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Eg. what is the difference between $(\lambda y.M)[x:=N]$ and $\lambda y.M[x:=N]$?

topkek
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1 Answers1

2

The substitution applies to the whole expression in the first term.

The substitution only applies to M in the second term.

In this case the two are equal. If you had $(\lambda x.M)[x:=N]$ they would not be equal any longer as the substitution would end rather than recursively work inside the body of the lambda.