; converts a Church numeral into an ordinary numeral 
(defn uh [f] ((f (fn [x] (+ x 1))) 0))
; returns the successor of a Church numeral
(defn sr [n] (fn [f] (fn [x] (f ((n f) x)))))
; adds two Church numerals
(defn ps [m n] ((n sr) m))
; raises one Church numeral to the power of another
(defn ep [m n] (n m))
; zero as a Church numeral
(defn zo [f] (fn [x] x))
; one as a Church numeral
(defn oe [f] (fn [x] (f x)))
; returns the predecessor of a Church numeral
(defn pd [n] (fn [f] (fn [x] (((n (fn [g] (fn [h] (h (g f))))) (fn [y] x)) (fn [z] z)))))
; returns the difference of two Church numerals
(defn st [m n] ((m pd) n))
; returns the absolute difference of two Church numerals
(defn ae [m n] (ps (st m n) (st n m)))
; returns a if m=n, and b otherwise
(defn il [m n a b] (((ae m n) (fn [x] b)) a))
; returns 1 if m=n and zero otherwise
(defn el [m n] (il m n oe zo))
; returns 1 if a^n + b^n = c^n, and zero otherwise
(defn ft [a b c n] (el (ps (ep a n) (ep b n)) (ep c n)))
; returns the first, second, third elements of a tuple
(defn fd [x y z] x)
(defn sd [x y z] y)
(defn td [x y z] z)
(defn mm [g]
	(let
		[
			a (g fd)
			b (g sd)
			c (g td)
		]
		(fn [h] (h a (sr b) (ps c (a b))))
	))
; returns f(n-1)+f(n-2)+...+f(0)
(defn sv [n f] (((n mm) (fn [g] (g f zo zo))) td))
; two as a Church numeral
(def to (ps oe oe))
; three as a Church numeral
(def te (ps to oe))
; 27 as a Church numeral
(def tn (ep te te))
; 27^27 as a Church numeral
(def lt (ep tn tn))
; Computes the number of solutions to x^n + y^n = z^n with 0 <= x,y,z,n-3 < 27^27.
; By Fermat's Last Theorem, the only solutions are the trival solutions x=0 or y=0.
; So the answer is (27^27)(2*27^27-1)=
; 393254100951105827236151817053824232565763475400186496084682581445313632500815.
(def tm
	(sv lt (fn[a]
		(sv lt (fn[b]
			(sv lt (fn[c]
				(sv lt (fn[d] (ft a b c (ps d te)))))))))))
(println (uh tm))