Eg. what is the difference between $(\lambda y.M)[x:=N]$ and $\lambda y.M[x:=N]$?
2026-03-26 21:07:25.1774559245
Lambda Calculus: What is the difference between a $\lambda$ term with and w/o parenthesis?
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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.