CS 291 Assignment #3

Introduction:

The Assignment

1. Define the function subsequence of type Eq a => [a] -> [a] -> Bool. It should return True if the first list of items is found in consecutive positions anywhere within the second list. For example:

   > subsequence [] [1,2,3]
   True
   > subsequence [1,2,3] []
   False
   > subsequence ['a', 'b'] ['a','b','c']
   True
   > subsequence [3,4] [1,2,3,4,5,6]
   True
   > subsequence [3,4] [1,2,3,5,4,6]
   False
   

2. Define the function sameOutput with type Integral a => (a -> a) -> (a -> a) -> a -> a -> Bool. It should take two input functions, both of which map integers to integers, and check to see if they return the same outputs for all input values within a specific range of integers. (The third and fourth arguments to sameOutput specify the range of integers to be checked.) For example, the first test below asks whether the identity function and the function that squares its argument return the same output for all integer values from 0 to 1. (They do.)

   > sameOutput (\x->x) (\x->x*x) 0 1
   True
   > sameOutput (\x->x) (\x->x*x) 0 10
   False
   > sameOutput ((+1).abs) (+1) 0 100
   True
   > sameOutput ((+1).abs) (+1) (-100) 100
   False
   

3. Define the function makeLoudVersion that takes a one-argument function as its input and returns a "loud" version of the function that maps inputs to strings as shown below. More specifically, if the input function is of type a -> b, the output function is of type a -> [Char] where the output string includes both the input and the output from the original function.

   > makeLoudVersion (+2)
   ERROR - Cannot find "show" function for:
   *** Expression : makeLoudVersion (flip (+) 2)
   *** Of type    : Integer -> [Char]
   
   > (makeLoudVersion (+2)) 5
   "fn (5) --> 7"
   > (makeLoudVersion length) [1,2,3]
   "fn ([1,2,3]) --> 3"
   > map (makeLoudVersion (+2)) [1,2,3,4]
   ["fn (1) --> 3","fn (2) --> 4","fn (3) --> 5","fn (4) --> 6"]
   

4. Define the function phoneSpell of type [Int] -> [[Char]]. It takes a list of integers as its input, and generates all possible "words" corresponding to those numbers given the standard phone keypad mapping of letters onto the number keys. (Keys 0 and 1 have no letters, all others have three letters except 7 and 9, which have four each.) Think recursively! For example, on the [8,7,9] input below, think about what phoneSpell [7,9] would give you, and how you'd patch that up to be the right answer for [8,7,9]. You might also want to use things like map, foldr1, etc., in your solution.

   > phoneSpell []
   []
   > phoneSpell [2]
   ["a","b","c"]
   > phoneSpell [2,9]
   ["aw","bw","cw","ax","bx","cx","ay","by","cy","az","bz","cz"]
   > phoneSpell [2,0,6]
   ["am","bm","cm","an","bn","cn","ao","bo","co"]
   > phoneSpell [8,7,9]
   ["tpw","upw","vpw","tqw","uqw","vqw","trw","urw","vrw","tsw","usw","vsw","tpx",
   "upx","vpx","tqx","uqx","vqx","trx","urx","vrx","tsx","usx","vsx","tpy","upy",
   "vpy","tqy","uqy","vqy","try","ury","vry","tsy","usy","vsy","tpz","upz","vpz",
   "tqz","uqz","vqz","trz","urz","vrz","tsz","usz","vsz"]
   > phoneSpell [2,1,0,5]
   ["aj","bj","cj","ak","bk","ck","al","bl","cl"]
   > length (phoneSpell [8,7,9,3,5,7,9])
   6912
   

Submitting: