Lectures on Lambda Calculus
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Lecture Notes on the Lambda Calculus Peter Selinger Department of Mathematics and Statistics Dalhousie University, Halifax, Canada Abstract This is a set of lecture notes that dev eloped out of cours es on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie Univ ersity in 2007 and 2013. To pics cove red in these notes include the un- typed lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-type d lambda calculus, the Curry- Howard isomorphism, weak and strong normalization , polymorphi sm, type inference, denota tional se- mantics, complete partial orders, and the language PCF. Contents 1 Introduction 6 1. 1 Ext en s io na l v s. inte ns iona l vi ew of func ti o ns . . . . . . . . . . . 6 1.2 The lambda calculus . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Untyped vs. typed lambda-calcu l i . . . . . . . . . . . . . . . . . 8 1.4 Lambda calculus and compu tability . . . . . . . . . . . . . . . . 9 1.5 Connections to computer science . . . . . . . . . . . . . . . . . . 10 1.6 Connections to logic . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Connections to mathematics . . . . . . . . . . . . . . . . . . . . 11 2 The untyped lambda calculus 11 2.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1
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