{{ solutions }}
{{ ex1 | replace("%%NAME%%", "mutable fields")}}
Define an OCaml record type to represent student names and GPAs. It should be
possible to mutate the value of a student's GPA. Write an expression defining a
student with name "Alice"
and GPA 3.7
. Then write an expression to mutate
Alice's GPA to 4.0
.
{{ ex1 | replace("%%NAME%%", "refs")}}
Give OCaml expressions that have the following types. Use utop to check your answers.
bool ref
int list ref
int ref list
{{ ex1 | replace("%%NAME%%", "inc fun")}}
Define a reference to a function as follows:
let inc = ref (fun x -> x + 1)
Write code that uses inc
to produce the value 3110
.
{{ ex2 | replace("%%NAME%%", "addition assignment")}}
The C language and many languages derived from it, such as Java, has an
addition assignment operator written a += b
and meaning a = a + b
.
Implement such an operator in OCaml; its type should be
int ref -> int -> unit
. Here's some code to get you started:
let ( +:= ) x y = ...
And here's an example usage:
# let x = ref 0;;
# x +:= 3110;;
# !x;;
- : int = 3110
{{ ex2 | replace("%%NAME%%", "physical equality")}}
Define x
, y
, and z
as follows:
let x = ref 0
let y = x
let z = ref 0
Predict the value of the following series of expressions:
# x == y;;
# x == z;;
# x = y;;
# x = z;;
# x := 1;;
# x = y;;
# x = z;;
Check your answers in utop.
{{ ex2 | replace("%%NAME%%", "norm")}}
The Euclidean norm of an
Write a function norm : vector -> float
that computes the
Euclidean norm of a vector, where vector
is defined as follows:
(* AF: the float array [| x1; ...; xn |] represents the
* vector (x1, ..., xn)
* RI: the array is non-empty *)
type vector = float array
Your function should not mutate the input array. Hint: although your first
instinct might be to reach for a loop, instead try to use Array.map
and
Array.fold_left
or Array.fold_right
.
{{ ex2 | replace("%%NAME%%", "normalize")}}
Every vector can be normalized by dividing each component by
Write a function normalize : vector -> unit
that normalizes a vector "in
place" by mutating the input array. Here's a sample usage:
# let a = [|1.; 1.|];;
val a : float array = [|1.; 1.|]
# normalize a;;
- : unit = ()
# a;;
- : float array = [|0.7071...; 0.7071...|]
Hint: Array.iteri
.
{{ ex2 | replace("%%NAME%%", "norm loop")}}
Modify your implementation of norm
to use a loop. Here is pseudocode for what
you should do:
initialize norm to 0.0
loop through array
add to norm the square of the current array component
return sqrt of norm
{{ ex2 | replace("%%NAME%%", "normalize loop")}}
Modify your implementation of normalize
to use a loop.
{{ ex3 | replace("%%NAME%%", "init matrix")}}
The Array
module contains two functions for creating an array: make
and
init
. make
creates an array and fills it with a default value, while init
creates an array and uses a provided function to fill it in. The library also
contains a function make_matrix
for creating a two-dimensional array, but it
does not contain an analogous init_matrix
to create a matrix using a function
for initialization.
Write a function init_matrix : int -> int -> (int -> int -> 'a) -> 'a array array
such that init_matrix n o f
creates and returns an n
by o
matrix
m
with m.(i).(j) = f i j
for all i
and j
in bounds.
See the documentation for make_matrix
for more information on the
representation of matrices as arrays.
{{ ex4 | replace("%%NAME%%", "doubly linked list")}}
Implement a data abstraction for a mutable doubly-linked list. Here is a representation type to get you started:
(** An ['a node] is a node of a mutable doubly-linked list.
It contains a value of type ['a] and optionally has
pointers to previous and/or next nodes. *)
type 'a node = {
mutable prev : 'a node option;
mutable next : 'a node option;
value : 'a
}
(** An ['a dlist] is a mutable doubly-linked list with elements
of type ['a]. It is possible to access the first and
last elements in constant time.
RI: The list does not contain any cycles. *)
type 'a dlist = {
mutable first : 'a node option;
mutable last : 'a node option;
}
Implement at least these operations:
- create an empty list
- insert a new first value
- insert a new last value
- insert a new node after a given node
- insert a new node before a given node
- remove a node
- iterate forward through the list applying a function
- iterate backward through the list applying a function
Hint: draw pictures! Reasoning about mutable data structures is typically easier if you draw a picture.