1. (5 points) Implement an OCaml function count, of type ¡¯a -> ¡¯a list -> int, in an ex- plicitly recursive manner. The function takes a value and a list and returns the count of the number of times that value appears in the list. For example, count 3 [1;7;3;4;3;5] returns the answer 2.
let rec count e lst =
match lst with
[] -> 0
| x::xs -> (if x=e then 1 else 0) + (count e xs)
2. (2 points each) Circle the best answer.
(a) Parametric polymorphism in OCaml allows programmers to: i. define multiple functions of the same name
ii. define one function with multiple names
iii. define one function that can be called with arguments of different types iv. define one function that can be called with lists of different lengths
iii
(b) OCaml does not support overloading. What might an OCaml programmer do to work around this limitation when it arises?
i. use polymorphism instead
ii. give different functions different names
iii. put functions of the same name in different modules iv. ii and iii above
v. all of the above iv
(c) Consider an invocation of a polymorphic function in OCaml:
i. the function implementation to invoke is determined at run time and the invocation is typechecked at run time
ii. the function implementation to invoke is determined at run time and the invocation is typechecked at compile time
iii. the function implementation to invoke is determined at compile time and the invo- cation is typechecked at run time
iv. the function implementation to invoke is determined at compile time and the invo- cation is typechecked at compile time
iv
(d) Suppose OCaml supported function overloading (for example, the way that + is over- loaded in Standard ML), and consider an invocation of an overloaded function:
i. the function implementation to invoke is determined at run time and the invocation is typechecked at run time
ii. the function implementation to invoke is determined at run time and the invocation is typechecked at compile time
iii. the function implementation to invoke is determined at compile time and the invo- cation is typechecked at run time
iv. the function implementation to invoke is determined at compile time and the invo- cation is typechecked at compile time
iv
3. (2 points each) Circle all answers that are true for each question.
(a) Which functions always return a list of length less than or equal to that of the argument
list?
i. List.map
ii. List.filter
iii. List.fold right iv. none of the above
i and ii
(b) Which functions always return a list of the same type as the argument list?
i. List.map
ii. List.filter
iii. List.fold right
iv. none of the above ii
(c) Which functions always return a list?
i. List.map
ii. List.filter
iii. List.fold right iv. none of the above
i and ii
(d) Which functions never return a list?
i. List.map
ii. List.filter
iii. List.fold right iv. none of the above
iv
4. (5 points) Implement count from Problem 1 again, but this time using a single call to List.fold right instead of explicit recursion.
let count e lst =
List.fold_right (fun x curr -> (if x=e then 1 else 0) + curr) lst 0
5. (2 points each) Circle the best answer.
(a) What are the advantages of static typechecking over dynamic typechecking?
i. earlier error checking
ii. each function body can be typechecked once, for all possible callers
iii. static typechecking never signals a false error iv. the first two answers above
v. the first three answers above vi. none of the above
iv
(b) What are the advantages of dynamic typechecking over static typechecking?
i. earlier error checking
ii. each function body can be typechecked once, for all possible callers
iii. dynamic typechecking never signals a false error iv. the second and third answers above
v. the first three answers above vi. none of the above
iii
(c) OCaml is considered statically typed because:
i. the majority of its typechecking is done at compile time ii. it never allows type errors to occur at run time
iii. the value of a variable never changes after initialization
iv. a well-typed program can never raise an exception at run time
i
(d) C is considered weakly typed because:
i. it does not support polymorphism
ii. it does not prevent array bounds violations
iii. it performs some typechecking at run time iv. it does not support type inference
ii
6. (2 points each)
Assume the following OCaml declarations have been entered in this order into the OCaml interpreter:
let x = 3;;
let f y = x + y;;
let x = 4;;
Give the value of each expression below, or say ¡°error¡± if it would cause a static or dynamic error.
(a) f
8
(b) f
7
(c) f 9
5
x
5, assuming OCaml used dynamic scoping
7. (2 points each)
Assume the following OCaml declarations have been entered in this order into the OCaml interpreter:
let g x y = x + y;;
let f = g 3;;
let y = 2;;
Give the value of each expression below, or say ¡°error¡± if it would cause a run-time error.
(a) f 5 8
(b) f x error
(c) f 5, assuming OCaml used dynamic scoping error
8. (2 points)
(a) Each (b) Each (c) Each (d) Each
Which is the best definition of static scoping?
variable usage can be bound to its associated declaration at compile time. variable¡¯s lifetime can be determined at compile time.
variable usage can be bound to its associated value at compile time. variable¡¯s value never changes after initialization
i
9. (5 points each) (Continues on the next page) Here¡¯s a simple signature for modules that implement a counter abstraction:
module type COUNTER = sig
type counter
val init : counter
val increment : counter -> counter val value : counter -> int
val reset : counter -> counter end
The value init is a counter initialized to zero. The function increment increments the given counter by one, value returns the number of times the counter has been incremented (since last being reset), and reset resets the given counter.
(a) Complete the following implementation of the COUNTER signature, in which the counter type is just a synonym for int:
module Counter : COUNTER = struct
type counter = int
(* provide implementations of init, increment, value, reset *)
let init = 0
let increment c = c + 1 let value c = c
let reset c = 0
end
(b) Complete the following implementation of the COUNTER signature, in which the counter type is a datatype that explicitly represents each increment of the counter (e.g., Inc(Inc Zero) denotes the counter value 2):
module Counter : COUNTER = struct
type counter = Zero | Inc of counter
(* provide implementations of init, increment, value, reset *)
let init = Zero
let increment c = Inc c
let rec value c = match c with
Zero -> 0
Inc c1 -> 1 + (value c1)
let reset = Zero
end
10. (2 points) Circle all answers that apply. Hiding the definition of the type counter (see the previous problem) provides which of the following benefits for the Counter module?
(a) It allows the definition of counter to be later changed without breaking clients of the module
(b) It enables strong, static typechecking of the module
(c) It ensures that clients can only modify a counter¡¯s value via the provided operations
(d) It increases efficiency at run time
i and iii
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