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    18 

    19 

    19 \section*{Handout 8 (A Functional Language)}

    20 \section*{Handout 8 (A Functional Language)}

    20 

    21 

    21 

    22 

    22 The language we looked at in the previous lecture was rather

    23 The language we looked at in the previous lecture was rather

    24 essentially estimated into a big monolithic chunk of code

    25 essentially estimated into a big monolithic chunk of code

    25 inside the main function. In this handout we like to have a

    26 inside the main function. In this handout we like to have a

    26 look at a slightly more comfortable language, which I call

    27 look at a slightly more comfortable language, which I call

    28 The Fun-language is a functional programming language. A small

    29 The Fun-language is a functional programming language. A small

    29 collection of programs we want to be able to write and estimate

    30 collection of programs we want to be able to write and estimate

    30 is as follows:

    31 is as follows:

    31 

    32 

    32 \begin{lstlisting}[numbers=none]

    33 \begin{lstlisting}[numbers=none]

   122 Let us first look at some clauses for compiling expressions.

   123 Let us first look at some clauses for compiling expressions.

   123 The compilation of arithmetic and boolean expressions is just

   124 The compilation of arithmetic and boolean expressions is just

   124 like for the While-language and do not need any modification.

   125 like for the While-language and do not need any modification.

   125 (recall that the \textit{estimate}-function for boolean

   126 (recall that the \textit{estimate}-function for boolean

   126 expression takes a third argument for the label where the

   127 expression takes a third argument for the label where the

   128 \emph{not} true---this is needed for compiling \pcode{if}s).

   129 \emph{not} true---this is needed for compiling \pcode{if}s).

   129 One additional feature in the Fun-language are sequences.

   130 One additional feature in the Fun-language are sequences.

   130 Their purpose is to do one calculation after another. The

   131 Their purpose is to do one calculation after another. The

   131 reason why we need to be careful however is the convention

   132 reason why we need to be careful however is the convention

   132 that every expression can only produce s single result

   133 that every expression can only produce s single result

   182 

   183 

   183 \noindent We also need to first generate code for the

   184 \noindent We also need to first generate code for the

   184 argument-expression of write, which in the While-language was

   185 argument-expression of write, which in the While-language was

   185 only allowed to be a single variable.

   186 only allowed to be a single variable.

   186 

   187 

   188 comes from function definitions and function calls. For this

   189 comes from function definitions and function calls. For this

   189 have a look again at the helper function in

   190 have a look again at the helper function in

   190 Figure~\ref{write}. Assuming we have a function definition

   191 Figure~\ref{write}. Assuming we have a function definition

   191 

   192 

   192 \begin{lstlisting}[numbers=none,mathescape]

   193 \begin{lstlisting}[numbers=none,mathescape]

   266 

   267 

   267 def add(x, y) = if x == 0 then y

   268 def add(x, y) = if x == 0 then y

   268                 else suc(add(x - 1, y));

   269                 else suc(add(x - 1, y));

   269 \end{lstlisting}

   270 \end{lstlisting}

   270 

   271 

   272 argument $x$ (index $0$) onto the stack, as well as the number

   273 argument $x$ (index $0$) onto the stack, as well as the number

   273 $1$. Then we add both elements leaving the result of the 

   274 $1$. Then we add both elements leaving the result of the 

   274 addition on top of the stack. This value will be returned by 

   275 addition on top of the stack. This value will be returned by 

   275 the \pcode{suc}-function. See below:

   276 the \pcode{suc}-function. See below:

   276 

   277