(* ~dick/cs620/fun.sml		Composition and others in SML *)
(* Two special functions Id and \bot *)
fun	Id(x)=x;

(*the next is one way to eemulate the idea of undefined values*)
exception Undefined;
fun	undef(x)=raise Undefined;
(* an alternative is to add an extra value to the types we are interested
   in... for type T, we might have
	datatype flat_T = Undef_T | Def of T;
   for example.
   A functor may help generate these as we need them.
*)

(* composition *)
(*See Ullman...also find function 'o'*)
(*demo*)
fun	foo2(F)=F o F;
(* what is the type of foo2?*)
fun sq(x:int)=x*x;
fun cu(x:int)=sq(x)*x;
fun qu(x:int)=(sq o sq) x;
fun bar(x:int)=if x=1 then raise Undefined else sq(x);
bar(2) handle Undefined=>42;
bar(1) handle Undefined=>42;

sq o cu;
sq(cu(2));
(sq o cu) 2;
print "----------------";
cu(2);
sq(it);
(sq o cu) 2;
print "----------------";
foo2(sq);
foo2(sq) 2;
foo2(foo2);
print "----------------";
sq(sq(sq(sq(2))));
foo2(foo2) sq 2;
print("		You can write cond(B,F,G)!\n");