The difference between Lists as pairs and Lists as recursors in the Lambda Calculus -

I think there are several ways to represent lists in Lambda calculus. I can write a list using the pair of

(T1, (T2, (T3, NIL))

which is the length of the Lambda period \ f Is equal to I FT1 (\ FT2 (\ FT3 TIL))

and more like doing

  head = \ ll ( \ H \ Th)  

How do lists work as recursors and how do I write them?

As the recursors the list is "natural fold".

The ctors are looking like this:

  nil = \ add \ zero. Zero bracket = \ head \ tail \ Add. \ Zero.  

After some optimization (body writing, beta / eta-acting everything), the word

  cons (1, (2, opposition ( 3, zero)))  

gets equal to

  \ add \ zero As you can notice, add 2 plus (add 2 (add zeros))  

List two ctor replacers (opposition -> add, zero -> zero) waiting for Has been, and becomes a fold.

Applying a (+) and 0 will give us the amount of the list, (*) and < Code> 1 - List product, Conflict again and some tail will give us the attached tail behind the initial list.

The head session is applied such that:

  head = \ l \def  

If this list is empty and takes a default value for return and gives head.

Although tail is difficult to implement and it will work with o (list-length).

In short, the list of recursors has been prepared.