Increase prelude usage in the examples

Just try to clean up our examples a little bits so they use prelude
functions instead of rolling their own.

examples/amulet-logo.ml

@@ -3,9 +3,7 @@
   See `assets/logo.svg' or `assets/logo.png' for an example of the output *)
 
 open import "prelude.ml"
-
-let map = (<$>)
-external val float_of_int : int -> float = "function(x) return x end"
+open import { lua = "lua/conversion.ml" }
 
 module Math =
   include import "lua/math.ml"

examples/church-lists.ml

@@ -1,4 +1,4 @@
-external val print : string -> unit = "print"
+open import "prelude.ml"
 
 type church 'a = ChurchList of forall 'r. ('a -> 'r -> 'r) -> 'r -> 'r
 
@@ -7,7 +7,7 @@ let unList (ChurchList l) = l
 let cons x xs = ChurchList (fun k z -> k x (unList xs k z))
 and nil = ChurchList (fun _ z -> z)
 
-let printList l =
-  unList l (fun x k () -> print x; k ()) (fun _ -> print "nil") ()
+instance show 'a => show (church 'a)
+  let show l = unList l (fun x k () -> show x ^ " :: " ^ k ()) (fun _ -> "nil") ()
 
-let main = printList (cons "foo" (cons "bar" nil))
+let () = print (cons 1 (cons 2 nil))

examples/gadt/term.ml

@@ -1,4 +1,4 @@
-external val ( * ) : int -> int -> int = "function(a, b) return a * b end"
+open import "prelude.ml"
 
 type term 'a =
   | Lit : int -> term int
@@ -12,8 +12,6 @@ let rec eval (x : term 'a) : 'a =
   | Fun x -> x
   | App (f, x) -> (eval f) (eval x)
 
-external val print : 'a -> unit = "print"
-
 let mul a b = App (App (Fun (fun x y -> x * y), a), b)
 
 let () = eval (App (Fun print, mul (Lit 123) (Lit 2)))