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--- pp:l02 [2020/03/23 15:04]
pdmatei [Function composition and function application]
+++ pp:l02 [2021/03/16 19:24] (current)
roxana_elena.stiuca [2.3. Strings in Haskell]
@@ Line 1: / Line 1: @@
-====== Pattern matching and basic types in Haskell ======
+====== 2. Pattern matching and basic types in Haskell ======
-. Extract the fourth element from a list of integers
+===== 2.1. Pattern matching =====
-. 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:
@@ Line 16: / Line 12: @@
 ''(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:
-. What are the types of ''x,y,z,w'' and that of ''l'' in the implementation below?
+.1.1. Write a function which returns the number of elements from a list. Use patterns.
+.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]'').
+.1.3 (!) Write the **same** function, this time using only the **cons** ('':'') operator as well as **patterns**.
+.1.4. Write a function which removes duplicates from a list of integers.
+===== 2.2. Types in Haskell =====
+.2.1. What are the types of ''x,y,z,w'' and that of ''l'' in the implementation below?
 <code haskell>
 f (x:y:z:w:l) = w
@@ Line 28: / Line 34: @@
 What is the difference?
+.2.2. What is the type of the function:
-. Write a function which filters out all negative numbers from a list. Use patterns.
-. What is the type of the function:
 <code haskell>
 f x y = (x,y)
@@ Line 38: / Line 41: @@
 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.
-. What is the type of the function:
+.2.3. What is the type of the function:
 <code haskell>
 f 'a' _ = []
@@ Line 46: / Line 49: @@
 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.
-. Let ''f "321CB" [("321CB", ["Matei", "Andrei", "Mihai"]), ("322CB",["George, Matei"])] = ["Matei", "Mihai"]''
+.2.4. Let f be the function below:
+<code haskell>
+    f "321CB" [("321CB", ["Matei", "Andrei", "Mihai"]), ("322CB",["George", "Matei"])] = ["Matei", "Mihai"]
+</code>
 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 =====
-. Write a function which returns ''True'' if the third largest element from a list is positive
+.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 =====
+.3.2. Write a function which takes a list of words and makes **all** letters uppercase.
-. Sometimes it really helps to define function via function composition. For instance:
+.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>
-What type does f have?
+.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?
+.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>
-. Rewrite exercise 28 via function composition:
-<code haskell>
-f l =
-</code>
-. 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>
-. Write the signature and implement the following function:
 <code haskell>
    f ["Matei", "Mihai"] ["Popovici","Dumitru"] = [("Matei","Popovici"), ("Mihai","Dumitru")]
 </code>
-. Implement the following function:
+.3.6. Implement the following function:
 <code haskell>
    f ["Matei", "Mihai"] ["Popovici","Dumitru"] = ["MPopovici", "MDumitru"]
 </code>
-. 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:
+.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:
 <code haskell>
-	x `f` y = x + y
+    f [("Dan Matei Popovici",9),("Mihai",4),("Andrei Alex",6)] =
+    	[(["Dan", "Matei", "Popovici"],10),(["Andrei", "Alex"],6)]
 </code>
-Implement a function for transforming lists into pairs, in exercise 32. and use it in the infix form.
-. Just in the same way, we can treat infix functions as prefix. We do this using round parentheses. Test:
-<code haskell>
-		:t (+)
-		:t (&&)
-		:t (++)
-</code>
-. What about function composition? Is it a special operator, or is it just a function as well? What does '':t (.)'' do?
-. 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>
-. Write a function of a single line, such that:
-<code haskell>
-f "Matei" = "{Matei}"
-</code>
-. Use only ''(:)'', ''reverse'' and functional composition ''.'' to solve exercise 38
-. What does the function ''($)'' to?
-    (Use :t, and make up some tests)
-. Write the following implementation using only ($):
-<code haskell>
-f "||" "Matei" = "||Matei||"
-</code>
-.  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):