Problem 1:
Suppose that the following list of bindings was entered into the OCaml
interpreter in the sequence shown. For each binding, write down :
(a) If the expression is accepted, the value bound ("fn" for functions) and its type,
(b) If the expression is rejected due to a type error, "type error",
(c) If the expression is rejected due to an unbound variable,
the name of the variable that is not bound.
Recall that if a type error occurs, then the variable binding does not
happen. Check your answers by entering this sequence into the interpreter.
# type tree =
Leaf of int
| Node of tree * tree;;
# let b = Leaf [3];;
# let e = Node (3, Leaf 5);;
# let z = Node (7, 7);;
# let c = Node (Leaf 3,Leaf 5);;
# let d = Node (Leaf 0,c);;
# let b = Node (c,d);;
# let f = fun a -> fun b -> a < b;;
# let g = f 0;;
# let z = g 4;;
# let x = g -3;;
Problem 2:
For each function below, determine if the function is tail recursive.
# let rec fact1 x = x * (fact (x-1));
# let fact2 x =
let rec helper (n,r) =
match n with
0 -> r
| _ -> helper ((n-1),(x*r))
in
helper (x,1)
;;
# let rec add1 (n,y) =
match n with
0 -> y
| _ -> 1 + add1 (n-1,y)
;;
# let rec add2 (n,y) =
match n with
0 -> y
| _ -> add2 (n-1,y+1);
Problem 3:
Write the following functions on trees described using the datatype tree
shown in Problem 1.