Hello, I need to use lambda calculus as a programming language to solve this question. I have added some additional information about lists that can be useful. Thank you for any help.

Question: Show that the following term -reduces to 6 : [3,2,1] times 1

Here the numerals 1, 2 ,3 , . . . denote the -terms for the corresponding Church numerals, and timesis the term for multiplication. You may use the fact that times n m reduces to the numeral nm.

Background info that can be useful

Lists Lists can be encoded in the lambda-calculus in the following way: [N1,N2,...,Nk] c.n.c N1 (c N2 (...(c Nk n)...))

Intuitively, the variable c represents the cons operation (which adds an item to the head of the list) and the variable n represents the empty list, nil: note that the term for the empty listis []=c.n.n.