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\author{Piyush P Kurur\\
  Office no: 224\\
  Dept. of Comp. Sci. and Engg.\\
  IIT Kanpur}


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\title{Fundamentals of Computing: Lecture 25}
\date{October 5, 2009}
\begin{document}
\begin{frame}
  \maketitle
\end{frame}

\begin{frame}
  \frametitle{Summary of last class}
  \pause
  \begin{itemize}
  \item A structure is a way of constructing product types.
    \pause
    \begin{spec}
      struct structure-name{
        field declarations
      };
    \end{spec}
    \pause
  \item If |foo| is of type |strunct Foo| and bar is a field of the structure |Foo|
    then the |bar| field of |foo| can be accessed via the expression |foo.bar|
    \pause
  \item Fields are both l-values as well as r-values.
    \pause
  \item Structures are passed as values to function which is unlike
    Java.
  \end{itemize}

\end{frame}

\begin{frame}
  \frametitle{Examples}
  \pause
  
  \begin{spec}
    struct Vector2D {
      double x;
      double y;
    };
  \end{spec}
  \pause
  \begin{spec}
    typedef struct{
      double x;
      double y;
    } Vector2D;
  \end{spec}
  \pause
  \begin{spec}
    struct Vector2D{
      double x;
      double y;
    } origin = {0,0};
  \end{spec}
\end{frame}

\begin{frame}
  Structures are \emph{not} passed as reference to functions.
 \pause
  \begin{code}
    #line 214 "lecture23.lhs"
    #include <stdio.h>
    void printVector(struct Vector2D);
    void shiftByOneUnit(struct Vector2D u);
    int main () {
      printf("Before shift: ");printVector(origin);
      shiftByOneUnit(origin);
      printf("After shift: ");printVector(origin);
    }
    void shiftByOneUnit(struct Vector2D u){
      u.x = u.x + 1;
    }
    void printVector(struct Vector2D u){
      printf("(%f,%f)\n",u.x,u.y);
    }
  
  \end{code}
\end{frame}


\begin{frame}
  \frametitle{Recursive data types}
  \begin{itemize}
  \item List.
    \pause
    A list is either an empty list or 
    an element followed by a list.
    \pause
  \item Binary trees.
    \pause
    A binary tree is either an empty Tree or a root
    node with two children left subtree and right subtree.
    \pause
  \item General trees (some times called Rose trees).  \pause Either
    an empty tree or a node with a Forest of subtrees.
  \end{itemize}
  \pause
  \begin{block}{Mathematically}
    \begin{eqnarray*}
      L  (a) &=& \bot + a \times L (a) \\
      BT (a) &=& \bot + a \times BT (a)  \times BT (a) \\
      T  (a) &=& \bot + a \times F (a) \\
      F  (a) &=& L (T (a))
    \end{eqnarray*}
  \end{block}

  
\end{frame}

\begin{frame}
  \frametitle{In Haskell this would be}
  \begin{spec}
data List    a = Empty | Cons a (List a)
data BinTree a = Empty | Node (BinTree a) a (BinTree a)
data Tree    a = Empty | Node a [Tree a]
  \end{spec}
\end{frame}
\begin{frame}
  \frametitle{How does one simulate this in |C|?}

  \pause
  An ugly dance involving structs and pointers.

  \pause

  \begin{spec}
    typedef struct Node Node;
    struct Node {
      int datum;
      Node * next;
    };
  \end{spec}

  \pause

  \begin{spec}
    typedef Node *List;
  \end{spec}

\end{frame}
\begin{frame}
  \frametitle{The |head| and |tail| function}
  \begin{spec}
    data List    a = Empty | Cons a (List a)
    head (Cons x _)  = x
    tail (Cons _ xs) = xs
  \end{spec}
  
  \only<2-3>{
    \begin{spec}
      int head(List l)
      {
        if( l == NULL) {error("head of an empty list");}
        else return (*l).datum
      }
      List tail (List l)
      {
        if( l == NULL) {error("tail of an empty list");}
        else return (*l).next
      }
    \end{spec}
  }
  \only<4->{
    \begin{spec}
      int head(List l)
      {
        if( l == NULL) {error("head of an empty list");}
        else return l -> datum
      }
      List tail (List l)
      {
        if( l == NULL) {error("tail of an empty list");}
        else return l -> next
      }
    \end{spec}
  }
  \uncover<3->{Since |(*foo).bar| often comes in practice}
  
\end{frame}

\end{document}