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Fix a typo.
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beastaugh authored and rzach committed Dec 5, 2023
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4 changes: 2 additions & 2 deletions content/lambda-calculus/lambda-definability/introduction.tex
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represents a function accepting two arguments $f$ and $x$, and
returns $f^n(x)$. Church numerals are evidently in normal form.

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

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