COSC 341 HW 1017 SOLUTIONS "More Haskell Exercises"

Question 1:
1. f a b = a ^ b

1. A. Show the blackbox and arrow description of the currying.

1. B. Explicitly give partially applied definitions for

      f 2 3

               f
  a    |-----------------|
-----> |                 |
       |        (f a)    |
  b    |       |-----|   |
-------|-----> |     |   |
       |       |     |---|--->  
       |       |     |   |
       |       -------   |
       |-----------------|
       
Code -- following the example of *Learn You a Haskell*, pp 60-61

f a b =
   a ^ b
   
For the function call f 2 3, the implicitly defined (curried) function is

f2 = f 2

Copy of GHCI interpretation:
*Main> f 2 3
8
*Main> f2 3
8


/****************************************************************************/

Question 2:
2. g a b c = a ^ b / c

2. A. Show the blackbox and arrow description of the currying.

2. B. Explicitly give partially applied definitions for

         g 2 3 4
         
               g
  a    |---------------------------------|
-----> |                                 |
       |        (g a)                    |
  b    |       |-------------------|     |
-------|-----> |                   |     |
       |       |                   |     |
       |       |       (g a b)     |     |
  c    |       |     |---------|   |     |
-------|-------|---->|         |   |     |
       |       |     |         |---|-----|---->
       |       |     |---------|   |     |
       |       |                   |     |
       |       |-------------------|     |
       |---------------------------------|
       

Code -- again, following the example of *Learn you a Haskell*, pp 60 - 61:

g a b c =
   a ^ b / c
   
g2' = g 2

g23' = g2' 3    --   AKA ( (g 2) 3 )
                
 Copy of GHCI interpretation:
 
*Main> g 2 3 4
2.0
*Main> g2' 3 4
2.0
*Main> g23' 4
2.0

/***************************************************************************/

Question 3:
3. disc a b c =
     b ^ 2 - 4 * a * c
  
3. A. Show the blackbox and arrow description of the currying.
   
3. B. Explicitly give partially applied definitions for 
  
        disc 1 2 1

         
               disc
  a    |---------------------------------|
-----> |                                 |
       |        (disc a)                 |
  b    |       |-------------------|     |
-------|-----> |                   |     |
       |       |                   |     |
       |       |      (disc a b)   |     |
  c    |       |     |---------|   |     |
-------|-------|---->|         |   |     |
       |       |     |         |---|-----|---->
       |       |     |---------|   |     |
       |       |                   |     |
       |       |-------------------|     |
       |---------------------------------|   
       
Code:  following the example of *Learn you a Haskell* pp 60-61.

disc a b c =
   (b ^ 2) - (4 * a * c)
   
disc1 = disc 1 

disc12 = disc1 2 


Copy of GHCI interpretation:
*Main> disc 1 2 1
0
*Main> disc1 2 1
0
*Main> disc12 1
0
    
   
Redo-ing 3B with different parameters, producing explicit code in the manner
of *Learn you a Haskell*, pp 60-61.
    disc 2 3 4

disc a b c =
   (b ^ 2) - (4 * a * c)
   
disc2 = disc 2

disc23 = disc2 3 
 
    
Copy of GHCI interpretation:    
*Main> disc 2 3 4
-23
*Main> disc2 3 4
-23
*Main> disc23  4
-23
    
/**************************************************************************/

Question 4:
4. A. Give a function that uses list comprehension to implement the
map function. Your function is named map'

4. B. Demonstrate your map' works on
map' (3:) [ [], [2, 4], [1, 2, 3, 4] ]
map' (++ "!") ["abc", "XYZ"]

map' fun li =
   [ fun x | x <- li ]
   
GHCI interpreter:

*Main> map' (3:) [ [], [2, 3], [1, 2, 3, 4] ]
[[3],[3,2,3],[3,1,2,3,4]]
*Main> map' (++ "!") ["abc", "XYZ"]
["abc!","XYZ!"]
*Main> 


/**************************************************************************/

Question 5:
5. A. Give a function using list comprehension and predicates to implement
the filter function. Your function is named filter'

5. B. Demonstrate your filter' works on
filter' (>3) [4, 2, 5, 1, 7]
filter' (`elem` ['a'..'z']) "What Planet Is THIS?"

CODE:
filter' pred li =
	[ x | x <- li, (pred x) == True ]


GHCI interpreter:

*Main> filter' (>3) [4, 2, 5, 1, 7]
[4,5,7]
*Main> filter' (`elem` ['a'..'z']) "What Planet Is THIS?"
"hatlanets"
*Main>