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pp:l02 [2021/03/13 14:10]
roxana_elena.stiuca changed 27 to be able to use copy-paste on code 		pp:l02 [2021/03/16 19:24] (current)
roxana_elena.stiuca [2.3. Strings in Haskell]
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 ====== 2. Pattern matching and basic types in Haskell ====== ====== 2. Pattern matching and basic types in Haskell ======
  
-21. Extract the fourth element from a list of integers +===== 2.1. Pattern matching =====
- +
-22. Write the same function which returns 0 if the list contains less that four elements and 0 otherwise. +
- +
-===== Pattern matching =====+
  
 It is likely that in the above implementations you used ''​head''​ and ''​tail'',​ or branch definitions combined with '​_'​ to solve the exercises. Haskell supports a more elegant means of //value introspection//,​ called **pattern matching**. For instance, in: It is likely that in the above implementations you used ''​head''​ and ''​tail'',​ or branch definitions combined with '​_'​ to solve the exercises. Haskell supports a more elegant means of //value introspection//,​ called **pattern matching**. For instance, in:
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 ''​(h:​t)''​ is a **pattern** which denotes a non-empty list where ''​h''​ is the first element and ''​t''​ is the rest of the list. In fact, ''​[]''​ is also a pattern denoting the empty lists. Patterns are **allways** surrounded by round parentheses. They can also be composite, as in the exercise below: ''​(h:​t)''​ is a **pattern** which denotes a non-empty list where ''​h''​ is the first element and ''​t''​ is the rest of the list. In fact, ''​[]''​ is also a pattern denoting the empty lists. Patterns are **allways** surrounded by round parentheses. They can also be composite, as in the exercise below:
  
-23. What are the types of ''​x,​y,​z,​w''​ and that of ''​l''​ in the implementation below?+2.1.1. Write a function which returns the number of elements from a list. Use patterns. 
 + 
 +2.1.2. Write a function which takes a list of integer lists, and concatenates them. (E.g. ''​f [ [1,​2,​3],​[4,​5] ] = [1,​2,​3,​4,​5]''​). 
 + 
 +2.1.3 (!) Write the **same** function, this time using only the **cons** ('':''​) operator as well as **patterns**.  
 + 
 +2.1.4. Write a function which removes duplicates from a list of integers. 
 + 
 +===== 2.2. Types in Haskell ===== 
 + 
 +2.2.1. What are the types of ''​x,​y,​z,​w''​ and that of ''​l''​ in the implementation below?
 <code haskell> <code haskell>
 f (x:y:z:w:l) = w f (x:y:z:w:l) = w
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 What is the difference? What is the difference?
     ​     ​
- +2.2.2. What is the type of the function:
-24. Write a function which filters out all negative numbers from a list. Use patterns. +
- +
-25. What is the type of the function:+
 <code haskell> <code haskell>
 f x y = (x,y) f x y = (x,y)
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 In the body of a function definition, '',''​ is a **base constructor** for pairs. The following are pairs: ''​(1,​2),​ ("​Matei",​20),​ ([1,​2],​3)''​. Note that there is no restriction on the type of the first and second values of a pair.  In the body of a function definition, '',''​ is a **base constructor** for pairs. The following are pairs: ''​(1,​2),​ ("​Matei",​20),​ ([1,​2],​3)''​. Note that there is no restriction on the type of the first and second values of a pair. 
  
-26. What is the type of the function:+2.2.3. What is the type of the function:
 <code haskell> <code haskell>
 f '​a'​ _ = [] f '​a'​ _ = []
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 In Haskell, the type ''​String''​ is equivalent to ''​[Char]''​ (hence strings are lists of chars). Strings can be introspected using patterns just like any other list. In Haskell, the type ''​String''​ is equivalent to ''​[Char]''​ (hence strings are lists of chars). Strings can be introspected using patterns just like any other list.
  
-27. Let f be the function below:+2.2.4. Let f be the function below:
 <code haskell> <code haskell>
     f "​321CB"​ [("​321CB",​ ["​Matei",​ "​Andrei",​ "​Mihai"​]),​ ("​322CB",​["​George",​ "​Matei"​])] = ["​Matei",​ "​Mihai"​]     f "​321CB"​ [("​321CB",​ ["​Matei",​ "​Andrei",​ "​Mihai"​]),​ ("​322CB",​["​George",​ "​Matei"​])] = ["​Matei",​ "​Mihai"​]
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 What is the signature of ''​f''?​ What is the signature of ''​f''?​
  
-What does ''​f''​ do (note that ''​Matei''​ and ''​Mihai''​ both start with letter '​M'​)?​ 
  
-Write an implementation for ''​f''​.+===== 2.3. Strings in Haskell =====
  
-28. Write a function which returns ''​True''​ if the third largest element from a list is positive+2.3.1. Write a function which takes a list of words and makes the first letter of each word uppercase.
  
-===== Function composition and function ​application =====+2.3.2. Write a function ​which takes a list of words and makes **all** letters uppercase.
  
-29. Sometimes it really helps to define function via function ​composition. For instance: +2.3.3. (!) Write a function ​which takes a text and a pattern and returns the number of occurrences of the pattern in the text.  
-<code haskell>​ +Example: 
-f x = (g.h) x +<code haskell>  
- where g x = 2*x +search "I eat green apples"​ "​eat" ​= 1 
-       h x = x + 1+search "​ababaab"​ "​aba" ​= 2
 </​code>​ </​code>​
  
-What type does f have? +2.3.4. (!) What does ''​f'',​ defined in exercise 2.2.4., do (note that ''​Matei''​ and ''​Mihai''​ both start with letter '​M'​)? Write an implementation for ''​f''​.
-What type does g have?+
  
-What does the following function do? +2.3.5. Write the signature and implement the following function:
- +
-<code haskell>​ +
-f x = ff x +
- where g x = 2*x +
-       h x = x + 1 +
-       ff = f.h +
-</​code>​ +
-What does the following function do? +
-<code haskell>​ +
-f x = ff x +
- where g x = 2*x +
-       h x = x + 1 +
-       ff = h.f +
-</​code>​ +
- +
-30. Rewrite exercise 28 via function composition:​ +
-<code haskell>​ +
-f l =  +
-</​code>​ +
- +
-31. Write a function which takes a list of pairs - student-name and grade, removes those with grades less than 5, splits the name in substrings, and adds one bonus point to people with three names. Example: +
-<code haskell>​ +
-    f [("Dan Matei Popovici",​9),​("​Mihai",​4),​("​Andrei Alex",​6)] = +
-    [(["​Dan",​ "​Matei",​ "​Popovici"​],​10),​(["​Andrei,​Alex"​],​6)] +
-</​code>​ +
- +
-32. Write the signature and implement the following function:+
 <code haskell> <code haskell>
    f ["​Matei",​ "​Mihai"​] ["​Popovici","​Dumitru"​] = [("​Matei","​Popovici"​),​ ("​Mihai","​Dumitru"​)]    f ["​Matei",​ "​Mihai"​] ["​Popovici","​Dumitru"​] = [("​Matei","​Popovici"​),​ ("​Mihai","​Dumitru"​)]
 </​code>​ </​code>​
  
-33. Implement the following function:+2.3.6. Implement the following function:
 <code haskell> <code haskell>
    f ["​Matei",​ "​Mihai"​] ["​Popovici","​Dumitru"​] = ["​MPopovici",​ "​MDumitru"​]    f ["​Matei",​ "​Mihai"​] ["​Popovici","​Dumitru"​] = ["​MPopovici",​ "​MDumitru"​]
 </​code>​ </​code>​
  
-34. Sometimes it helps to use functions in infix form. For instance, instead of ''​mod x 2'',​ we can write ''​x `mod` 2''​. We can also define infix functions:​ +2.3.7. Write a function ​which takes a list of pairs - student-name and grade, removes those with grades less than 5, splits ​the name in substrings, and adds one bonus point to people with three names. Example:
- +
-   x '​f'​ y = x + y +
- +
-Implement ​a function ​for transforming lists into pairs, ​in exercise 32. and use it in the infix form. +
- +
-35. Just in the same way, we can treat infix functions as prefix. We do this using round parentheses. Test:+
 <code haskell> <code haskell>
- :t (+) +    f [("Dan Matei Popovici",​9),("​Mihai",​4),​("​Andrei Alex",​6)] = 
- :t (&&) +    ​ [(["​Dan",​ "​Matei",​ "​Popovici"​],​10),​(["​Andrei",​ "​Alex"​],​6)]
- :t (++)+
 </​code>​ </​code>​
  
-36. What about function composition?​ Is it a special operator, or is it just a function as well? What does '':​t (.)''​ do? 
  
-37. What does the function below do? Take parts of the function below, and test them. 
-<code haskell> 
-f l = (((++) "?"​).((:​) '>'​)) l 
-</​code>​ 
  
-How about? 
-<code haskell> 
-f = (((:) '>'​).(++"?"​)) 
-</​code>​ 
- 
-38. Write a function of a single line, such that: 
-<code haskell> 
-f "​Matei"​ = "​{Matei}"​ 
-</​code>​ 
- 
-39. Use only ''​(:​)'',​ ''​reverse''​ and functional composition ''​.''​ to solve exercise 38  
- 
-40. What does the function ''​($)''​ to?  
-    (Use :t, and make up some tests) 
- 
-41. Write the following implementation using only ($): 
-<code haskell> 
-f "​||"​ "​Matei"​ = "​||Matei||"​ 
-</​code>​ 
  
-42.  Solve exercise 13. from [[pp:​l02|Lab 2]] using ''​$''​ (''​++''​ and ''​reverse''​ are also permitted) and other improvements (treat the case when the list has fewer elements):