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Notes on Simply Typed Lambda Calculus \Lambda Ralph Loader y

Summary: Notes on Simply Typed Lambda Calculus \Lambda
Ralph Loader y
February, 1998
The purpose of this course is to provide an introduction to –­calculi,
specifically the simply typed lambda calculus (– ! ).
–­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 pro­
gramming languages, or more realistically, a solid core on which to build a
functional language.
Logical information in two ways. First, typed –­calculi can be used dir­
ectly 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 –­calculi underly the term structure of
higher order logics.
There are many different –­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
instead aims to explain a good range of theoretical techniques, most of which
are applicable to a much wider range of languages than we will actually study.


Source: Aczel, Peter - Departments of Mathematics & Computer Science, University of Manchester


Collections: Mathematics