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Types

*Lecturer: Professor A.M. Pitts*

*No. of lectures:* 8

*Prerequisite courses: Semantics of Programming Languages, Foundations of Functional Programming*

**Aims**

The aim of this course is to show by example how type systems for
programming languages can be defined and their properties developed,
using techniques that were introduced in the Part IB course on * Semantics of Programming Languages*.

**Lectures**

**Introduction.**The role of type systems in programming languages. Formalizing type systems. [1 lecture]**ML polymorphism.**ML-style polymorphism. Principal type schemes and type inference. [2 lectures]**Polymorphic reference types.**The pitfalls of combining ML polymorphism with reference types. [1 lecture]**Polymorphic lambda calculus.**Syntax and reduction semantics. Examples of datatypes definable in the polymorphic lambda calculus. Applications. [2 lectures]**Further topics.**The Curry-Howard correspondence as a source of type systems. Dependent types. [2 lectures]

**Objectives**

At the end of the course students should

- appreciate how type systems can be used to constrain or describe the dynamic behaviour of programs
- be able to use a rule-based specification of a type system to infer typings and to establish type soundness results
- appreciate the expressive power of the polymorphic lambda calculus

**Recommended reading**

* Pierce, B.C. (2002). *Types and programming languages*. MIT Press.

Cardelli, L. (1997). Type systems. In *CRC handbook of computer science and engineering*. CRC Press.

Cardelli, L. (1987). Basic polymorphic typechecking. *Science of computer programming*, vol. 8, pp. 147-172.

Girard, J-Y. (tr. Taylor, P. & Lafont, Y.) (1989). *Proofs and types*. Cambridge University Press.

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