CS 3721: Programming Languages Lab
Lab #11: Exceptions and tail recursion
Exceptions(Adapted from JM 8.1). Consider the following ML code.
exception Excpt of int;
1: fun twice(f,x) = f(f(x)) handle Excpt(x) => x;
2: fun pred(x) = if x = 0 then raise Excpt(x) else x - 1;
3: fun dumb(x) = raise Excpt(x);
4: fun smart(x) = pred(x) - 1 handle Excpt(x) => 1;
The following list the sequence of events occured during the evaluation of
twice(dumb, 1). In particular, it lists which function is called with what ar-
guments, which funtion call returns with what value, what exception gets raised
in which function call, and what exception is handled in which function call.
twice(dumb, 1) called;
twice function entered at line 1;
dumb(1) called at line 1;
dumb function entered at line 3;
Excpt(1) raised at line 3;
dumb function exits;
Excpt(1) handled at line 1;
twice(dumb,1) returns 1.
Continuation Passing Supp ose we have the following function definition
length in ML.
fun length(y) = if null y then 0 else 1 + length(tl(y));
It is converted to tail recursion using continuation passing in the following.
fun length2(y,K) = if null y then K 0 else length2(tl(y), fn res => K(res+1));
1. List the sequence of events occured during the evaluation of twice(smart, 2).
2. Translate the following ML code to tail recursion using continuation pass-
ing style.
datatype tree = LEAF of int | NODE of tree*tree
fun inTree(x, LEAF(y)) = x = y
| inTree(x, NODE(y,z)) = inTree(x,y) orelse inTree(x,z);
Test your implementation with the following invocations (first return true,
second return false).
inTree(3, NODE(LEAF(5),NODE(LEAF(6),LEAF(3))), fn x=>x);
inTree(3, NODE(LEAF(5),NODE(LEAF(6),LEAF(7))), fn x=>x);
