Introduction to Lambda Calculus (1994) [143 citations — 4 self]
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author = {Henk Barendregt and Erik Barendsen},
title = {Introduction to Lambda Calculus},
year = {1994}
}
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Abstract:
ion is said to bind the free variable x in M . E.g. we say that x:yx has x as bound and y as free variable. Substitution [x := N ] is only performed in the free occurrences of x: yx(x:x)[x := N ] yN(x:x): In calculus there is a similar variable binding. In R b a f(x; y)dx the variable x is bound and y is free. It does not make sense to substitute 7 for x: R b a f(7; y)d7; but substitution for y makes sense: R b a f(x; 7)dx. For reasons of hygiene it will always be assumed that the bound variables that occur in a certain expression are dierent from the free ones. This can be fullled by renaming bound variables. E.g. x:x becomes y:y. Indeed, these expressions act the same way: (x:x)a = a = (y:y)a and in fact they denote the same intended algorithm. Therefore expressions that dier only in the names of bound variables are identied. 8 Introduction to Lambda Calculus Functions of more arguments Functions of several arguments can be obtained by iteration of applica...
