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Is there any lambda function which takes as input a lambda term $\lambda x_1x_2...x_n.f$ which is a function of $n$ variables and produces, $\lambda x_1x_2...x_n.\sim f$ . $\sim$ denotes "not". If we know the value of $n$, we can come up with the desired function easily.

Example: $n=2$. Desired function is : $\lambda px_1x_2.\sim p@x_1@x_2$ which will do this operation. $\lambda x_1x_2.f(x_1,y_1) -> \lambda x_1x_2.\sim f(x_1,y_1)$

I am looking for a for a lambda function which can do this operation and which does not change depending on the value of n.

Thanks a lot.

arindam mitra
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  • Your question doesn't have much sens, as P is itself a lambda term, so you define "not" ($\neg$) as $\neg\lambda x.y\rightarrow \lambda x.\neg y$. Many definitions follow this property, like the identity for example. – Xoff Jan 07 '15 at 05:52
  • what i tried to mean is f (or P, i just edited) does not have any more lambda inside it. – arindam mitra Jan 07 '15 at 20:21

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