Course pages 2017–18
Types
Principal lecturer: Dr Neel Krishnaswami
Taken by: Part II
Past exam questions
No. of lectures: 12
suggested hours of supervisions: 3
Prerequisite courses: Computation Theory, Semantics of Programming Languages
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. The emphasis is on type systems for functional languages and their connection to constructive logic.
Lectures
- Introduction. The role of type systems in programming
languages. Review of rule-based formalisation of 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 (PLC). Explicit versus
implicitly typed languages. PLC syntax and reduction
semantics. Examples of datatypes definable in the polymorphic lambda
calculus. [3 lectures]
- Dependent types. Dependent function types. Pure type
systems. System F-omega. [2 lectures]
- Propositions as types. Example of a non-constructive
proof. The Curry-Howard correspondence between intuitionistic
second-order propositional calculus and PLC. The calculus of
Constructions. Inductive types. [3 lectures]
Objectives
At the end of the course students should
- be able to use a rule-based specification of a type system to
carry out type checking and type inference;
- understand by example the Curry-Howard correspondence between
type systems and logics;
- appreciate the expressive power of parametric polymorphism and
dependent types.
Recommended reading
* Pierce, B.C. (2002). Types and programming languages. MIT
Press.
Pierce, B. C. (Ed.) (2005). Advanced Topics in Types and
Programming Languages. MIT Press.
Girard, J-Y. (tr. Taylor, P. & Lafont, Y.) (1989). Proofs and
types. Cambridge University Press.