Lecture 2: Terms and Types

Slides : Recording

Today’s lecture introduced the first topic for the course, on types in programming languages: some of the ways they are used, and their relation to the mathematical models of lambda-calculus and type theory. Students identified a range of languages that use types, with some variation across what they are used for and how they are implemented. The lecture introduced the simply-typed lambda-calculus: its terms and types with α-conversion and β-reduction. The next lecture will start with some examples of programming language support for first-class functions.

Link: Slides for Lecture  2; Recording of Lecture 2

Homework

1. Watch This

MIT Technology Review: 35 Innovators under 35 Jean Yang Assistant Professor of Computer Science Carnegie Mellon University Links: Video (2’18”); Prof. Yang at CMU

2. Do This

• Find out what the Blub Paradox is.

• Read the article that named it

3. Read This

Read this paper and do some of the exercises.

• Achim Jung. A Short Introduction to the Lambda-Calculus.

You may find it helpful to also read pages 1–7 of Pierce’s Foundational Calculi for Programming Languages which introduces the untyped lambda-calculus.

Other Reading

The first of these is secretly about lambda-calculus terms and their execution. The second is much less colourful but is useful background reading.

Alligator Eggs! A Puzzle Game Bret Victor Links: Alligator Eggs; Animation
First-Class Function Wikipedia I think this a fair overview, leading in to issues of anonymous functions, closures, and higher-order functions in programming languages. Links: Wikipedia page now; Wikipedia page as at 2018-09-20

References

A Set of Postulates for the Foundation of Logic Alonzo Church Annals of Mathematics Series 2, 33:346–366. Princeton, 1932. The original lambda-calculus. Links: Paper at JSTOR (may require payment); Prepaid access through Edinburgh University Library (EASE login)
Types and Programming Languages Benjamin C. Pierce MIT Press, 2002 A comprehensive introduction to type systems in computer science and programming languages. Links: Author’s page; Publisher’s page; Edinburgh University Library copies
Advanced Topics in Types and Programming Languages Benjamin C. Pierce, Editor MIT Press, 2005 Builds on the previous book with chapters presenting several concrete applications of types to programming, each written by experts in the field. Links: Author’s page; Publisher’s page; Edinburgh University Library copies