Automated Reasoning (2017-18): This course is being updated

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The lectures are given by:

The Teaching Assistant (TA) is:

Demonstrator times:

Help and Feedback

If you run into difficulties and are not making satisfactory progress then seek help. The earlier you ask for help the more likely it is that your problems can be solved without damaging your performance in the course.

Note: This is a challenging course, which introduces you to novel techniques and skills. You are expected to learn them over a short period of time.

To seek help

Various kinds of feedback are provided during the course.

Lecture Schedule

Lectures are held in Semester 1 on:

Note that there are no lecture notes for the course. Instead, recommended reading is associated with each lecture. This reading is usually from:

There will be one lecture on the coursework assignment to provide some general information and background. Note: These lectures do not necessarily coincide with the hand-out dates for the assignment sheet. Students should start work on their coursework as soon as they are handed out rather than wait for the lectures, if these come later on.

Please note: At any point of the course, the future schedule gives a strong indication of the topics to be covered. However, some details might change.

Week Date Title Recommended Reading
1 Tue 19th Sep 2017 1. Introduction Bundy, Ch. 1
[background] Formal Proof by Tom Hales.
[background] Logicomix
Fri 22nd Sep 2017 2. Propositional Logic and Natural Deduction
H&R Sec 1.1, 1.2, 1.3, start of 1.4
[background] Wadler's Propositions as Types
2 Tue 26th Sep 2017 3. Natural Deduction and Starting with Isabelle
Isabelle Theory file for Lecture 3
H&R Sec 1.2, 1.4
Sec 5.1-5.7 of Tutorial on Isabelle/HOL
Prop.thy Isabelle theory file
Fri 29th Sep 2017 4. Propositional Reasoning in Isabelle
Sec 5.1-5.7 of Tutorial on Isabelle/HOL
[background] Pollack's How to Believe a Machine-Checked Proof
[background] How do they verify a verifier of formalized proofs?
3 Tue 3rd Oct 2017 5. First-order Logic
H&R Secs 2.1-2.4
FOL.thy Isabelle theory file
[background] Logitext - an interactive L-system FOL prover
Fri 6th Oct 2017 6. Representation
Bundy Ch. 4
4 Tue 10th Oct 2017 7. Introduction to Higher Order Logic in Isabelle Sec 1.1-1.4 of Tutorial on Isabelle/HOL
N&K Sec 2.1-2.2
Fri 13th Oct 2017 8. Representation II: Locales in Isabelle/HOL
Isabelle Theory file for Lecture 8
Tutorial on Locales
[background] Interpretation of Locales in Isabelle
5 Tue 17th Oct 2017 9. Coursework: Proving and Reasoning in Isabelle/HOL See coursework files
Fri 20th Oct 2017 10. Isar — A Language for Structured Proofs
Isar Demo Theory
The Isabelle/Isar Quick Reference Manual
N&K Ch. 5
6 Tue 24th Oct 2017 11. Program Verification using Hoare Logic (TBC)
Lecture by Petros Papapanagiotou
Isabelle's Hoare Logic library
H&R Sec 4.1-4.3
N&K Sec 12.2.1
[background] Reading on Hoare Logic (especially pages 1-27, 37-48).
Fri 27th Oct 2017 12. Guest Lecture (TBC)
7 Tue 31st Oct 2017 13. Unification Bundy, Sec 17.1-17.4
Fri 3rd Nov 2017 14. Rewriting I Bundy, Ch. 9
Sec 3.1 of Tutorial on Isabelle/HOL
8 Tue 7th Nov 2017 15. Rewriting II Bundy, Ch. 9
Fri 10th Nov 2017 16. Inductive Proof (in Isabelle)
Isabelle Theory file for Lecture 6
H&R Sec 1.4.2
[background] The Automation of Mathematical Induction
9 Tue 14th Nov 2017 17. AR Assignment lecture Q&A
Fri 17th Nov 2017 18. Exam Review Past papers (Note: these also contain material not in the current course):
10 Tue 21st Nov 2017 19. TBC
Fri 24th Nov 2017 20. TBC


Each tutorial sheet will be released the week before it's due to take place. Solutions will usually be added the week after that of the tutorial.
Week Title Solutions
3 Tutorial 1: Propositional logic and some Isabelle
4 Tutorial 2: First order logic and more Isabelle
5 Tutorial 3: Representation and reasoning in Isabelle using locales
6 Tutorial 4: Structured proofs in Isabelle
7 Tutorial 5: Reasoning about Hoare Logic in Isabelle [thy]
8 Tutorial 6: Unification and Rewrite Rules [pdf]
9 Tutorial 7: Rewrite Rules and Induction [pdf]

Additional Isabelle Exercises

These are additional self-help exercises for you to familiarize yourself with theorem proving in Isabelle. Note that some of the statements that you're asked to prove may overlap with those in the tutorials.

Acknowledgement: Some of these originate from an annual Isabelle/HOL lab course taught at the Technische Universit√§t M√ľnchen.

Title Files
Propositional logic [pdf][thy]
Predicate logic [pdf][thy]
A riddle: The rich grandfather [pdf][thy]
A Bad Axiomatization [pdf][thy]


Useful Resources

Assessment and Coursework

There will be one item of assessed coursework for this course, which will count for 40% of the overall mark (the other 60% is assessed by exam).

The dates for the coursework are as follows:


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