Reference no: EM133257882

Use Ocaml 

Fractions

Defined a type synonym for fractional value as followed:

type fraction = int * int

Also here is a function add to add fractions. An abbreviated version of the function from class is shown below:

let add ((n1,d1) : fraction) ((n2,d2) : fraction) : fraction =
 (n1 * d2 + n2 * d1, d1 * d2)

Write a function named mul with the same type as add that will multiply two fractional values.

For example:

• mul (2,1) (3,1) evaluates to (6,1)
• mul (2,3) (3,4) evaluates to (6,12)

Next, write a function named simplify that takes a fraction as input and returns the reduced version that is mathematically equivalent but with the property that the only common divisor of the numerator and denominator is 1.

For example:

• simplify (2,6) evaluates to (1,3)
• simplify (1,4) evaluates to (1,4)
• simplify (2,3) evaluates to (2,3)
• simplify (mul (2,3) (3,4)) evaluates to (1,2)

If you use any functions that we developed in class to solve this problem then provide proper attribution in a comment.

Note that add and mul do not simplify their results, that task is left to simplify.

Tuples and Lists

Write a function compute_lengths that takes a list of strings as input and returns a list in which each string is paired with its length (as computed by String.length).

For example

• compute_lengths [ "Hello"; "Hi"; "" ] evaluates to [ ("Hello", 5); ("Hi", 2); ("", 0) ])
• compute_lengths [ ] evaluates to [ ]

Next, write a function named make_strings that takes a list of type (char * int) list and returns a string list in which for each pair in the list c and i a string is constructed by repeating the character c, i times. Experiment with the function String.make to see how to use it for this purpose.

For example

• make_strings [ ] evaluates to [ ]
• make_strings [ ('a', 3); ('x', 0); ('4', 4) ] evaluates to [ "aaa"; ""; "4444" ]

Points, distances, triangles, and perimeters

To represent geometric points on a 2-dimentional plane we may define the following type synonym:

type point = float * float

The first element of the pair indicates a point's position on the x-axis and the second, its position on the y-axis.

Define a function distance of type

 point -> point -> float

that computes the distance between the 2 input points. You may find the functions Float.abs and Float.sqrt to be useful. Again, experiment with them in utop to fully understand their behavior.

For example:

• distance (1.0, 1.0) (2.0, 2.0)) evaluates to 1.414
• distance (2.0, 2.0) (1.0, 1.0) evaluates to 1.414
• distance (1.0, 1.0) (3.0, 3.0) evaluates to 2.828
• distance (2.0, 3.5) (0.2, 4.5) evaluates to 2.059
• distance (-1.0, -1.0) (0.0, 0.0) evaluates to 1.414

Next, we define a type synonym for triangles as being a triple of 3 points as follows:

type triangle = point * point * point

Now write a function named perimeter that computes the perimeter of a triangle. This is the distance "all the way around" the triangle and can be implemented by adding the distance between all 3 pairs of connected points in the triangle.

For example:

• eqf (perimeter ((1.0, 1.0), (3.0, 1.0), (3.0, 3.0))) 6.828 evaluates to true
• eqf (perimeter ((1.0, 1.0), (3.0, 2.0), (2.0, 3.0))) 5.886 evaluates to true

Finally, write a function named triangle_perimeters that computes a list of perimeters when given a list of triangles. Feel free to use the perimeter function you just implemented.

For example:

• triangle_perimeters [ ((1.0, 1.0), (3.0, 1.0), (3.0, 3.0)); ((1.0, 1.0), (3.0, 2.0), (2.0, 3.0)) ] evaluates to [ 6.828; 5.886 ]