[SOLVED] CS ocaml CSE 130, Spring 2015 Name/ID Instructor: Ranjit Jhala

CSE 130, Spring 2015 Name/ID Instructor: Ranjit Jhala
Midterm Exam
Instructions: read these first!
Do not open the exam, turn it over, or look inside until you are told to begin.
Switch off cell phones and other potentially noisy devices.
Write your full name on the line at the top of this page. Do not separate pages.
You may refer to hand-written or printed cheat sheets, but no computational devices (such as laptops, calculators, phones, iPads, friends, enemies, pets, lovers).
Read questions carefully. Show all work you can in the space provided. Where limits are given, write no more than the amount specified.
The rest will be ignored.
Avoid seeing anyone elses work or allowing yours to be seen.
Do not communicate with anyone but an exam proctor.
If you have a question, raise your hand.
When time is up, stop writing.
The points for each part are rough indication of the time that part should take.
Question
Points
Score
1
20
2
15
3
15
Total:
50

CSE 130, Spring 2015 Midterm Exam Page 1 of 6
1. [20 points] For each of the following OCaml programs, write down the Value of the given variable, or circle Error if you think there is a type or run-time error.
(a) [5 points]
let ans =
letx =0 in let a1 = let x = 1 in
fun y z -> [x;y;z]
in
let a2 = let x = 100 in
a1 x
in a2 x
Value ans = The next two parts share the following type and function definition:
type a tree = Leaf
| Node of a * a tree * a tree
let rec fold f b t = match t with
| Leaf ->b
| Node (x, l, r) -> f x (fold f b l) (fold f b r)
let t0 = Node ( cat
, Node (dog, Leaf, Leaf)
, Node (hippo, Leaf, Leaf))
(b) [4 points]
let ans =
let f = (fun _ vl vr -> 1 + vl + vr) in
fold f 0 t
Error Value ans =
(c) [4 points]
let ans =
let f = (fun x vl vr -> vl x vr) in
fold f t0
Error Value ans =
Error

CSE 130, Spring 2015 Midterm Exam Page 2 of 6 The next two parts share the following type and function definition:
type a option = None | Some of a
let rec find f xs = match xs with
| [] -> None
| (x::xs) -> if f x then
Some x else
find f xs
let xs0 = [2;4;8;16;32]
(d) [4 points]
let ans = let f x = x > 10 in
find f xs0
Error
(e) [3 points]
Value ans =
let ans = let f x = (x mod 2) = 1 in
find f xs0
Error
Value ans =

CSE 130, Spring 2015 Midterm Exam Page 3 of 6 2. [15 points]
For this problem, you will write some functions that: use Ocamls lists to implement a Set API. We will represent sets of values of type a by using lists.
type a set = Set of a list
(a) [2 points] First, implement a function
val empty : a set
by filling in the definition below
let empty = =
(b) [5 points] Write a function
val member : a -> a set -> bool
suchthatmember x sreturnstrueifxisinthesetcorrespondingtosandfalseotherwise.
let member x s = match s with | ->
| ->
(c) [3 points] Write a function
val add : a -> a set -> a set
suchthatadd x sreturnsasetwhichhasalltheelementsofsandalsotheelementx.
let add x s = match s with | ->

CSE 130, Spring 2015 Midterm Exam Page 4 of 6 We can use add to obtain a function
val union : a set -> a set -> a set
suchthatunion s1 s2returnsanewsetwhichhasalltheelementsofs1andalsotheelementsofs2.
let union s1 s2 = match s2 with
| Set x2s -> List.fold_left (fun s x -> add x s) s1 x2s
(d) [5 points] Finally, write a function
val del : a -> a set -> a set
suchthatdel x scontainsalltheelementsofsexcepttheelementx.Hint:UseList.filter.
let del x s = match s with | ->
When you are done, you should see the following behavior at the Ocaml prompt:
# let s0 = empty;;
# (mem 1 s0, mem 2 s0) ;;
: bool * bool = (false, false)
# let s1 = add 1 s0 ;;
# (mem 1 s1, mem 2 s1) ;;
: bool * bool = (true, false)
# let s2 = add 2 s1 ;;
# (mem 1 s2, mem 2 s2) ;;
: bool * bool = (true, true)
# let s3 = union s1 s2 ;;
# (mem 1 s3, mem 2 s3) ;;
: bool * bool = (true, true)
# let s4 = del 1 s3 ;;
# (mem 1 s4, mem 2 s4) ;;
: bool * bool = (false, true)

CSE 130, Spring 2015 3. [15 points]
Consider the following small subset of NanoML: type binop = Plus
type expr = Const of int
Midterm Exam
Page 5 of 6
| Var of string
| Bin of expr * binop * expr
| Let of string * expr* expr
| App of expr * expr
| Fun of string * expr
Well-formed Expressions: The following expressions e1, e2, e3 are good in that all the variables that are used are defined i.e. bound in the expression:
(* e1 === 1 + 2 *)
let e1 = Bin (Const 1, Plus, Const 2)
(* e2 === let x = 1 in
let y = 2 in x+y *)
let e2 = Let (x, Const 1,
Let (y, Const 2,
Bin (Var x, Plus, Var y)))
(* e3 === let x = 10 in
(fun y -> x + y) x *)
let e3 = Let (x, Const 10,
App (Fun (y, Plus (Var x, Plus, Var y))
,Var x))
Ill-formed Expressions: However, the following expressions e1, e2 and e3 are bad because they contain unde- fined(orunboundvariables).Thatis,ifyoutrytoevaluatetheminanemptyenvironment(i.e.runeval ([], e)) youwillgetavariable not bounderror:
(* e1 === 1 + x *)
let e1 = Bin (Const 1, Plus, Var x)
(* e2 === let y = 2 in
x+y *)
let e2 = Let (y, Const 2,
Bin (Var x, Plus, Var y))

CSE 130, Spring 2015 Midterm Exam Page 6 of 6
(* e3 === (let z = 10 in (funy->y+z))z *)
let e3 = App (Let (z, Const 10,
Fun (y, Plus (Var y, Plus, Var z)))
,Var z)
(a) [12 points] Use empty, add, union and del to write a function val free : expr -> string set
suchthatfree ereturnsthesetoffreevariablesinanexpressione.
let rec free e = match e with |Varx ->
| Const n ->
| Bin (e1, op, e2) ->
| App (e1, e2) -> |Let(x,e1,e2) -> | Fun (x, e1) ->
When you are done, you should get the following behavior:
# mem x (free e1) ;;
: bool = false
# mem x (free e1) ;;
: bool = true
(b) [3 points] Next, use free to complete the implementation of let isWellFormed e =
When you are done, you should get the following behavior:
# List.map isWellFormed [e1; e2; e3];;
: bool list = [true; true; true]
# List.map isWellFormed [e1; e2; e3];;
: bool list = [false; false; false]