Course pages 2018–19
Types
Principal lecturer: Dr Neel Krishnaswami
Taken by: Part II CST 50%, Part II CST 75%
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]
- Propositions as types. The Curry-Howard correspondence
between intuitionistic propositional calculus and simply-typed
lambda calculus. Inductive types and iteration. Consistency and
termination. [2 lectures]
- Polymorphic lambda calculus (PLC). PLC syntax and
reduction semantics. Examples of datatypes definable in the
polymorphic lambda calculus. Type inference. [3 lectures]
- Monads and effects. Explicit versus implicit effects. Using
monadic types to control effects. References and
polymorphism. Recursion and looping. [2 lectures]
- Continuations and classical logic. First-class continuations
and control operators. Continuations as Curry-Howard for classical logic.
Continuation-passing style. [2 lectures]
- Dependent types. Dependent function types. Indexed datatypes.
Equality types and combining proofs with programming. [2 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;
- understand how types can be used to control side-effects in
programming;
- 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.