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beastaughrzach
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Fix a typo.
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content/lambda-calculus/lambda-definability/introduction.tex

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represents a function accepting two arguments $f$ and $x$, and
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returns $f^n(x)$. Church numerals are evidently in normal form.
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A represention of natural numbers in the lambda calculus is only
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A representation of natural numbers in the lambda calculus is only
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useful, of course, if we can compute with them. Computing with Church
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numerals in the lambda calculus means applying a $\lambd$-term~$F$ to
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such a Church numeral, and reducing the combined term~$F\, \num n$ to
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of the computation as being the number~$m$. We can then think of~$F$
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as defining a function $f\colon \Nat \to \Nat$, namely the function
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such that $f(n) = m$ iff $F\, \num n \red \num m$. Because of the
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Church-Rosser property, normal forms are unique if they exist. So if
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Church--Rosser property, normal forms are unique if they exist. So if
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$F\, \num n \red \num m$, there can be no other term in normal form,
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in particular no other Church numeral, that $F \, \num n$ reduces to.
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