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Unit name 
Types and Lambda Calculus 
Unit code 
COMS30009 
Credit points 
10 
Level of study 
H/6

Teaching block(s) 
Teaching Block 1 (weeks 1  12)

Unit director 
Dr. Steven Ramsay 
Open unit status 
Not open 
Prerequisites 
COMS10003 Mathematical Methods for Computer Scientists or MATH10004 Foundations & Proof
COMS11700 Theory of Computation
COMS10006 Functional Programming
COMS22201 Language Engineering

Corequisites 
None

School/department 
Department of Computer Science 
Faculty 
Faculty of Engineering 
Description
Type systems are one of the most basic tools at the disposal of programmers in their daily work, and the underlying theory is one of the richest in computer science. This unit provides an introduction to this theory by studying its formalisation in the lambda calculus.
Intended learning outcomes
By the end of the unit students will be able to:
 Describe functions using lambda notation and calculate using the beta rule.
 Argue that lambda terms satisfying given properties do or do not exist.
 Argue that given properties of lambda terms are or are not decidable.
 Construct derivations of typing judgements to show that terms are well typed.
 Identify systems for which principal types exist and construct principal types for terms.
 Organise type systems by their expressive power and the computability of inference.
 Explain the role of lambda calculus and formal type systems as a foundation for modern programming languages.
Teaching details
20 lectures; problem classes. One dropin session per week.
Assessment Details
2hour written exam (100%)
Reading and References
There is no required reading, but the following are useful references:
 H. P. Barendregt. The Lambda Calculus, its Syntax and Semantics. College Publications, 2012.
 J. R. Hindley and J. P. Seldin. Lambda Calculus and Combinators: An Introduction. Cambridge University Press, 2008.
 B. C. Pierce. Types and Programming Languages. MIT Press, 2002.
 H. P. Barendregt, W. Dekkers and R. Statman. Lambda Calculus with Types. Cambridge University Press, 2013.