@TECHREPORT{Loader98noteson, author = {Ralph Loader}, title = {Notes on simply typed lambda calculus}, institution = {}, year = {1998} }

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Abstract

The purpose of this course is to provide an introduction to λ-calculi, specifically the simply typed lambda calculus (λ →). λ-calculi are formalisms that are useful in computer science. They are languages that express both computational and logical information. Computational information in that they can be see as functional programming languages, or more realistically, a solid core on which to build a functional language. Logical information in two ways. First, typed λ-calculi can be used directly as logics—these are ‘intuitionistic type theories ’ such as the calculus of constructions (e.g., used in the ‘Lego ’ theorem proving software developed in this department). Second, typed λ-calculi underly the term structure of higher order logics. There are many different λ-calculi—everyone working in the field has their own pet language(s)—but they generally fall into a few classes of broadly similar languages. This course does not provide a wide ranging survey, but