Church numerals without functions
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05-11-2019 - |
Question
This is really a second part to my first question, but I felt that this was different enough from the first part that it merited its own question.
So, using Church numerals, we define
$3 = {\lambda} f. {\lambda}x.f(f(f(x)))$,
and
$4 = {\lambda} f. {\lambda}x.f(f(f(f(x))))$.
We can then add with an expression like
$3\ g\ (4\ g\ z)$
And this reduces to:
$(g (g (g (g (g (g (g\ z)))))))$.
But, of course, this is not how we would define $7$ in the scheme above. $7$ would be
${\lambda}g.{\lambda}z.(g (g (g (g (g (g (g\ z)))))))$.
Why is it still legitimate to call the application $3\ g\ (4\ g\ z)$ "7" when we can no longer perform functions with it?
No correct solution
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