CIS 301. Captain's Log: Logical Foundations of Programming, Spring 2002.

• January 18: No lecture. Instructor away on conference.
• January 21: No lecture. University holiday.
• January 23: Introduction to course. Syllabus handed out. Why study this course? Examples of propositions.
• January 25: Homework 1 out. Syntax of propositions, atomic propositions, "compound" propositions built using propositional connectives, natural deduction, sequents; proof rules for and-introduction and elimination, double negation intoduction and elimination. Examples.
• January 28: Implication elimination (Modus Ponens), Modus Tollens, examples.
• January 30: University cancellation of classes.
• February 1: Homework 1 in. Homework 2 out. Implication introduction, temporary assumptions, disjunction introduction, examples. An example of provable equivalence.
• February 4: Disjunction elimination, examples.
• February 6: The notion of contradiction, rules for unary negation: negation introduction, negation elimination, bottom elimination; derived rules: modus tollens, double negation introduction, RAA; examples. Proof of Law of Excluded Middle (LEM).
• February 8: Graded Homework 1 and solutions handed out. Homework 2 in. Homework 3 out. Provable equivalences in propositional logic (including DeMorgan's laws). Uses of LEM in proofs. Reading pp. 1--38.
• February 11: Provable equivalences (concluded); using provable equivalences in derivation of proofs of other sequents.
• February 13: Propositional logic as a formal language; BNF of well-formed propositional formulae; tree representation of formulae. Reading pp. 38--51.
• February 15: Graded Homework 2 and solutions handed out. Homework 3 in. Semantics of formulae; soundness and completeness of propositional logic. Reading pp. 38--51. Exam 1 will take place week of March 4 2002. Lecture notes summarizing February 13 lecture handed out.
• February 18: Lecture summary for February 15 and notes for February 18 handed out; consequence of soundness and completeness; truth tables; how to prove semantic equivalence; satisfiability, validity and a theorem connecting the two; intro. to mathematical induction.
• February 20: Graded Homework 3 and solutions handed out. Notes for lecture handed out; mathematical induction, course of values induction, structural induction. Examples. DATE OF EXAM 1: FRIDAY, MARCH 8.
• February 22: Homework 4 in. Homework 5 out. Induction, continued.
• February 25: Structural induction on trees and lists.
• February 27: Exam 1 from Fall 2001. Induction concluded with example on distributivity of list append and example showing equivalence of two different definitions of factorial. SYLLABUS FOR EXAM 1: EVERYTHING COVERED TILL TODAY (February 27 2002). More precisely: pp. 1--68 in the book (omit *proofs* of soundness and completeness; however, study their statements and consequences); Section 1.5.1 (omit Definition 1.41, Lemma 1.42, pp. 74); You should be conversant with Problems 1--10 in Exercise 1.13 (pp. 75). Also study notes handed out in class. Exam will be open book, open notes, open solutions to homework assignments.
• March 1: Graded Homework 4 out; Homework 5 in. Solution to Problem 2 in Homework 5. Conjunctive normal form (CNF).
• March 4: CNF continued: Example translation of formula into CNF; Negation normal form.
• March 6: Graded Homework 5 out; Solutions to Homeworks 4 and 5 out; Discussion on exam 1; specification of function CNF. Reading till page 83.
• March 8: Exam 1. No lecture.
• March 11: Homework 6 out. Intro. to Chapter 2, Predicate logic. BNF of predicate logic formulae.
• March 13: Free and bound variables; substitution. Reading: pp. 90--109.
• March 15: Hints on Assignment 6, including lexicographic induction.
• March 18, March 20, March 22: No lectures, Spring break.
• March 25: Graded exam 1 + solutions out. Assignment 6 in. Assignment 7 out. Natural deduction rules for predicate logic. Reading: pp. 112--125.
• March 27: Examples of proofs in predicate logic.
• March 29: Assignment 7 in. Assignment 8 out. Examples of proofs, contd.
• April 1: Graded Assignment 6 and soultions out. Examples of proofs, theorem on substituting variable that doesn't occur free in a formula. SECOND EXAM on FRIDAY, APRIL 12. SYLLABUS: Normal forms, induction (mathematical induction, course of values induction and structural induction), predicate logic: pp. 69--84, 90--128, excluding pp. 110-111. Please read solutions to homework assignments also. Exam 2 from Fall 2001.
• April 3: Graded Assignment 7 and solutions out. Handout on proof of theorem covered on April 1. Proof of theorem, ended. Intro. to Chapter 4. A small imperative language, the notion of state. Representing state using a function. Operations on state: update, lookup.
• April 5: No lecture, University open house.
• April 8: Solutions to Assignment 8 out. Semantics of a simple imperative language.
• April 10: Graded Assignment 8 out. Handout: Practice problems on induction. Exam 2 review.
• April 12: No lecture, Exam 2.
• April 15: Pre- and post-conditions. Proof calculus using pre- and post- conditions. Soundness of the proof calculus.
• April 17: Graded exam 2 and solutions out. Rule of consequence; checking preconditions and postconditions using proof rules.
• April 19: Assignment 9 out, due WEDNESDAY April 24 (note non-standard due date). Examples using loop invariants; minimal-sum section. Reading pp. 216--257 (please use the Errata sheet for pp. 255.) Exam 3 will be on Friday May 3, 2002.
• April 22: Minimal-sum section worked out. Note correction in homework assignment 9: 4.1 3(a) is sufficient, you don't need to do part (b).
• April 24: Proof of minimal-sum section completed; Total correctness; example proofs: factorial and sum of elements in an array. Reading: pp. 216--260.
• April 26: Handout: The plateau problem; algorithm and correctness proof. SYLLABUS FOR EXAM 3: Chapter 4 of text + handout.
• April 29: Finishing correctness proof of the plateau problem. LAST LECTURE. Note: (1) Office hours as usual this week. (2) Assignment 10 due Tuesday April 30 by 4 PM. (3) Exam 3 on Friday. May 3. Exam 3 from Fall 2001.