====Objective:====

Learn the basics of the Julia Language.

----

====Preparation:====

For this lab, you should use at least Julia v.0.4.  You may use the binary hosted in Dr. Wingate's home directory, at

''/users/faculty/wingated/cs330/languages/julia-2e358ce975/bin''

or you may install Julia yourself.

----

====Deliverables:====

For this lab, you will need to implement the following functions and data structures in Julia:
  * ''area''
  * ''in_shape''
  * ''greyscale''
  * ''invert''
  * ''count_person''
  * ''average_age''
  * ''tree_map''
  * ''add_last_name''
  * ''eye_colors''



=== Shapes ===
Define the following data structures.
<code Julia>
abstract Shape

type Position
  x::Real
  y::Real
end

type Circ <: Shape
  center::Position
  radius::Real
end

type Square <: Shape
  upper_left::Position
  length::Real
end

type Rect <: Shape
  upper_left::Position
  width::Real
  height::Real
end
</code>


=== Area ===
<code Julia>
function area(shape) ...
</code>
Returns the area of the given shape.
where ''Shape'' is some concrete instance of the abstract shape type class. For this a few of the following instead of testing for class member ship it is easier to write three different functions, one for each concrete instance of shape. ie: ''function area(shape::rect)...''

=== In_Shape===
<code Julia>
function in_shape(shape::Shape, position::Position) ...
</code>
Returns if the position is inside the shape. Assume standard math coordinates where y is positive going up. The bounds are inclusive.

=== Pixel ===
Define the Following type in your code
<code Julia>
type Pixel
  r::Real
  g::Real
  b::Real
end
</code>

=== Greyscale ==
<code Julia>
function greyscale(picture::Array{Pixel,2}) ...
</code>
Takes a 2d array of pixels and greys out each pixel. This is done by averaging together the r g b values and then setting r g b to the average.

Hint: Julias map works over  multi-dimensional arrays

=== invert ===
<code Julia>
function invert(picture::Array{Pixel,2}) ...
</code>
Takes a 2d array and pixels and inverts each one. Inverting is done by setting r to `255 - r` and the other two in the same manner.

=== Trees ==
Define the following types in your code
<code Julia>
abstract TreeItem

type Person <: TreeItem
  name::AbstractString
  birthyear::Integer
  eyecolor::Symbol
  father::TreeItem
  mother::TreeItem
end
 
type Unknown <: TreeItem
end
</code>

=== Count Persons ===
<code Julia>
function count_persons(tree)
</code>
Counts the number of people in the tree. Unknowns do not count as people.

=== Average Age ===
<code Julia> 
function average_age(tree)
</code>
Calculates the average age of the people in the tree. Use this years date 2017. Unknowns do not count as people.

=== tree map ===
<code Julia>
function tree_map(f, tree)
</code>
Takes a function f and applies it to each known member of the tree. The function f takes one parameter and returns a treeItem. Tree_map will return a *new* tree. Tree_map should leave the original tree unchanged, unless f applies a mutation.

=== add last name===
<code Julia>
function add_last_name(name::AbstractString, tree)
</code>
Appends name to the end of the name of each member of the tree. You should use tree_map. You do not need to add a space in front of the name.

Hint: Julia uses ''*'' for string concatenation.

=== eye_colors ===
<code Julia>
function eye_colors(tree)
</code>
Returns a list of all eye colors in the tree. A color can appear more than once. For grading visit the order child, father, mother.

hint: Julia arrays can be appended using the ; for example [a;b;c] will create a list with a, b, and c in it. The empty list [] is ignored.