# Hoare Logic and Model Checking

**As discussed in the revision lecture, I upload a small note on errata in past exam questions and the exercise sheet. I will try to update this in case there are more.
**

Supervision materials and past exam information are taken from the 20/21 course.

## Revision class

Lecture |
1-up |
4-up |
Remarks |
|||

Revision class |

## Part 1: Hoare logic

### Slides

Lecture |
1-up |
4-up |
Remarks |
|||

1: Introduction to Hoare logic | ||||||

2: Examples in Hoare logic | Why3 web UI and Why3 manual | |||||

3: Formalising the semantics of Hoare logic | ||||||

4: Introduction to separation logic | John C. Reynolds. Separation Logic: A Logic for Shared Mutable Data Structures. | |||||

5: Verifying abstract data types in separation logic | Note update on slide 19 compared to handout. | |||||

6: Extending Hoare logic | Note small updates compared to handout. |

### Supervision questions (Hoare logic)

Jean Pichon Pharabod's Hoare Logic exercise sheet has a list of suggested supervision questions for the Hoare logic part of the course. Supervisors are encouraged to pick a varied subset of questions, with the aim that students are comfortable with finding and proving loop invariants for abstract data types in separation logic. Mike Gordon's exercise set contains some additional exercises.

### Past exam questions (Hoare logic)

Care should be taken when revising using past exam papers; a change of emphasis in the course content (starting 2016/17) caused new material to be added, while material that was focused on in earlier years is now only being skimmed over. Further, the current Hoare Logic and Model Checking course is a descendent of many similar courses offered by the Computer Laboratory in previous years, which often had radically different syllabuses. However, the following exam sub-components of exam questions from previous years are still relevant:

- (Hoare Logic and Model Checking) Paper 8, Question 7, 2019.
- (Hoare Logic and Model Checking) Paper 9, Question 7, 2018.
- (Hoare Logic and Model Checking) Paper 7, Question 8, 2017.
- (Hoare Logic and Model Checking) Paper 7, Question 8, 2016.
- (Hoare Logic) Part (b) and subsection (i) of Part (c); Paper 7, Question 7, 2015.
- (Hoare Logic) Paper 7, Question 7, 2013.
- (Hoare Logic) Parts (a), (b), (c), (d), (e); Paper 8, Question 8, 2013.
- (Hoare Logic) Parts (a) and (b); Paper 8, Question 8, 2012.
- (Hoare Logic) Parts (b) and (c); Paper 8, Question 2, 2011.
- (Hoare Logic) Parts (a) and (b); Paper 7, Question 6, 2011.
- (Specification and Verification I) Part (a); Paper 7, Question 14, 2010.
- (Specification and Verification I) Parts (a), (b), (d) and (e); Paper 7, Question 14, 2009.
- (Specification and Verification I) Parts (a) and (b); Paper 8, Question 16, 2008.
- (Specification and Verification I) Parts (a), (c), (e) and (i); Paper 7, Question 6, 2007.
- (Specification and Verification I) Parts (a), (b), (c), (d), (f), (g) and (h); Paper 7, Question 6, 2006.

## Part 2: Model checking

### Slides

Lecture |
1-up |
4-up |
Remarks |
|||

7: Introduction to model checking | ||||||

8: Temporal logic | Fixed typo on slide 21. | |||||

9: Temporal logic (continued) | Note minor udpates with respect to the handouts. | |||||

10: Implementing model checking | Note fixes compared to handouts. OCaml code for naive model checker wwctlmc.ml | |||||

11: Relating temporal models | Note changes compared to handouts. The last slide includes some links for model checkers. |

### Supervision questions (Model checking)

Jean Pichon Pharabod's exercise sheet is largely based on previous sheets due to Mike Gordon (link -- exercises and solution notes) and Dominic Mulligan (link) (notation differs).

### Past exam questions (Model checking)

Care should be taken when revising using past exam papers; a change of emphasis in the course content (starting 2016/17) caused new material to be added, while material that was focused on in earlier years is now only been skimmed over. Further, the current Hoare Logic and Model Checking course is a descendent of many similar courses offered by the Computer Laboratory in previous years, which often had radically different syllabuses. However, the following exam sub-components of exam questions from previous years are still relevant:

- (Hoare Logic and Model Checking) 2019 Paper 9 Question 8
- (Hoare Logic and Model Checking) 2018 Paper 7 Question 7
- (Hoare Logic and Model Checking) 2017 Paper 9 Question 13 (notation differs)
- (Hoare Logic and Model Checking) 2016 Paper 9 Question 12
- (Temporal Logic and Model Checking) 2015 Paper 8 Question 6 not part
*(e)* - (Temporal Logic and Model Checking) 2014 Paper 8 Question 8
- (Temporal Logic and Model Checking) 2012 Paper 7 Question 13
- (Temporal Logic and Model Checking) 2012 Paper 9 Question 12 (the question should say "for every reachable state s", as pointed out by an anonymous student)
- (Temporal Logic and Model Checking) 2011 Paper 7 Question 10 not part
*(c)* - (Temporal Logic and Model Checking) 2011 Paper 9 Question 11 only parts
*(b)*and*(c)*

Older questions (beware that sometimes notation differs from that in the current course):

- (Specification and Verification II) 2009 Paper 7 Question 15 not covered, but part
*(a)*is worth discussing - (Specification and Verification II) 2007 Paper 9 Question 8 only parts
*(a)*and*(c)* - (Specification and Verification II) 2006 Paper 7 Question 7 not part
*(d)*and part*(b)*only sketchily covered - (Specification and Verification II) 2005 Paper 7 Question 7 only parts
*(a)*and*(b)*(the rest of the question is `enrichment')? - (Specification and Verification II) 2003 Paper 7 Question 7 not parts
*(d)*and*(e)* - (Specification and Verification II) 2002 Paper 7 Question 2
- (Specification and Verification II) 2000 Paper 8 Question 13
- (Specification and Verification II) 1999 Paper 8 Question 13 not really part of the course as taught, but useful background on BDDs
- (Specification and Verification II) 1998 Paper 7 Question 11 not the second point