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--- pp:2023:haskell:l07 [2023/04/19 23:37]
tpruteanu
+++ pp:2023:haskell:l07 [2023/04/27 01:17] (current)
mihai.udubasa [Lambda calculus as a programming language (optional)] fix typo
@@ Line 69: / Line 69: @@
 **A:** We can evaluate any of them, and it is guaranteed by [[https://en.wikipedia.org/wiki/Church%E2%80%93Rosser_theorem | Church-Rosser theorem]] that if the expression is reducible, we will eventually get the same $ \beta $**-normal form**.
-To not just randomly choose **redexes**, there exist // reduction strategies //, from which we will use the **Normal Order** and **Applicative Order**: \\
+To not just randomly choose **redexes**, there exist //reduction strategies//, from which we will use the **Normal Order** and **Applicative Order**: \\
   * **Normal Order** evaluation consist of always reducing the //leftmost//, //outermost// **redex** (whenever possible, subsitute the arguments into the function body) \\
   * **Applicative Order** evaluation consist of always reducing the //leftmost//, //innermost// **redex** (always reduce the function argument before the function itself) \\
@@ Line 86: / Line 86: @@
 The [[https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis | Church-Turing thesis]] asserts that any //computable// function can be computed using lambda calculus (or Turing Machines or equivalent models). \\
-For the curios, a series of additional exercises covering this topic can be found here: [[pp:2023:haskell:l07-extra|Lambda Calculus as a programming language]]. \\
+For the curious, a series of additional exercises covering this topic can be found here: [[pp:2023:haskell:l07-extra|Lambda Calculus as a programming language]]. \\
 ===== 7.2 Intro to Haskell =====
@@ Line 101: / Line 101: @@
 Remember: [[pp:2023:scala:l01|Lab 1. Introduction to Scala]]
-**7.2.1.** Implement a tail-recursive function that computes the factorial of a natural number. Start from the code stub below:
+**7.2.1.** Implement a tail-recursive function that computes the factorial of a natural number.
 <code haskell>
 fact :: Int -> Int
 fact = undefined
 </code>
-**7.2.2.** Implement a tail-recursive function that computes the greatest common divisor of two natural numbers:
+**7.2.2.** Implement a tail-recursive function that computes the greatest common divisor of two natural numbers.
 <code haskell>
-gcd :: Int -> Int -> Int
+mygcd :: Int -> Int -> Int
-gcd a b = undefined
+mygcd a b = undefined
 </code>
 **7.2.3.** Implement the function ''mySqrt''  which computes the square root of an integer $ a $.
@@ Line 122: / Line 122: @@
 }
 </code>|<code haskell>
-f l = case l of {
+f l = case l of
   [] -> ...
-  (x:xs) => ...
+  (x:xs) -> ...
-}
 </code> | <code haskell>
 f [] = ...
@@ Line 134: / Line 133: @@
 </code> |
-**7.2.4.** Implement funtions ''minimum'' and ''maximum'' that take a list of ints, and return the smallest/biggest value in the list.
+**7.2.4.** Implement funtions ''mymin'' and ''mymax'' that take a list of ints, and return the smallest/biggest value in the list.
 **7.2.5.** Implement a function ''unique'' that takes a list of ints, and removes all duplicates.
@@ Line 144: / Line 143: @@
   * a string representation of the number otherwise
-**7.2.7.** Extend the function from **7.2.5.** with the following rules:
+**7.2.7.** Extend the function from **7.2.6.** with the following rules:
   * **'Bazz'** if the number is divisible by 7
   * **'FizzBazz'** if the number is divisible by 21
@@ Line 168: / Line 167: @@
 </code>
 </note>
+==== Types in Haskell ====
+In Haskell, functions are curried by default, **i.e.** a function:
+<code haskell>
+f a b = ...
+</code>
+is the same as:
+<code haskell>
+f = \a -> \b -> ...
+</code>
+So, if $ a $ is a ''Int'' and $ b $ a ''Double'', and $ f $ returns a ''Char'', it would have the following type:
+<code haskell>
+f :: Int -> Double -> Char
+</code>
+**7.2.8.** Check the type signature of the following functions:
+  * ''foldl''
+  * ''foldr''
+  * ''filter''
+  * ''map''
+<note important>
+If a function is not ambigous, ''ghc'' can infer the type signature, for **educational** purposes, going forward you will have to write signatures for all functions you define, this is considered good practice and helps prevent bugs.
+</note>
+<note tip>
+In ''ghci'', you can check the type of a expression with: '':t''
+</note>
+===== 7.3 Brain Twisters =====
+**7.3.1.** Implement ''map'' using ''foldl'' and ''foldr''.
+<code haskell>
+mymapl :: (a -> b) -> [a] -> [b]
+mymapr :: (a -> b) -> [a] -> [b]
+</code>
+**7.3.2.** Implement ''filter'' using ''foldl'' and ''foldr''.
+<code haskell>
+myfilterl :: (a -> Bool) -> [a] -> [a]
+myfilterr :: (a -> Bool) -> [a] -> [a]
+</code>
+**7.3.3.** Implement ''foldl'' using ''foldr''.
+<code haskell>
+myfoldl :: (a -> b -> a) -> a -> [b] -> a
+</code>
+**7.3.4.** Implement ''bubbleSort''.
+<code haskell>
+bubbleSort :: [Int] -> [Int]
+</code>
+**7.3.5.** Implement ''quickSort''.
+<code haskell>
+quickSort :: [Int] -> [Int]
+</code>