# IMC011 Semantics and Domain Theory, Fall 2023

## Introduction

Denotational Semantics is about assigning a mathematical meaning to syntax (in particular, that of programming languages) which is, in some sense, independent of how the syntax is presented, or what computational rules it may obey (which are properly the subject matter of Operational Semantics).

Domain Theory is the mathematics of the objects, sets-with-structure, and mappings between them, which serve as a vehicle for denotational semantics.

## Material

1. Lecture Notes on Denotational Semantics by Andrew Pitts, Glynn Winskel and Marcelo Fiore, abbreviated to DENS for now. (Available via internet: PDF file)
2. Grondslagen van de Informatica 2 course notes by Erik Barendsen, August 1988, abbreviated to GI2 for now
3. Selected sections from From computation to foundations via functions and application: The lambda-calculus and its webbed models by Chantal Berline, Theoretical Computer Science 249 (2000) pp. 81-161.
4. Exercises for the exercises classes will appear on this webpage on a weekly basis.
5. Answers to the exercises will appear on brightspace on a weekly basis.

Fresh up material for those who haven't followed Semantiek and Correctness or Berekeningsmodellen or have forgotten some of that:

1. Material on operational semantics of While (called IMP by Pitts et al.) can be found in Hanne Riis Nielson en Flemming Nielson: Semantics with applications, Wiley 1999 (freely available). If you haven't done "Semantics and Correctness NWI-IBC026", read sections 1.2, 1.3, 2.1, 2.2.
2. For a recap of lambda calculus, here is a set of selected pages from Introduction to Lambda Calculus by Barendregt and Barendsen. As exercises you may try 2.5 -- 2.10. If you haven't done "Berekeningsmodellen NWI-IBC025", please study these notes.

1. Ch. 3.1 and 3.2 of Domains and Lambda Calculi by Roberto Amadio and Pierre-Louis Curien, Cambridge University Press, 1998, pp: 484
2. Ch. 13 of Formal Semantics of Programming Languages by Glynn Winskel, MIT Press, Cambridge, Massachusetts, 1993.
3. Ch. 2 and Ch. 8 until page 260 of Semantics of Programming Languages: Structures and Techniques, by Carl Gunter, MIT Press, Cambridge, Massachusetts, 1992.

## Structure

The course is divided roughly into 3 parts:

• Denotational Semantics of "While" and Domain Theory
• Operational and Denotational Semantics of PCF
• Models of the untyped lambda calculus

## Examination

There is a written exam, which is "open book", so you can take the course notes and your own notes to the exam. Apart from that there is a small assignment, see below.

## Set up

The course consists of 2 hours hoorcollege Monday, 8:30--10:15 in HG00.62, plus "self study" and a "werkcollege" (exercise class) on Tuesday, 8:30-10:15 in HFML0220.

## The course by week

The following is the preliminary weekly schedule (subject to change). See the schedule (rooster) and read the brightspace mails for the most up to date information.
Year-week Order Date Material Exercises, discussed on:
36 1 4/9 Slides and Section 1.1 of DENS exercises, 12/9
37 2 11/9 Section 1.2 of DENS and recap of Operational Semantics of "While" exercises, 19/9
38 3 18/9 Sections 2.1, 2.3, 3.1 of DENS (skip 2.2, slide 27 and 2.4) exercises, 26/9
39 No lecture
40 4 2/10 Sections 2.2, 2.4, 3.2 of DENS exercises, 10/10
41 5 9/10 Sections 3.3, 4.1, 4.2 of DENS exercises, 17/10
42 6 16/10 Sections 4.3, 5.1, 5.2, 5.3 of DENS exercises, 24/10
43 7 23/10 in HG00.071 Sections 5.4, 5.5, 5.6 of DENS + presentation of the assignment exercises, 7/11
44 No lecture, autumn break
45 8 6/11 Chapter 6 of DENS exercises, 14/11
46 9 13/11 Chapter 7 of DENS exercises, 21/11
47 10 20/11 Chapter 8 of DENS and Stable models first part exercises 1--4, 28/11
48 11 27/11 Stable models continued exercises 5--10, 5/12
49 12 4/12 Lambda calculus recap and Models of lambda calculus: the notes of Berline exercises, 12/12
(If lambda calculus is new: read the Introduction to Lambda Calculus and try ex. 2.5 -- 2.10.)
50 13 11/12 Sections 3.1, 3.2 and 3.3 of GI2 exercises, 19/12
51 14 18/12 Chapter 4 of GI2 exercises
3 15/1, 8:30-11:30 EXAM

## Written Exam

The written exam is "open book", so you can take the course notes and your own notes to the exam. Dates:

## Assignment

The deadline for the assignment is January 20. The resit deadline for the assignment is April 8.
In the assignment, you are requested to apply your knowledge on denotational semantics to a concrete programming language or programming concept (of your own choice). This should result in a short note (max 10 pages). See the assignment explanation. Your work should be sent to the teacher via mail, as a pdf file. You can do the assignment in couples; please write clearly on the title page the names and student numbers of the authors of the assignment.

herman at cs dot ru dot nl