Ch. 5 of Stoy's text.)


Grading:  2 midterms, each worth 100 points, a 150 point final, and
50 points of homework.  The homework may include some simple
programming  exercises.  85% of the total points gets you an "A",
65% a "B", etc.


Related Readings

C.A.R. Hoare, "An Axiomatic Basis for Computer Programming," 
CACM, vol. 12, pp. 576-580.

  The "origional" paper on axiomatic sematics.

C.A.R. Hoare, "Communicating Sequential Processes,"  CACM, Aug. 1978,
vol. 21, no. 8, pp. 666-677.

  Some of the ideas presented here may be covered, as time permits.
  The transputer programming environment is a implementation of
  some of Hoare's ideas.

J.E. Stoy, Denotational Semantics: The Scott-Strachey Approach to
Programming Language theory,  MIT Press, Cambridge Mass., 1977.

  Chapter 5 is a very readable introduction to the lambda calculus,
  and contains a number of useful exercises.

Hindley and Seldin, Introduction to Combinators and the
lambda-calculus, Cambridge Press, 1986.

  An up to date and comprehensive survey of the theory of
  combinators and the lambda-calculus.  This covers the
  theoretical side of denotational semantics, while the Schmidt
  text covers the (relatively) applied aspects.