(* Thunks. *)
let force = fun x -> x 0 in
(* Church Booleans. *)
let false = fun x -> fun y -> y in
let true = fun x -> fun y -> x in
let k = true in
let cond = fun p -> fun x -> fun y -> p x y in
let forcecond = fun p -> fun x -> fun y -> force (p x y) in
let bool2int = fun b -> cond b 1 0 in
let _ = print (bool2int true) in
let _ = print (bool2int false) in
(* Church pairs. *)
let pair = fun x -> fun y -> fun p -> cond p x y in
let fst = fun p -> p true in
let snd = fun p -> p false in
(* Church naturals. *)
let zero = fun f -> fun x -> x in
let one = fun f -> fun x -> f x in
let plus = fun m -> fun n -> fun f -> fun x -> m f (n f x) in
let two = plus one one in
let three = plus one two in
let four = plus two two in
let five = plus four one in
let six = plus four two in
let succ = plus one in
let mult = fun m -> fun n -> fun f -> m (n f) in
let exp = fun m -> fun n -> n m in
let is_zero = fun n -> n (k false) true in
let convert = fun n -> n (fun x -> x + 1) 0 in
let _ = print (bool2int (is_zero zero)) in
let _ = print (bool2int (is_zero one)) in
let _ = print (bool2int (is_zero two)) in
(* Factorial, based on Church naturals. *)
let loop = fun p ->
  let n = succ (fst p) in
  pair n (mult n (snd p))
in
let fact = fun n ->
  snd (n loop (pair zero one))
in
let _ = print (convert (fact four)) in
let _ = print (convert (fact five)) in
(* Fibonacci, based on Church naturals. *)
let loop = fun p ->
  let fib1 = fst p in
  pair (plus fib1 (snd p)) fib1
in
let fib = fun n ->
  snd (n loop (pair one one))
in
let _ = print (convert (fib five)) in
let _ = print (convert (fib six)) in
(* Predecessor. *)
let loop = fun p ->
  let pred = fst p in
  pair (succ pred) pred
in
let pred = fun n ->
  snd (n loop (pair zero zero))
in
let _ = print (convert (pred six)) in
(* Comparison, yielding a Church Boolean. *)
let geq = fun m -> fun n ->
  m pred n (k false) true
in
let _ = print (bool2int (geq four six)) in
let _ = print (bool2int (geq six one)) in
(* Iteration. *)
let iter = fun f -> fun n ->
  n f (f one)
in
(* Ackermann's function. *)
let ack = fun n -> n iter succ n in
let _ = print (convert (ack two)) in
(* A fixpoint. *)
let fix = fun f -> (fun y -> f (fun z -> y y z)) (fun y -> f (fun z -> y y z)) in
(* Another version of fact. *)
let fact = fun n ->
  fix (fun fact -> fun n -> forcecond (is_zero n) (fun _ -> one) (fun _ -> mult n (fact (pred n)))) n
in
let _ = print (convert (fact zero)) in
let _ = print (convert (fact one)) in
let _ = print (convert (fact two)) in
let _ = print (convert (fact three)) in
let _ = print (convert (fact four)) in
let _ = print (convert (fact five)) in

print 42