Functional Data Structures

Dr. Mohammad Abdulaziz, Prof. Tobias Nipkow, Summer semester 2019

• Module: IN2347 SS19
• Lectures: 2 lecture hours per week, Fri 8:30-10:00 MI Hörsaal 3
• Tutorials: 2 lecture hours per week, Fri, 12:15-13:45 MI Hörsaal 2
• Start of lectures: first week (April 26). Start of tutorials: first week (April 26)
• Tutors: Mohammad Abdulaziz

The course introduces students to the design and analysis of data structures for functional programming languages. It assumes that the students are familiar with functional programming and with running time analysis of algorithms. The course covers a range of functional data structures with an emphasis on their precise analysis. Proofs of both functional correctness and complexity will be a core part of the course. Proofs are carried out with the help of a computer-based proof assistant Isabelle. An introduction to Isabelle is part of the course.

The syllabus is still evolving. There is likely to be an emphasis on search trees and priority queues.

At the end of the course students should be familiar with a number of efficient functional data structures and algorithms and should be able able to prove both functional and complexity properties about them with the theorem prover Isabelle.

On this page: News Lecture and Exercises Homework Important notice Literature

News

• The written exam
  • You will be allowed to use 1 handwritten or printed A4 sheet of paper, but nothing else.
  • A few questions may be Isabelle-specific, but the majority will deal with programs and proofs.
  • Proofs must be detailed and readable but need not conform exactly to the Isabelle syntax. Major proof steps, especially inductions, need to be stated explicitly. Minor proof steps (corresponding to by simp, by blast etc) need not be justified if you think they are obvious, but you should say which facts they follow from (e.g. IH, definition, lemma X).
  • The questions will all be formal (you need not write an essay) but will not all be proofs but also function definitions, calculations etc.
• Please bring your laptop, with Isabelle 2018 installed, to the tutorials.

Material Material will be provided via a bitbucket repository, such that you can easily keep up to date. Lectures will be recorded using the TTT tool. The recordings can be downloaded from the TTT Recordings Website (as soon as they have been processed and uploaded). Last year's recordings: here

Exercises Provided via the bitbucket repository.

Homework

Homework is the heart and soul of this course and most homework needs to be carried out with Isabelle.

• Solved homework should be uploaded to the submission system according to the following instructions.
  • Register an account in the system and send the tutor an e-mail with your username.
  • Select the competition "FDS2019" and submit your solution following the instructions on the website.
  • The system will check that your solution can be loaded in Isabelle2018 without any errors and reports how many of the main theorems you were able to prove.
  • You can upload multiple times; the last upload before the deadline is the one that will be graded.
  • If you have any problems uploading, or if the submission seems to be rejected for reasons you cannot understand, please contact the tutor.
  General hints:
  • If you cannot prove a lemma, that you need for a subsequent proof, assume this lemma by using sorry.
  • Define the functions as simply as possible. In particular, do not try to make them tail recursive by introducing extra accumulator parameters -- this will complicate the proofs!
  • All proofs should be straightforward, and take only a few lines.
• Make sure that your submission gets a "Passed" status in the system. We will not grade it otherwise!
• The latest submission date is given on each exercise sheet. Late submissions will not be graded! If you have a good excuse (such as being very sick), you should contact the tutors before the deadline.
• Discussing ideas and problems with others is encouraged. When working on homework problems, however, you need to solve and write up the actual solutions alone. If you misuse the opportunity for collaboration, we will consider this as cheating.
  Plagiarizing somebody else's homework results in failing the course immediately. This applies for both parties, that is, the one who plagiarized and the one who provided his/her solution.
• Important: all homework is graded and contributes 40% towards the final grade.

Important notice

• You must be familiar with some functional programming language like Haskell, Objective Caml, Standard ML or F# (e.g. Introduction to Informatics 2 (IN0003)).
• You must have taken a first course on data structures and algorithms (e.g. Fundamentals of Algorithms and Data Structures (IN0007)).
• You must have taken some basic course in discrete mathematics where you learned about sets, relations and proof principles like induction (e.g. Discrete Structures).
• You need not be familiar with formal logic but you must be motivated to learn how to write precise and detailed mathematical proofs that are checked for correctness by a machine, the theorem prover Isabelle.
• At the end of the course there will be a written or oral examination, depending on the number of students. Throughout the course there will be homework assignments. They will involve the use of Isabelle and will be graded. The final grade will combine the grades from the examination (60%) and the homework (40%).
• All lectures are in English.

Literature

There is currently no book that covers the material of the course. However, this is the canonical reference to functional data structures:

• Chris Okasaki. Purely Functional Data Structures. Cambridge University Press, 1999.