MI-AFP homework #05

Homework to practice advanced work with typeclasses

Task

1. You've already done some implementation of area and circumference for various shapes in the third homework. Now you will do something similar, but using typeclasses in Data.Shapes!
   • First, implement instances of Validable for each shape type with function valid that says if given shape is valid (its attributes are acceptable, i.e., not negative, forming a triangle).
   • Then, design on your own the Shape2D typeclass which is a subclass of Validable, define area and circumference (remove dummy ones). During the design consider using valid - for invalid shape, both functions should return zero.
   • Finally, implement instances of Shape2D for each shape type.
2. Data.SortedList = implement all necessary functions to make data type SortedList to be an instance of Semigroup, Monoid, Functor, Applicative, Monad. After applying (<>) the resulting list must be sorted. Sadly, Functor, Applicative, and Monad won't allow you to use Ord constaint so the result won't be sorted. Implement some sort function if you want to... It is forbidden to just delegate to list and use fromList and toList.
3. The final (and also the most interesting) task is to implement functions and instances for next data type to represent integers - the RomanNumeral (from Data.RomanNumeral)! It is a representation of an integer as Roman numeral, for example, 125 is "CXXV".
   • The biggest challenge is to implement functions integral2RomanNumeral and romanNumeral2Integral (related with pack and unpack). There is something already prepared in Data.RomanNumeral.Helpers. Take a look and feel free to edit as you need.
   • After having pack and unpack working, it will be very easy to make instances of Bounded, Eq, Ord, Num, Enum, and Integral (you might need some more due to dependencies) for the RomanNumeral.

Hints & general requirements:

• You should not hardcode any string or character in Data.RomanNumeral - use only those defined in Data.RomanNumeral.Helpers or enhance it.
• Being DRY is essential, do not repeat code. Name expressions to reuse then, introduce helper functions.
• Local names (via where or let-in) in functions should be introduced to make the code more readable. Creating very simple helper functions in module scope is not nice. If you need some complicated functions create separate "private" module.
• Make your code as clean as possible. Prefer pattern matching and syntactic sugar everywhere it is reasonable.
• You must understand your code completely!

Notes

• If you encounter some trouble, create an issue in your repository.
• In case you find a bug or have an idea how to improve assignment project, create an issue or PR in this repository.
• It might happen that tests are not 100% bulletproof, but your solution should be correct. If you want, propose tests enhancements.

License

This project is licensed under the MIT License - see the LICENSE file for more details.