Finished haskell-part

* Notes now is multimarkdown
 * Notes has "checklist"
 * Haskell examples are complete

Notes.md

@@ -1,4 +1,12 @@
-# WTFunctional: Modifying your WTF-Count using functional programming #
+Title:          WTFunctional: Modifying yout WTF-Count using functional programming  
+Author:         Oliver Rümpelein
+html header:    <link rel="stylesheet"
+                href="http://yandex.st/highlightjs/7.3/styles/default.min.css">
+                <script src="http://yandex.st/highlightjs/7.3/highlight.min.js"></script>
+                <script>hljs.initHighlightingOnLoad();</script>
+
+
+# [%title] #
 
 ## Content ##
 
@@ -8,24 +16,27 @@
    + functions as first class “objects”: i.e. C++, 5; is a valid statement
    + lambdas
    + lists, maps, filters, folds 
-     => readability, less code reproduction, threadsafety…
    + currying => just convenience
-   + code example: Pythagoraian triangles.
+   + code example: Pythagoraian triangles, bubble sort
  * Phuncy: The pythonic way is functional!
-   + Not strictly functional
+   - Not strictly functional
-   + recursion, fafco
+   - recursion, fafco
-   + lambda syntax
+   - lambda syntax
-   + map, fold => example (sum of squares?)
+   - map, fold => example (sum of squares?)
      - python lambda syntax: lambda a,b: a+b
      - fold with reduce
      - don't return lists, but iterators!
-     - Note: 2: map, filter, reduce
+     - Note: 2: map, filter, reduce, list comprehension
-           3: map, filter, functools.reduce()
+             3: map, filter, functools.reduce(), list comprehension
-        ```Removed reduce(). Use functools.reduce() if you really need it;
+
-           however, 99 percent of the time an explicit for loop is more
+
-           readable.```
+     - The python2 to 3 page states:
-       Why use it? => Multi-processing!
+       “Removed `reduce()`. Use `functools.reduce()` if you really need it;
-       ```
+       however, 99 percent of the time an explicit `for` loop is more
+       readable.”
+     - Why use it? => Multi-processing, WTF Count.
+       
+       ```python
        a = list(range(10))
      
        b = 0
@@ -34,19 +45,20 @@
        print(b)
        ```
        vs.
-       ```
+       
+       ```python
        from functools import reduce
        print(reduce(lambda x,y: x+y,map(lambda x: x**2,range(10))))
        ```
-   + currying: not really, but binding via lambdas or functools.partial() or
+   - currying: not really, but binding via lambdas or functools.partial() or
                https://mtomassoli.wordpress.com/2012/03/18/currying-in-python/
-   + decorators!
+   - decorators!
-   + still FP, has advantages and is heavily used, i.e. in genomics (works on
+   - still FP has advantages and is heavily used, i.e. in genomics (works on
      tons of lengthy lists)
  * FunCtional++: On the fast lane
-   + "Classical" C++ has some functional stuff, bust i.e. no lambdas (hardly usable)
+   - "Classical" C++ has some functional stuff, bust i.e. no lambdas (hardly usable)
-   + Changed with the new C++11-standard
+   - Changed with the new C++11-standard
-   + Buzzwords:
+   - Buzzwords:
       - `map` defines a Datatype in C++!
       - lambdas in C++
         ```[](int x, int y) { return a<b;} ;```

examples/01_haskell.hs

@@ -0,0 +1,35 @@
+extract :: [a] -> a
+extract [] = error("Too few objects")
+extract (x:xs) = x
+a = extract [1,2,3,4,5]
+
+addto :: (Num a) => [a] -> a -> [a]
+addto [] _ = [] -- edge case (list empty)
+addto (x:xs) y = (x+y) : addto xs y
+b = [1..4]
+-- c == [5,6,7,8]
+c = addto b 4
+
+-- d == [25,36,49,64]
+d = map (^2) c
+
+-- e == [6,8]
+e = filter (\x -> (mod x 2) == 0) c
+
+mfold :: (t -> t1 -> t1) -> t1 -> [t] -> t1
+mfold f z [] = z
+mfold f z (x:xs) = f x (mfold f z xs)
+msum = mfold (+) 0
+g = msum [1..100]
+
+pt = [(a,b,c) | a <- [1..15], b <- [1..a], c <- [1..b], a^2 == b^2 + c^2]
+
+bsort :: (t -> t -> Bool) -> [t] -> [t]
+bsort f [] = []
+bsort f (x:xs) = (bsort f a) ++ [x] ++ (bsort f b)
+  where a = [ y | y <- xs, not (f x y) ]
+        b = [ y | y <- xs, (f x y) ]
+
+mbsort = bsort (\x y -> (x < y))
+h = [1, 20, -10, 5]
+i = mbsort h

examples/01_haskell_recursion.hs

@@ -1,12 +0,0 @@
-extract :: [a] -> a
-extract [] = error("Too few objects")
-extract (x:xs) = x
-a = extract [1,2,3,4,5]
-
-addto :: (Num a) => [a] -> a -> [a]
-addto [] _ = [] -- edge case (list empty)
-addto (x:xs) y = (x+y) : addto xs y
-b = [1..4]
--- c == [5,6,7,8]
-c = addto b 4
-

tex/wtf.bib

@@ -0,0 +1,5 @@
+@online{whichfold,
+title={Foldr Foldl Foldl' - HaskellWiki},
+urldate={2016-04-21},
+url={https://wiki.haskell.org/Foldr_Foldl_Foldl%27},
+}

tex/wtfunctional.tex

@@ -3,6 +3,8 @@
 \usepackage{babel}
 \usepackage{csquotes}
 \usepackage{tabularx}
+\usepackage[backend=biber, style=numeric,]{biblatex}
+\bibliography{wtf}
 
 \usepackage{fontspec}
 \setsansfont{Fira Sans}
@@ -97,35 +99,32 @@
 \end{frame}
 
 \begin{frame}[fragile]{Syntax – Lists (1)}
-    Lists in Haskell can only hold data of one type. They are defined using
+    \begin{itemize}[<+->]
-    \haskellcmd{a = [1,2,3,4]} or similar.
+    \item Lists in Haskell can only hold data of one type. They are defined using
-
+        \haskellcmd{a = [1,2,3,4]} or similar.
-    \pause
+    \item An automatic range can be obtained by using \haskellcmd{b = [1..4]},
-    Furthermore, an automatic range can be obtained by using
+        where the last number is inclusive.
-    \haskellcmd{b = [1..4]}, where the last number is inclusive.
+    \item If possible, Haskell will try to inhibit the step
-
+        automatically. \haskellcmd{c = [1,3..7]} yields
-    \pause
+        \haskellcmd{[1,3,5,7]}.
-    If possible, Haskell will try to inhibit the step automatically
+    \item When leaving out the end specifier, a range can be infinite. In this case,
-    \haskellcmd{c = [1,3..7]} yields \haskellcmd{[1,3,5,7]}.
+        it's up to the programmer to constrain things.
-
+    \end{itemize}
-    \pause
-    When leaving out the end specifier, a range can be infinite. In this case,
-    it's up to the programmer to constrain things.
 \end{frame}
 
 \begin{frame}[fragile]{Syntax – Lists (2)}
-    Two arrays can be concatenated using the \haskellcmd{++} operator
+    \begin{itemize}[<+->]
-    \haskellcmd{[1,2,3] ++ [4..7]}
+    \item Two lists can be concatenated using the \haskellcmd{++} operator:
-
+        \haskellcmd{[1,2,3] ++ [4..7]}
-    Single objects get pushed to the front using \haskellcmd{:}:
+    \item Single objects get pushed to the front using
-    \haskellcmd{1:[2..7]}.    
+        \enquote{\haskellcmd{:}}: \haskellcmd{1:[2..7]}.    
-
+    \item This can also be used vice versa to extract single values from lists:
-    This can also be used vice versa to extract single values from lists
+        \begin{haskell}
-    \begin{haskell}
+            extract (x:xs) = x
-        extract (x:xs) = x
+            -- a = 1
-        -- a = 1
+            a = extract [1..5]
-        a = extract [1..5]
+        \end{haskell}
-    \end{haskell}
+    \end{itemize}
 \end{frame}
     
 \begin{frame}[fragile]{Syntax – Recursion}
@@ -139,8 +138,83 @@
         c = addto b 4
     \end{haskell}
 \end{frame}
+
+\begin{frame}[fragile]{Lambdas}
+    \begin{itemize}[<+->]
+    \item By now: lambda-functions well known from other programming languages
+    \item Represent \enquote{anonymous} functions, i.e. locally defined functions
+        without associated name
+    \item Can simply be passed to algorithms, i.e. sort.
+    \item Syntax: \haskellcmd{\var1 var2 -> retval}
+    \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{Maps, Filters}
+    \begin{itemize}[<+->]
+    \item A \emph{Map} applies a function to all elements of a list:
+        \haskellcmd{map (^2) c}\quad (square the elements of c)
+    \item A \emph{Filter} does exactly that to a list:
+        \haskellcmd{filter (\x -> (mod x 2) == 0) c} \quad (even numbers in c,
+        filtering done using a lambda function)
+    \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{Folds (1)}
+    \begin{itemize}[<+->]
+    \item \emph{Folds} (or sometimes \emph{reductions}) create single values
+        using whole lists, i.e. sums over all elements
+    \item Often implemented using recursion
+    \item Need a function, an initialization value and a list
+    \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{Folds (2)}
+    \uncover<+-> Example: Self written Right fold and sum: 
+    \begin{haskell}
+        mfold f z [] = z
+        mfold f z (x:xs) = f x (mfold f z xs)
+        msum = mfold (+) 0
+        -- g == 5050
+        g = msum [1..100]
+    \end{haskell}
+    \uncover<+->{Note that this gets pretty resource hungry with large
+      lists, better use left-folds for this (see~\cite{whichfold})}
+\end{frame}
+
+\begin{frame}[fragile]{Example: Pythagorean triangles}
+    Get all Pythagorean triangles with a hypotenuse off length at most 15:
+    \begin{haskell}
+        > [(a,b,c) | a <- [1..15],
+                     b <- [1..a],
+                     c <- [1..b],
+                     a^2 == b^2 + c^2]
+        [(5,4,3),(10,8,6),(13,12,5),(15,12,9)]
+    \end{haskell}
+\end{frame}    
+
+\begin{frame}[fragile]{Example: Bubble-sort}
+    Recursive, functional bubble-sort algorithm:
+    \begin{haskell}
+        bsort f [] = []
+        bsort f (x:xs) = (bsort f a) ++ [x] ++ (bsort f b)
+          where a = [ y | y <- xs, not (f x y) ]
+                b = [ y | y <- xs, (f x y) ]
+        mbsort = bsort (\x y -> (x > y))
+    \end{haskell}
+    \pause Result:
+    \begin{haskell}
+        λ> h = [1, 20, -10, 5]
+        λ> mbsort h
+        [-10,1,5,29]
+    \end{haskell}
+\end{frame}
+
+\begin{frame}[plain]{References}
+    \printbibliography
+\end{frame}          
 \end{document}
 
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