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# Assignment #5: Polymorphic Types and Functional Programming in ML

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CSE 305
Assignment #5: Polymorphic Types and Functional Programming in ML

Note: This assignment may be done by a pair of students.
The need for polymorphic types in programming can be seen from the C program bfirst_A5.c posted on
Piazza. This program requires two different monomorphic types for lists, one for a list of integers and
another for a list of trees, in addition to two variations for each function operating on lists – icons,
tcons, iaddback, and taddback. In this assignment, you are to create in ML a functional version of the
above program, in order to demonstrate the conciseness of polymorphic typing as well as the power of
type inference in providing static typing checking without declaring types for any variables.
Problem 1.
Assume the following ML type for binary trees (* was accidentally omitted in initial posting):
datatype ‘a tree = leaf | node of ‘a * ‘a tree * ‘a tree;
Complete the definition below for insert(i, tr) which will insert a value i into tr so as to
maintain the binary search tree property.
fun insert(i, leaf) = __________________
| insert(i, node(v,left,right)) =
if i = v then __________________________
else if i < v then _____________________
else ______________________________;
In the above code, ML will assume v to be of type int by default. In completing the definition of
insert, note that you do not update the input tree; rather, you need to construct a new tree in which
the value to be inserted is placed in the correct position. Test your definition by running the following
function, making sure to place the code for testcase after insert:
fun testcase() =
let val t1 = node(100,leaf,leaf);
val t2 = insert(50, t1);
val t3 = insert(150, t2);
val t4 = insert(200, t3);
val t5 = insert(125, t4);
val t6 = insert(175, t5);
val t7 = insert(250, t6);
val t8 = insert(25, t7);
val root = insert(75, t8)
in root
end;
Submit online a file insert.sml containing the type definition for tree as well as the code for
testcase and insert.
Problem 2.
Define a function that returns a list of integers that we would get from a breadth-first traversal of a BST.
Develop your answer by completing the definition below for bfirst.
fun bfirst(tr) =
let fun bf([], ans) = ____________
| bf(leaf::t, ans) = _____________________
| bf(node(v,t1,t2)::t, ans) = __________________
in bf(________,__________)
end;
Note that function bf will be tail-recursive and the second parameter, ans, is used to accumulate the
final answer. Test out bfirst by running the following function:
fun test_bfirst() = bfirst(testcase());
Submit online a file bfirst.sml containing the type definition for tree and the code for insert,
testcase and bfirst.
Problem 3.
Consider the following depth-first (“in order”) traversal of a BST.
fun dfirst(leaf) = []
| dfirst(node(v,t1,t2)) = dfirst(t1) @ [v] @ dfirst(t2);
Following the strategy of bfirst, develop a tail-recursive version of dfirst, called dfirst2. That
is, the function dfirst2 should make use of a tail-recursive helper function, say df (analogous to bf),
which will use an accumulator-passing style in order to construct the answer. Test out dfirst2 by
running the following function:
fun test_dfirst2() = dfirst2(testcase());
Submit online a file dfirst.sml containing the type definition for tree and the code for insert,
testcase and dfirst2.
Team-work and On-line Submission:
1. This assignment may be done by a team of at most two students. Write both student names at
the top of all program files when submitting them.
2. It is fine to do the assignment solo. Write your name at the top of each file and submit it.
End of Assignment #5

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