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Lambda Calculus

Keywords: alpha conversion, beta reduction, terms

Categories: Knowledge Representation


Author(s): Alan Smaill

Various formal systems based on that invented by Church to formalise the properties of functions acting on arguments and being combined to form other functions. This involves `lambda-abstraction'. The function f given by:

f(x)=x+1

can be written using lambda-abstraction as:

f = λx.x+1

so that:

f(1)=(λx.x+1)(1)=2

Application is written as juxtaposition, e.g., fx for f(x) . Terms made up using application and lambda abstraction can be manipulated in various ways, e.g., rename bound variables (alpha conversion), and rewrite (λx.fx)a as fa

(beta reduction). Lambda calculus is the formalism that underlies Lisp.


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