Lecture 2: Terms and Types

Title slideFriday’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. This lecture presented the simply-typed lambda-calculus and some examples of programming language support for first-class functions.

Link: Slides for Lecture 2

Homework

Read this paper and do some of the exercises.

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

Other Reading

Colourful alligators with colourful eggs Alligator Eggs!
A Puzzle Game
Bret Victor

Links: Alligator Eggs; Animation

Screenshot of web page 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 2016-09-23

References

church-paper 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 (paywall); Prepaid access through Edinburgh University Library

Pierce: Types and Programming Languages 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
Pierce: Advanced Topics in Types and Programming Languages Advanced Topics in Types and Programming Languages
Benjamin C. Pierce, Editor
Builds on the previous book with chapters presenting several concrete applications of types to programming, each by experts in the field.
Links: Author’s page; Publisher’s page; Edinburgh University Library copies
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