;Task:
In [[wp:Church_encoding#Church_numerals|the Church encoding of natural numbers]], the number N is encoded by a function that applies its first argument N times to its second argument.

* '''Church zero''' always returns the identity function, regardless of its first argument. In other words, the first argument is not applied to the second argument at all.
* '''Church one''' applies its first argument f just once to its second argument x, yielding '''f(x)'''
* '''Church two''' applies its first argument f twice to its second argument x, yielding '''f(f(x))'''
* and each successive Church numeral applies its first argument one additional time to its second argument, '''f(f(f(x)))''', '''f(f(f(f(x))))''' ...  The Church numeral 4, for example, returns a quadruple composition of the function supplied as its first argument.


Arithmetic operations on natural numbers can be similarly [[wp:Church_encoding#Calculation_with_Church_numerals|represented as functions on Church numerals]].

In your language define:

* Church Zero,
* a Church successor function (a function on a Church numeral which returns the next Church numeral in the series),
* functions for Addition, Multiplication and Exponentiation over Church numerals,
* a function to convert integers to corresponding Church numerals,
* and a function to convert Church numerals to corresponding integers.


You should:

* Derive Church numerals three and four in terms of Church zero and a Church successor function.
* use Church numeral arithmetic to obtain the the sum and the product of Church 3 and Church 4,
* similarly obtain 4^3 and 3^4 in terms of Church numerals, using a Church numeral exponentiation function,
* convert each result back to an integer, and return it or print it to the console.

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