2013-04-23-book-problems.md

Haskell

Day 1: Logical

Find

• The Haskell wiki

• A Haskell online group supporting your compiler of choice

  GHCI

Do

• How many different ways can you find to write allEven?

• Write a function that takes a list and returns the same list in reverse.

• Write a function that builds two-tuples with all possible combinations of two of the colors black, white, blue, yellow, and red. Note that you should include only one of (black, blue) and (blue, black).

• Write a list comprehension to build a childhood multiplication table. The table would be a list of three-tuples where the first two are integers from 1–12 and the third is the product of the first two.

• Solve the map-coloring problem using Haskell.

  In Prolog

  different(red, green). different(red, blue).
  different(green, red). different(green, blue).
  different(blue, red). different(blue, green).
  
  coloring(Alabama, Mississippi, Georgia, Tennessee, Florida) :- 
    different(Mississippi, Tennessee),
    different(Mississippi, Alabama),
    different(Alabama, Tennessee),
    different(Alabama, Mississippi),
    different(Alabama, Georgia),
    different(Alabama, Florida),
    different(Georgia, Florida),
    different(Georgia, Tennessee).

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Day 2: Spock's Great Strength

Find

• Functions that you can use on lists, strings, or tuples

  List String Tuple

• A way to sort lists

  sort sortBy

Do

• Write a sort that takes a list and returns a sorted list.
• Write a sort that takes a list and a function that compares its two argu- ments and then returns a sorted list.
• Write a Haskell function to convert a string to a number. The string should be in the form of $2,345,678.99 and can possibly have leading zeros.
• Write a function that takes an argument x and returns a lazy sequence that has every third number, starting with x. Then, write a function that includes every fifth number, beginning with y. Combine these functions through composition to return every eighth number, beginning with x + y.
• Use a partially applied function to define a function that will return half of a number and another that will append \n to the end of any string.

Bonus

• Write a function to determine the greatest common denominator of two integers.
• Create a lazy sequence of prime numbers.
• Break a long string into individual lines at proper word boundaries.
• Add line numbers to the previous exercise.
• To the above exercise, add functions to left, right, and fully justify the text with spaces (making both margins straight).