CMSI 3801: Languages and Automata I Practice Questions

Recall Questions

Do you like spaced repetition learning? Have you used Anki or Quizlet? Whether or not spaced repetition works for you, periodically working on flash-card like questions can be a lot of fun, and just may help you retain information.

For this course, recall questions tied to language-independent concepts are found at the bottom of the course notes pages.

Additional recall questions tied to specific programming languages can be found at the Programming Languages Explorations companion website.

Short Answer Questions

Here are some questions that might be found on an in-class paper-and-pencil exam.

How do Python and JavaScript differ in their approach updating non-local variables?
Python requires the nonlocal keyword to do this, while JavaScript does not.
What is the difference between the way JavaScript and Rust handle the sequence:
```
let x = 3;
let x = 3;
```
This is a redeclaration error in JavaScript (Identifier 'x' has already been declared). In Rust, two variables are declared, with the second shadowing the first. You do get a warning though, saying the first variable is never used, but there is no error.
What is the difference between an expression and a statement?
An expression produces a value, while a statement does not. Statements perform actions.
How did Go “fix” the most unintuitive aspect of the C switch statement?
It eliminated implicit fallthrough.
Why is it that the simple act of doing an operation 10 times so easy in Ruby but so annoyingly complex in C-like languages?
Ruby has a built-in times method on integers, while C-like languages require a loop with a counter that you don’t care about!
What is tail recursion and why is it useful?
What is the non-deterministic statement of Go? Of Erlang?
What is so awesome about having large structs or arrays be immutable?
You don’t have to copy them. Reference to them can be safely shared.
What does it mean for a type to be extra-lingual?
It means that types are not themselves values.
How does one query the type of an expression at run time in JavaScript? Python? Ruby?
What are the main differences between a type and a class?
What is a mixin?
Why do languages like Ruby have a single type Array but in other languages like Java, Rust, and Swift there exist many parameterized array types?
Type checking is often concerned less with whether two types are identical, but rather when elements of one type T1 can be assigned to an Lvalue constrained to be of type T2. In what situations is this check made?
(1) variable initialization, (2) assignment, (3) passing arguments to parameters, (4) returning from a function.
What is the difference between type conversion and type coercion?
In the conditional expression x ? y : z of a typical statically-typed language, what type checking and inference rules would a compiler be required to enforce?
Checks: the type of x must be boolean and the types of y and z must be compatible. Inference: the type of the entire expression is the least general type of both y and z.
In what sense is the type inference capabilities of ML and Haskell more powerful that that on Go, Rust, Java, and Swift?
Why (do you think) does Java not infer the types of parameters in normal methods but does infer them for lambdas?
I couldn't find in the definition of C whether the language employs shallow or deep binding. Why?
C doesn’t have nested functions.
What are covariance, contravariance, and invariance?
In what way is a record like a dictionary? In what why are they different?
Both records and dictionaries are comprised of key-value pairs. The difference is that records are intended to model the properties of a single thing, while dictionaries are indented to show the values of a single property across many things.
What does it mean for a record or dictionary to be ordered?
What mechanism do many languages use to avoid unions?
If someone talks about static arrays and dynamic arrays, what are they probably referring to?
Given the Python definition def f(): yield 1; yield 2; yield 3, what is wrong with writing for i in f: print(i)? What should we write instead?
In Python, why should you be scared of using default arguments that are lists? Do you have to worry about this in JavaScript?
Python defaults for parameters are evaluated only once, at the time the function is defined. So all calls to the function use the SAME list! If you mutate that list in the function, then that mutation is seen in future calls. JavaScript, on the other hand, evaluates the default on every call.
In Python, len("Hello, 世界") == 9, but in Rust, "Hello, 世界".len() == 13. Why is this?
Python counts the number of code points, while Rust counts the number of bytes. In the UTF-8 encoding, each of the final two characters requires 3 bytes.
What is the first thing you should do in the implementation of an overloaded assignment operator in C++?
Make sure the source and target of the assignment are not the same! Assignment destroys the target before the copy/move, so if you were doing x = x for example, you have to early exit before destroying anything.
Write a C++ expression, using std::fill, that fills the first 100 elements of the C-style array a of integers with 0s.
std::fill(a, a+100, 0)
In JavaScript, how do you set an object’s prototype after the object has already been created?
Object.setPrototypeOf(myObject, theNewPrototype)
In JavaScript, how does one “wait” for a whole bunch of async functions to all ”finish”?
Promise.all(arrayOfPromises).then(callback)
In C++, Do the types int, float, and double have fixed bit sizes? If so, what are they? If not, why not?
No, C++ is a systems language whose numeric types map directly to the machine’s underlying registers, using whatever size those registers are.
In Python, the expression list(t), for some tuple t, produces the list containing the elements of t in order. Can you write a function in Haskell to do the same thing, i.e., build a list from some arbitrary tuple? If so, give the Haskell function that does it. If not, explain why Haskell can’t do this.
Haskell can’t! There’s no type for an arbitrary-sized tuple!
In JavaScript, Why is [1,12] < [1,3] true but [1,42] < [1,3] false? Why are both expressions false in Python and Haskell?
JavaScript < turns arrays into strings before comparing, and "1,12" < "1,3". Python and Haskell do numeric element-by-element comparison and 1=1 and 12 > 3.
In Java, if you wanted to average some integers, you could write Stream.of(1,2,3).collect(Collectors.averagingInt(f)) for some particular function f. What should f be here?
x -> x or Integer::new
The Java expression IntStream.range(1, n+1).reduce((x, y) -> x * y) is a good attempt to produce the factorial of n, but it doesn’t produce an integer. What does it produce? How can you modify it (slightly) to produce the integer factorial?
This returns an optional! To get an actual integer, we should use the two-argument version of reduce, passing in 1 as the first argument. You can also do an .orElse(1) at the end.
Suppose r was a (Java) Reader object. How do you get the lowercased lines of the reader into an array, eliminating all duplicates?
r.lines().distinct().map(String::toLowerCase).toArray(String[]::new)
In Python, why should you be scared of using default arguments that are lists? Do you have to worry about this in JavaScript?
Python defaults for parameters are evaluated only once, at the time the function is defined. So all calls to the function use the SAME list! If you mutate that list in the function, then that mutation is seen in future calls. JavaScript, on the other hand, evaluates the default on every call.
In Swift, Are if-let, while-let, or guard-else constructs required to access an element of an optional array? If not, what is a more concise way to access the element?
No, for optional array a and integer i, you get the convenient a?[i].
Define your very own Swift generic linked list as an indirect enumeration, using the definition “A list is either empty or a value (called the head) connected to a list (called the tail).” (Just define the type, you don’t need to include any methods.)
```
indirect enum MyList<T> {
  case empty
  case node(head: T, tail: MyList)
}
```
Why and when do we extend protocols in Swift?
To add functionality to protocols that already exist. And most awesomely, when we need to create default methods for all adopters of the protocol.
For each of the languages JavaScript, Python, Java, C++, and Haskell, is the language’s “null value” a member of the language’s string type (respectively: "string", str, String, std::string, String, [Char]), or if not, what related type is it a member of? For example, if you were asked about Swift, you would say: “nil is not a member of the type String, but it is a member of String?”.
JS: no, null ∈ the Null type.
Python: no, None ∈ NoneType.
Java: YES!!! BILLION DOLLAR MISTAKE!!!
C++: no, nullptr is not in the std::string type, but ∈ char* and std::string*.
Haskell: no, Nothing ∈ Maybe String.
Some languages don’t have loops; they make you use recursion. So, a good programmer should be fluent in translating a function with loops into a recursive one. Here’s an iterative function written in C++:
```
int c(int n) {
  int steps = 0;
  while (n > 1) {
    n = n % 2 == 0 ? n / 2 : 3 * n + 1;
    steps++;
  }
  return steps;
}
```
When written recursively, the function body can reduced to a single expression! Express this function as a one-liner in JavaScript, Python, Java, C++, Swift, Kotlin, or Haskell: your choice! If using Haskell, use guards rather than an if expression.
So many possible answers here. Here is the direct translation (slow)
- JavaScript: function c(n) { return n<=1 ? 0 : n%2===0 ? 1+c(n/2) : 1+c(3*n+1) }
- Python: def c(n): return 0 if n<=1 else 1+c(n//2) if n%2==0 else 1+c(3*n+1)
- Java: static int c(int n) { return n<=1 ? 0 : n%2==0 ? 1+c(n/2) : 1+c(3*n+1); }
- C++: int c(int n) { return n<=1 ? 0 : n%2==0 ? 1+c(n/2) : 1+c(3*n+1); }
- Swift: func c(n: Int) -> Int { return n<=1 ? 0 : n%2==0 ? 1+c(n/2) : 1+c(3*n+1); }
- Kotlin: fun c(n: Int): Int { return n<=1 ? 0 : n%2==0 ? 1+c(n/2) : 1+c(3*n+1); }
- Haskell: c n | n<=1 = 0 | even n = 1+c(n `div` 2) | otherwise = 1+c(3*n+1)
The tail-recursive way is better. Left as an exercise to you.
Given a = [10,20,30,30,40,30], draw a picture of the world after b = delete 30 a that shows you understand persistent data structures. (delete is from Data.List).
The first two nodes are copied; the rest can be shared.
```
  a ------>  10 ----> 20 ----> 30 ----> 30 ----> 40 ----> 30
                                        ^
                                        |
  b ------>  10 ----> 20 ---------------+
```
In Haskell, why are (/ 2) and (/) 2 different functions, but (elem 21) and (elem) 21 are the same function?
Since / is an infix operator, (/ 2) is a right operator section which divides its argument by 2, but (/) 2 is a function which returns 2 divided by its argument! Alternatively, since elem is a regular prefix operator, there is no section here, and (elem 2) and (elem) 2 are just putting parentheses where they already belong anyway.
What kinds of objects do Haskell’s search/lookup/find functions return?
Maybes
Many languages use split to break a string into a list of characters, and join to turn an array of characters into a string. How do you do these two operations in Swift?
Array(s) breaks a string into a list of chars, String(a) joins a list of strings into a single string.
When would you choose an atomic variable over a mutex?

Problems

Here are some problems that require some thinking, and some actual work. They may involve writing little scripts, or making sketches. They aren’t exactly short-answer problems.

Syntax

Translate the following expression into (a) postfix and (b) prefix notation, in both cases without using parentheses:
```
(-b + sqrt(4 × a × c)) / (2 × a)
```
Do you need a special symbol for unary negation? Why or why not?
JavaScript's implicit semicolon insertion is often considered to be poorly designed because the following four cases aren't exactly intuitive:
```
function f() {
    return
       { x: 5 }
}
```
```
let b = 8
let a = b + b
(4 + 5).toString(16)
```
```
let place = "mundo"
["Hola", "Ciao"].forEach((command) => {
  console.log(command + ", " + place)
})
```
```
const sayHello = function () {
    console.log("Hello")
}
(function() {
    console.log("Goodbye")
}())
```
What is being illustrated in each of the above? Go, Python, Scala, and Ruby all allow line endings to end statements and you don't hear people complaining about them the way they do about JavaScript. Pick one of these four languages and show why they don’t have problems with the four "problematic" cases of JavaScript.

Names, Scopes, and Bindings

What is meant by the scope of a binding? Give examples of both spatial and temporal scope, using examples from the programming language of your choice.
Give three examples from C which a variable is live but not in scope. Make sure each example is of a different quality than the others; for example, don't just hide three global variables in a single function and claim you have three examples.
Give an example of a program in C that would not work correctly if local variables were allocated in static storage as opposed to the stack. For the purposes of this question, local variables do not include parameters.
In C, f(2) should return 2, but if local variables were allocated statically, it would return 3.
```
void f(int x) {
    int a = 2;
    int b;
    if (x < 0) {
        a = 3;
        return 0;
    } else {
        b = f(-x);
        return b + a;
    }
}
```
What does this script print under (a) static scoping and (b) dynamic scoping?
```
var x = 100;
function setX(n) {x = n;}
function printX() {console.log(x);}
function first() {setX(1); printX();}
function second() {var x; setX(2); printX();}
setX(0);
first();
printX();
second();
printX();
```
Static scope rules result in an output of 1122, while dynamic rules result in 1121. This is because with static scoping, the second execution of setX changes the global x to 2, so that the last printX in the script prints 2. With dynamic scope, the second setX call changes the local x to 2, leaving the global x unaffected.

What does this script print under (a) static scoping and (b) dynamic scoping?

var x = 1
function h() {var x = 9; return g();}
function f() {return x;}
function g() {var x = 3; return f();}
print f() * h() - x

What does this script print under (a) static scoping and (b) dynamic scoping?

var x = 1
function h() {var x = 0; return g()}
function f() {return x}
function g() {var x = 8; return f()}
print f() - h() + x

Show the output of the following, assuming dynamic scope and (a) deep binding, and (b) shallow binding.

function f(a) {
    var x = a - 1
    function g() {
        print x + 25
    }
    h(g)
}
function h(p) {
    var x = 80;
    p()
}
f(7)

Show the output of the following, assuming dynamic scope and (a) deep binding, and (b) shallow binding.

function g(h) {
  var x = 2;
  h()
}
function main() {
  var x = 5
  function f() {
    print x + 3
  }
  g(f)
}
main()

(a) 8, (b) 5

Explain what would need to be done to make deep binding work with dynamic scoping, assuming that association lists were used to implement the scope rules. (Hint: think of turning the association lists into "A-trees".)
When you call the passed function, save the existing pointer to the top of the association list and replace it with a pointer to just before the point that the function was defined. Then enter the bindings for the new function as a "branch" in the association list (which is now a tree). When the function finally returns, chop off that branch and restore the pointer.
Does the following Python code serve as a valid experiment as to whether Python is statically or dynamically scoped? Why or why not?
```
x = 3
def f():
    print x
def g():
    x = 5
    f()
g()
```
The following is not a valid experiment as to whether Ruby is statically or dynamically scoped. Why not?
```
x = 3
def f(); puts x; end
def g(); x = 5; f(); end
g()
```
This fragment of Java code illustrates something about scope. Or does it? Relate it to other similar problems we've seen regarding scope.
```
public void fail() {
    class Failure extends RuntimeException {}
    throw new Failure();
}
```

Expressions

Define the terms precedence, associativity, fixity, arity, giving plenty of examples of each.
Write an expression (in as many languages as you can) to produce an array of length 100 filled with 0s. For C++, show three versions: one with raw arrays, one with std::array and one with std::vector, and use std::fill if appropriate.
The Java expression IntStream.range(1, n).reduce((x, y) -> x * y) is a good attempt to produce the factorial of n, but it doesn’t produce an integer. What does it produce? How can you modify it (slightly) to produce the integer factorial?
Write a list comprehension (in as many languages as you can, but of course in at least Python and Haskell) for all pairs (2-tuples) of integers where the first element is in the range 1..5 inclusive and the second is in the range 1..3 inclusive.
Here's an operator chart from some unnamed language. Operators are listed in decreasing precedence (highest precedence operators are at the top of the table; lowest precedence operators are at the bottom). Operators listed on the same line have the same precedence.

Operator(s) Assoc Arity Fixity
§ # 1 Prefix
∀ ⊥ 1 Postfix
% • ¥ L 2 Infix
⊗ ∇ ⇒ R 2 Infix
Draw the expression tree for the following
```
# # A ⇒ # B ∇ C ¥ D % E ∇ F % G • H ⊥ ∀ ⊗ § I ∀
```
The expression a–f(b)–c*d can produce different values depending on how a compiler decides to order, or even parallelize operations. Give a small program in the language of your choice (or even one of your own design) that would produce different values for this expression for different evaluation orders. Please note that by "different evaluation orders" we do not mean that the compiler can violate the precedence and associativity rules of the language.

Operator(s)	Assoc	Arity	Fixity
§ #		1	Prefix
∀ ⊥		1	Postfix
% • ¥	L	2	Infix
⊗ ∇ ⇒	R	2	Infix

Types

JavaScript is considered mostly “weakly-typed” because it generally performs coercions. However, in a few cases, it does throw TypeError. What are the cases in which this error is thrown?
In the Java programming language, if the class Dog were a subclass of class Animal, then objects of class Dog[] would be compatible with the type Animal[]. Write a fragment of Java code that shows that this requires dynamic type checking. Include in your answer a well-written explanation that shows you truly understand the difference between static and dynamic types.
If both Dog and Rat are subclasses of Animal, this code
```
  Animal[] pets = new Dog[4];
  pets[0] = new Rat();
```
compiles fine but when executed throws an ArrayStoreException, that's right, a run-time typecheck error. This means Java is NOT 100% statically typed because this typecheck occurs at run time. A language can only be called 100% statically typed if all type conflicts are detected at compile time.

Here's a variation of M-J. Dominus' Spectacular Example.

local
    fun split [] = ([],[])
      | split [h] = ([h], [])
      | split (x::y::t) = let val (s1,s2) = split t in (x::s1,y::s2) end
    fun merge c ([], x) = x
      | merge c (x, []) = x
      | merge c (h1::t1, h2::t2) =
          if c(h1,h2)<0 then h1::merge c(t1,h2::t2) else h2::merge c(h1::t1,t2);
in
    fun sort c [] = []
      | sort c x = let val (p, q) = split x
                     in merge c(sort c p, sort c q)
                   end;
   end;

During type inference, give the types assigned to
- the parameter c within sort
- the function split
- the function merge
- the y in the third clause of split?
Give the type of sort and explain why it is not what you would expect.
How do you rewrite the function to make it actually do a mergesort?

Here's some code in some language that looks exactly like C++. It is defining two mutually recursive types, A and B.
```
struct A {B* x; int y;};
struct B {A* x; int y;};
```
Suppose the rules for this language stated that this language used structural equivalence for types. How would you feel if you were a compiler and had to type check an expression in which an A was used as a B? What problem might you run into?
Consider the following C declaration, compiled on a 32-bit little endian machine:
```
struct {
    int n;
    char c;
} A[10][10];
```
If the address of A[0][0] is 1000 (decimal), what is the address of A[3][7]?

Explain the meaning of the following C declarations:

double *a[n];
double (*b)[n];
double (*c[n])();
double (*d())[n];

Translate each of the following declarations in C to Go:

double *a[n];
double (*b)[n];
double (*c[n])();
double (*d())[n];

Consider the following declaration in C:
```
double (*f(double (*)(double, double[]), double)) (double, ...);
```
Describe rigorously, in English, the type of f.
Suppose you were designing a programming language (yes it could happen) and you chose the following types: Null, Boolean, Number, String, Array, Dictionary, and Function. Suppose you wanted to make the language 100% weakly typed. In order to do this you would have to come up with a rule for implicitly converting any expression of any type into a reasonable "equivalent value" in another type, essentially completing this table:

To→
From↴ Bool Num Str Arr Dict Fun
Null false
0 "" [] {}
Bool false→0
true→1
Num 0→false
else true
Str ""→false
else true
Arr []→false
else true
Dict {}→false
else true
Fun true

Explain how you would complete this table.

Pointers and References

If possible, write a program in Go that makes a variable point to itself. That is, for some variable x, make it so that *x == x. If this is not possible, state why it is not possible.
If possible, write a program in Rust that makes a variable point to itself. That is, for some variable x, make it so that *x == x. If this is not possible, state why it is not possible.
If possible, give C++ type and object declarations to make a variable point to itself, that is, make it so that p == *p. If it is not possible to do so, state why no such variable can be defined.
In C++ you can say (x += 7) *= z but you can't say this in C. Explain the reason why, using precise, technical terminology. See if this same phenomenon holds for conditional expressions, too. What other languages behave like C++ in this respect?

Control Flow

The following pseudocode shows a mid-test loop exit:
```
while (true)
    line := readLine();
    if isAllBlanks(line) then exit end;
    consumeLine(line);
end;
```
Show how you might accomplish the same task using a while or repeat loop, if mid-test loops were not available. (Hint: one alternative duplicates part of the code; another introduces a Boolean flag variable.) How do these alternatives compare to the mid-test version?
Assume we wanted to write a function called If in Java or C or JavaScript, such that the call If(c, e1, e2) would return e1 if c evaluated to true, and e2 if it evaluated to false. Show why, in these languages, such a function is absolutely not the same as the conditional expression c?e1:e2. You can show a code fragment that would return different results based on whether the function were called versus the conditional expression were evaluated.
In Java, C, and JavaScript, all function arguments are evaluated before they are called. The evaluation of (p==null ? null : p.value) is null-safe, whereas the call If(p==null, null, p.value) is not: it throws a NullPointerException if p is null. A more blatant example can be seen in the difference between (true ? 1 : formatMyHardDrive()) and If(true, 1, formatMyHardDrive()).
Frank Rubin used the following example (rewritten here in C) to argue in favor of a goto statement:
```
int first_zero_row = -1;              /* assume no such row */
int i, j;
for (i = 0; i < n; i++) {             /* for each row */
    for (j = 0; j < n; j++) {         /* for each entry in the row */
        if (A[i][j]) goto next;       /* if non-zero go on to the next row */
    }
    first_zero_row = i;               /* went all through the row, you got it! */
    break;                            /* get out of the whole thing */
    next: ;
}                                     /* first_zero_row is now set */
```
The intent of the code is to set first_zero_row to the index of the first all-zero row, if any, of an n × n matrix, or -1 if no such row exists. Do you find the example convincing? Is there a good structured alternative in C? In any language? Give answers in the form of a short essay. Include a good introductory section, a background section describing views on the goto statement throughout history, a beefy section analyzing alternatives to Rubin's problem, and a good concluding section. Talk about solutions in at least three languages. You may find higher order functions such as every, some, and forEach to be helpful.

Functions

Some languages do not require the arguments to a functions call to be evaluated in any particular order. Is it possible that different evaluation orders can lead to different arguments being passed? If so, give an example to illustrate this point, and if not, prove that no such event could occur.
In C++ and Java, it is not permitted to have two functions that differ only in return type overload each other. In Ada it is allowed. What is the reason for this situation? Even though other languages do allow this flexibility in overloading, the compiler needs some sophistication. What exactly is involved? Be very precise in your explanation and illustrate it with code fragments.
Write a function that accepts a function $f$ and a list $[a_0, a_1, \ldots, a{_n-1}]$ and returns the list $[a_0, f(a_1), f(f(a_2)), f(f(f(a_3))), \ldots]$. For example, if you pass as arguments the function that doubles its inputs, and the list $[4, 3, 1, 2, 2]$, then the return value would be $[4, 6, 4, 16, 32]$.
Write a tail-recursive function or method (in as many languages as you can) that produces the sum of squares in an array. This is just to give you practice with tail-recursion; I know there are better ways to compute the sum-of-squares.
A possible JavaScript solution is:
```
function ss(a) {
  function s(i, acc) {
    return i == a.length ? acc : s(i+1, a[i]*a[i]+acc)
  }
  return s(0, 0);
}
```
A possible Ruby solution is:
```
def ss(a)
  s = Proc.new{|i,acc| i==a.length ? acc : s[i+1, a[i]*a[i]+acc]}
  s[0, 0]
end
```
Write a tail-recursive function to compute the minimum value of an array or list in Python, C, JavaScript, Go, and perhaps a few other languages. Obviously these languages probably already have a min-value-in-array function in a standard library, but the purpose of this problem is for you to demonstrate your understanding of tail recursion. Your solution must be in the classic functional programming style, that is, it must be stateless. Use parameters, not nonlocal variables, to accumulate values.
Write a code fragment (in as many languages as you can) that fills an array, indexed from 0 through 9, such that slot i of the array contains a function (or pointer to a function if your language demands it) that divides its argument by the square of i.
Write a tail recursive function (in as many languages as you can) that takes in an array, and returns a new array just like the old one, except with the values at even-numbered indexes removed. (It is okay to use a "helper" that is tail-recursive). For example:
```
withoutEvens([4,6,true,null,2.3,"xyz"]) => [6,null,"xyz"]
```
In as many languages as you can (but include C, Java, JavaScript, and Python for sure), write a pair of functions, $f$ and $g$, such that every time you call $f$, you get back 5 less than the result of the previous call to $f$ or $g$, and every time you call $g$, you get back double the absolute value of the result of the last call to $f$ or $g$. The initial value is 0. It is possible to do this in one line of Perl.
Write the following function in Standard ML, where your implementation must be tail recursive.
Given: a list [a₀, a₁, ..., a_n-1],
Return: a₀*a₁ + a₂*a₃ + a₄*a₅ + ....

For example, if given [3, 5, 0, 28, 4, 7] we return 15 + 0 + 28 = 43. If there are an odd number of elements in the list, assume there is an extra 1 for padding.

Here is, by the way, a non-tail-recursive formulation:
```
fun sum_of_prods [] = 0
  | sum_of_prods (x::nil) = x
  | sum_of_prods (x::y::t) = x * y + sum_of_prods t;
```
Write a JavaScript function, without using eval, that accepts an array of integers $a$, and a function $f$, and returns an array of functions, each of which, when called, invokes $f$ on the corresponding element of $a$. For example, if your function was called $g$, then calling g([6,3,1,8,7,9], dog) would return an array of functions $p$ such that, for example, calling p[3]() would invoke dog(8).
```
function g(a, f) {
    var b = [];
    for (var i = 0; i < a.length; i++) {
        b[i] = function(i){return function(){f(a[i])};}(i);
    }
    return b;
}
```
Write some JavaScript that adds a new method to arrays so that if I call this method on an array with two parameters $f$ and $g$, I get back a new function which, when called with one argument $k$, returns the composition of $f$ and $g$ applied to the $k$th element of the original array. Hint: If we defined the functions square and addSix the obvious way, and we called this new method weird, then:
```
[4, 6, 7, 3, 5, 2, 4].weird(addSix, square)
```
would return the function z such that
```
z(2) == 55
```
because the element at index 2 within the array is 7 and $7^2 + 6 = 55$.
In Go, Rust, Swift, C, and C++ arrays and records can be allocated on the stack, not just on the heap. When making assignments of aggregates to variables, compilers usually generate code to deposit the values in temporary storage. Why is this necessary in general? After all, in
```
Weekdays := Day_Set(False, True, True, True, True, True, False);
```
we could construct the aggregate directly in the variable Weekdays. Give an example of an assignment statement that illustrates the necessity of constructing an aggregate in temporary storage (before copying to the target variable).
In Java, you generally implement callbacks via registration of listeners that implement a known interface, rather than using method pointers. Create a Swing component called AngleReader which displays a picture of a circle and notifies all its listeners of the angle, in degrees, that the mouse cursor makes with the horizontal axis of the circle as the mouse moves over it.
Complete the following definition of a dot product function in ML:
```
val dot =
    let
        fun transpose ... =
    in
        ....
    end;
```
The transpose function should work like this
```
transpose ([x1,...,xn],[y1,..,yn]) = [(x1,y1),...,(xn,yn)]
```
raising Domain if the arrays have different lengths. The body of the definition of dot (between the in and end) should contain only instances of the functions transpose, o, foldr, map, op*, op+, and the value 0.
Explain what is printed under (a) call by value, (b) call by value-result, (c) call by reference, (d) call by name.
```
x = 1;
y = [2, 3, 4];
function f(a, b) {b++; a = x + 1;}
f(y[x], x);
print x, y[0], y[1], y[2];
```
1. Under call by value, the arguments do not change; so the script prints 1 2 3 4.
2. Under call by value/result, the increment of x does not take place until after the subroutine returns. It prints 2 2 2 4.
3. Under call by reference, the increment of b changes x immediately, so the new value of x, namely 2, is used to update a, which is still y[1], and that becomes 2 + 1 = 3, so it prints 2 2 3 4.
4. Under call by name, b++ changes x immediately so x becomes 2. Then, since a refers to the expression {y[x]}, it will need to compute y[2] which is 3. The script prints 2 2 3 3.
Show the output of the following code fragment under call by value, (b) call by value-result, (c) call by reference, and (d) call by name.
```
x = 1
y = [2, 3, 4]
function f(a, b) {a--; b = x - 1}
f(x, y[x])
print x, y[0], y[1], y[2]
```
Explain what is printed under (a) call by value, (b) call by value-result, (c) call by reference, (d) call by name.
```
x = 1;
y = 2;
function f(a, b) {a = 3; print b, x;}
f(x, x + y);
print x;
```
Using your favorite language and compiler, write a program that determines the order in which subroutine arguments are evaluated.
Consider the following (erroneous) program in C:
```
void do_something() {
    int i;
    printf("%d ", i++);
}
int main() {
    int j;
    for (j = 1; j <= 10; j++) do_something();
}
```
Local variable i in subroutine do_something is never initialized. On many systems, however, the program will display repeatable behavior, printing 0 1 2 3 4 5 6 7 8 9. Suggest an explanation. Also explain why the behavior on other systems might be different, or nondeterministic.
Give an example which shows that default parameters are unnecessary in C++ because you can always get the desired effect with overloading.

What does the following program output?

with Ada.Text_IO, Ada.Integer_Text_IO;
use Ada.Text_IO, Ada.Integer_Text_IO;

procedure P is
  A: Integer := 4;
  type T is access Integer;
  B: T := new Integer'(4);
  C: T := new Integer'(4);

  procedure Q (X: in out Integer; Y: T; Z: in out T) is
  begin
    X := 5;
    Y.all := 5;
    Z.all := 5;
  end Q;

begin
  Q (A, B, C);
  Put (A);
  Put (B.all);
  Put (C.all);
end P;

In some implementations of an old language called Fortran IV, the following code would print a 3. Can you suggest an explanation? (Hint: Fortran passes by reference.) More recent versions of the Fortran language don't have this problem. How can it be that two versions of the same language can give different results even though parameters are officially passed "the same way." Note that knowledge of Fortran is not required for this problem.
```
      call f(2)
      print* 2
      stop
      end
      subroutine f(x)
          x = x + 1
          return
      end
```

Modules, Classes, and Abstract Data Types

Make a module (in as many languages as you can) with a function called nextOdd (or next_odd or nextodd depending on the language’s culture). The first time you call this subroutine you get the value 1. The next time, you get a 3, then 5, then 7, and so on. Show a snippet of code that uses this subroutine from outside the module. Is it possible to make this module hack-proof? In other words, once you compile this module, can you be sure that malicious code can't do something to disrupt the sequence of values resulting from successive calls to this function?
Make a module (in as many languages as you can) that contains (1) a (private) string, initialized to "MI", (2) a function which retrieves the value of this string, and (3) four other methods, each of which changes the string to another string according to the following:
- If the current string ends in an "I", add "U", e.g. "MI" → "MIU".
- Append the second through last characters of the string onto itself, e.g. "MIIU" → "MIIUIIU".
- Replace any occurrence of "III" with "U", e.g. "MUIIIU" → "MUUU".
- Remove any "UU", e.g. "MIUUUI" → "MIUI".
Remember, the point is that the string inside the module can not be changed by any operation other than the four defined above.
What can't you do with a Perl package named m, s, or y?
Consider the implementation of a Container class framework with the following abstract base class Container (here using C++ syntax):
```
template <class Item>
class Container {
public:
  unsigned numberOfItems() {return currentSize;}
  bool isEmpty() {return currentSize == 0;};
  virtual void flush() = 0;
  ~Container() {flush();}
private:
  unsigned currentSize;
};
```
Here the idea is that each particular (derived) container class shall implement its own flush() operation (which makes sense because different containers are flushed in different ways: there may be arrays, linked lists, rings or hashtables used in the representation), and when a container is destroyed its flush() operation will be automatically invoked. However, the idea is flawed and the code as written causes a terrible thing to happen. What happens?

Object-Orientation

What philosophers call a "class" mathematicians call a "set" (i.e., a collection of unordered, unique, values). So, a philosopher says that every member of a subclass is also a member of the superclass. But a C++ programmer says that every member of a superclass is also a member of its subclass! What is going on here?
Write a three-page paper on the nature of identity in object oriented philosophy. Include some code fragments to illustrate your main points.
It is certainly possible to make a Person class, then subclasses of Person for different jobs, like Manager, Employee, Student, Monitor, Advisor, Teacher, Officer and so on. But this is a bad idea, even though the IS-A test passes. Why is this a bad idea and how should this society of classes be built?
One of the most important ways in which object oriented programming helps us to manage complexity is through the ability to group related classes into a hierarchy of subclasses and superclasses. Dynamic binding (run-time polymorphism) allows us to operate on collections of objects from different classes in a hierarchy safely. Furthermore, systems which are programmed using dynamic binding are more easily extendible.
1. What construct is used in non-object oriented programming languages to simulate class hierarchies, and why do we say that it is unsafe?
2. Why are inheritance-like structures in non-OOPLs harder to extend?
Why is it said that implementation inheritance is at odds with encapsulation?
Inheritance is not always appropriate. Discuss the reasons why a design with a superclass Person and subclasses for different jobs (e.g., programmer, manager, ticket agent, flight attendant, supervisor, student, etc.) is a lousy design. Give an alternative.
In designing a class hierarchy in C++, when should you make an operation virtual and when should you make an operation non-virtual? Give examples.
Write a Perl “class” for machine parts that have an identification number (a positive integer divisible by 5), a weight (a positive floating-point number) and a name (which must consist entirely and exclusively of alphabetic characters). Provide a “constructor” that takes in a string consisting of the id, weight, and name, respectively in which
- the string may have leading and trailing spaces
- the three fields are separated by a vertical bar
- the weight is not expressed in scientific notation: it can have an integral value, but if it does have a decimal point, then it is followed by a non-empty fractional part. There is no "E" part, ever. It's simple.
The constructor will check for a valid argument by matching against a regex, and if all is cool, will split the string to assign to its fields.
Write a Python class for students that have an id, name, birthday, and transcript. The transcript is a dict, indexed by semester name, whose values are dicts mapping course numbers to grades. Supply methods to read the id, read and write the name, read and write the birthday, get the grade for a given course (in any semester), and add an item to the transcript. Did you encapsulate (i.e. hide) the properties inside the class so they were protected from direct access from outside the class? Why or why not?
Find some old "procedural" code you have written and rewrite in an object-oriented fashion. I don't mean that you have to use inheritance or polymorphism; all I am really looking for is that you wrap some functions up in a sensible class.
A common pattern that comes up a lot is the need to assign unique identifiers to objects of a given class, for example:
```
class Item {
    private int id;
    private static int numberOfItemsCreated = 0;
    public Item() {id = numberOfItemsCreated++;}
    // pretend that there are more members here...
};
```
As you can see, every item that gets created will get a unique id. Because this pattern occurs frequently, it might be nice to generalize this and make make something reusable out of it so we don't have to write this code inside every class that needs ids. Perhaps we need an interface or abstract class. Tell me why these two suggestions won't work with a detailed, technical answer. Then tell me something that will work. (Note: there is nothing wrong with the access modifiers above; the problems with my two suggestions have to do with the nature of interfaces and abstract classes.)
Given a utility class, can you always rewrite it as a singleton? Given a singleton, can you always rewrite it as a utility class? If so, when would you choose one over the other?
Explain how, in C++, you can get access to, and indeed modify, a protected component of an object that someone else declared. As a concrete example, let's say someone has declared
```
    class C {protected: int x; ...};
    C c;
```
then your job is to assign a new value to c.x. Assume there are no public operations of C that modify x that you know of. Also, do not use any preprocessor tricks (like #define protected public).
What makes more sense, to inherit a list from a stack or a stack from a list?
Why did the designers of the C++ standard library containers emphatically reject an inheritance hierarchy of containers?
In C++ you can write
```
class C {int x;};
C c;
C* p = &c;
cout << p;
```
and there is no compile-time nor link time error, despite the fact that operator<<(C*) is not a member of ostream (since that class was declared before you declared C), nor for that matter did anyone declare the global function
```
    ostream& operator<<(ostream&, C*);
```
So why does it all work? Explain exactly what gets printed and why.
What happens to the implementation of a C++ class if we “redefine” a field in a subclass? For example, suppose we have:
```
class Base {
    public int a;
    public String b;
}

class Derived extends Base {
    public float c;
    public int b;
}
```
Does the representation of a Derived object contain one b field or two? If two, are both accessible, or only one? Under what circumstances? Answer for C++, Java, Python, Kotlin, Scala, or any similar language.
If Dog is an abstract class in a C++ program, why is it acceptable to declare variables of type Dog*, but not of type Dog? Does this problem even make sense to ask in Java or Python?

Concurrency

Write a short paper distinguishing actors, goroutines, and coroutines, using examples from at least three programming languages.
Compare and contrast each of the following synchronization mechanisms: locks, barriers, mutexes, countdowns, semaphores, condition variables, and semaphores. For each, show how do define the mechanism in Java and in Go, if the language supports them directly, with a small example.
Discuss the difficulties of implementing a secure Post Office object in Ada, Erlang, Go, or Rust that meets the following requirements. The post office is to maintain a collection of P.O. boxes, each belonging to some task. Any task can put a letter into another task's box, but only the owner of a particular box can open it and read the letters.
A relay is an agent task created by one task to relay a message to another. For example, if a calling task wishes to send a message to another but does not wish to wait for a rendezvous, the caller can create a relay task to send the message. (Note that relays are only appropriate to use when there are no out parameters in the called entry.) Sketch in detail a body for an Java thread, Kotlin coroutine, Ada task, Erlang process, or Go goroutine that uses a relay to invoke a service of another agent, passing a message in the invocation.
In Ada, if two tasks are executing a Put procedure at the same time, their outputs may be interleaved. (This could produce amusing and even distasteful results, e.g. writing "sole" in parallel with "ash") Show how to set things up so only one task is writing at a time.
Why do Java programmers not have to worry about the situation in the previous problem (interleaving of text output written to a stream)?
One of the nice features of Quicksort is that it allows a great deal of parallelism in an implementation. After partitioning, the slices on either side of the pivot can be sorted in parallel. It is very easy to set things up to do this in languages such as occam, but tedious in Ada and Java. Code up a parallel version of Quicksort in Ada or Java and explain why it is messy.
In Ada, what happens when you try to call an entry in a task that has terminated? Comment on the following code fragment as a possible approach to calling entry E of task T only if T has not terminated.
```
if not T'Terminated then
    T.E;
end if;
```
In Java, what happens if you invoke a method on a thread that has completed?
Two JavaScript programmers are arguing over the best way to implement a little timer widget. The first programmer prefers:
```
let countDown = function () {
    let i = 10;
    let update = function () {
        document.getElementById("t").innerHTML = i;
        if (i-- > 0) setTimeout(update, 1000);
    }
    update();
}
```
The second argues that this is better:
```
let countDown = function () {
    let update = function (i) {
        document.getElementById("t").innerHTML = i;
        if (i-- > 0) setTimeout(function () {update(i)}, 1000);
    }
    update(10);
}
```
Your role is to figure out which programmer is right, if any. Make a fairly extensive list of the pros and cons of each approach. Your list will be graded on completeness, neatness, correct usage of terminology (don't forget to mention "anonymous function" and "closure"), and how articulately you express yourself. Bad grammar will impact your grade negatively. You may want to consider readability and (especially) performance.

Metaprogramming

What is it about Ruby that make its metaprogramming facilities among the most powerful and expressive of all major programming languages?

Programming Problems

Keep sharp by practicing your programming skills.

Write a function or method (in as many languages as you can) that randomly permutes a string.
Write a function or method (in as many languages as you can) that generates powers of some base and sends them to a callback as they are generated, up to some limit.
Write a generator function (in as many languages as you can, provided they support generators) that generates powers of some base up to some limit.
Write a function or method (in as many languages as you can) that doubles each item in an array. If your language allows adding methods to an array class (or provides for extensions), use that feature.
Write a command line script (in as many languages as you can) that writes successive prefixes of its first input argument, one per line, starting with the first prefix, which is zero characters long.
Write a command line script (in as many languages as you can) that reports the number of non-blank, non-commented lines in the file named by the first argument. Blank lines are those that have either no characters or consist entirely of whitespace; commented lines are those that begin with the # character.
Write a function (in as many languages as you can) that accepts a number of U.S. cents and returns a tuple containing, respectively, the smallest number of U.S. quarters, dimes, nickels, and pennies that equal the given amount. If your language has adivmod operator, write two solutions, one using the operator and one that does not.
Write a function (in as many languages as you can) that accepts a string and returns the string which is equivalent to its argument but with all ASCII vowels removed.
Consider the problem of determining whether two trees have the same fringe: the same set of leaves in the same order, regardless of internal structure. An obvious way to solve this problem is to write a function fringe that takes a tree as argument and returns an ordered list of its leaves. Then we can say:
```
def same_fringe(t1, t2):
    return fringe(t1) == fringe(t2)
```
However, fully computing the fringes of both trees is extremely inefficient, given that you should be able to return false at the first mismatch, so the fringes should be computed lazily. Write an efficient (lazy) version of same_fringe in as many languages as you can.
Write a function (in as many languages as you can) that interleaves two lists. If the lists do not have the same length, the elements of the longer list should end up at the end of the result list. For C++, write this three ways: using C-style arrays, using std:array, and using std::vector.
Write (in as many languages as you can) two functions (called f and g) such that every time you call f, you get back 10 less than the result of the previous call to f or g, and every time you call g, you get back three times the absolute value of the result of the last call to f or g. Here's a catch: you must arrange things so that any "state" you need is completely private to f and g.
Write a function (in as many languages as you can) to return the number of ASCII vowels in a string, as a one liner making use of regular expressions if your language supports them.
Write a function (in as many languages as you can) to return whether a given string is in the set, using regular expression matching.
1. Strings of characters beginning and ending with a double quote character, that do not contain control characters, and for which the backslash is used to escape the next character. (These are similar to, but not exactly the same as, string literals in C.)
2. The paren-star form of comments in Pascal or ML: strings beginning with (* and ending with *) that do not contain *). Note comments "don't nest".
3. Numbers in JSON.
4. All non-empty sequences of letters other than "read", "red", and "real".
Implement a concurrent priority queue in Ada two ways: (1) with a server task to provide synchronization and (2) with a protected object.
Implement a concurrent priority queue in Go two ways: (1) with a goroutine to provide synchronization via select statements and (2) using a mutex.

Program Analysis

There are a number of skills beyond just slinging code that will set you apart from peers. These include being able to explain what programs are saying (or doing), being able to explain why certain programs are incorrect or insecure, and being able to explain why certain programs are correct or secure. Here are a few such problems.

Consider this Python script:
```
a = [lambda: i for i in range(10)]
b = [a[i]() for i in range(10)]
```
At the end of this script, what is the value of b? Explain in detail why this is. Support your analysis with a sketch.
Consider this old-fashioned JavaScript script that uses the hated var that you should never use in your own code:
```
var a = [];
for (var i = 0; i < 10; i++) {
    a[i] = function () {return i;}
}
var b = [];
for (var j = 0; j < 10; j++) {
    b[j] = a[j]();
}
```
At the end of this script, what is the value of b? Explain in detail why this is. Support your analysis with a sketch.
For each of the following code fragments, explain what happens when evaluating them. Make sure you convey in your explanation a thorough understanding of Ruby objects, classes, singleton classes, etc.
```
dog="spike"; class <<dog; def bark; "arf"; end; end; dog.bark
```
Evaluates to "arf", since we essentially gave this one dog its own bark method, by attaching it to its own singleton class.
```
class <<"sparky"; def bark; "woof"; end; end; "spraky".bark
```
```
class <<"sparky"; def bark; "woof"; end; end; "sparky".bark
```
```
dog="sparky"; class <<dog; def bark; "woof"; end; end; dog.bark
```
Evaluates to "woof", because we attached the bark method to the object referenced by the variable dog, through its metaclass.
```
class <<"sparky"; def bark; "woof"; end; end; "sparky".bark
```
Raises a NoMethodError because the object in whose metaclass we added the bark method WAS NOT the same string object we tried to call bark on.
```
class <<:sparky; def bark; "woof"; end; end; :sparky.bark
```
Raises a TypeError because Ruby does not allow metaclasses on symbol objects. Maybe this is because Ruby treats symbols in such a super-special way an never puts them in the object pool. It probably holds them as plain old small integers.
```
class <<2; def bark; "woof"; end; end; 2.bark
```
raises a TypeError for the same reason as for symbols.
```
class Counter
  attr_reader :val; @val = 0; def bump(); @val += 1; end
end
Counter.new.bump; Counter.new.val
```
One of the freshman tried to write a Ruby dot-product method. It came out like this:
```
def dot(a, b)
  a.zip(b).map{|x,y| x*y}.inject{|x,y| x+y}
end
```
1. Her first unit test failed. What was her test, and why did it fail?
  The first unit was assert_equal(dot([], []), 0) and it failed because her method returned nil, not 0.
2. She fixed that problem with this
```
def dot(a, b)
  a.zip(b).inject(0){|x,y| x+y[0]*y[1]}
end
```
  Eventually she wrote a unit test with the first array longer than the second and got a TypeError. She fixed that by raising an ArgumentError if the arguments to dot had different lengths. Show her fixed up method.
```
def dot(a, b)
  raise ArgumentError if a.length != b.length
  a.zip(b).inject(0) {|x,y| x+y[0]*y[1]}
end
```
3. Then she got fancy and put her method into the array class
```
class Array
  def *(a)
    ..............her code here..............
  end
end
```
  And the unit tests worked: [3,4,2] * [1,5,0] == 23 for example. But this fancy * definition had a very nasty side effect, which, if she did this in real production code, would have probably broken something big time. What went down with this definition?
  There is already a * operator in the array class; any new definition replaces the old one. Old code using Array * int and Array * string will break badly, because ints and strings can’t be converted to arrays.

What's wrong with this Java code, if anything, and why?

class Pair implements Cloneable {
    private Object first, second;

    public Pair(Object x, Object y) {first = x; second = y;}
    public first() {return first;}
    public second() {return second;}
}

To→ From↴	Bool	Num	Str	Arr	Dict
Null	false	0	""	[]	{}
Bool		false→0 true→1
Num	0→false else true
Str	""→false else true
Arr	[]→false else true
Dict	{}→false else true
Fun	true