
diff -r 7c7854feccb5 -r 7dac350b20a1 handouts/ho08.tex
--- a/handouts/ho08.tex	Fri Nov 22 13:03:13 2019 +0000
+++ b/handouts/ho08.tex	Sun Nov 24 01:03:38 2019 +0000
@@ -67,8 +67,10 @@
 
 The grammar of the Fun-language is slightly simpler than the
 While-language, because the main syntactic category are
-expressions (we do not have statements). The grammar rules are
-as follows:
+expressions (we do not have statements in Fun). The grammar rules are
+as follows:\footnote{We of course have a slightly different (non-left-recursive)
+grammar for our parsing combinators. But for simplicity sake we leave
+these details to the implementation.}
 
 
 \begin{plstx}[rhs style=,margin=1.5cm]
@@ -100,11 +102,13 @@
 starts the computation in the program. For example
 
 \begin{lstlisting}[numbers=none]
-def fact(n) = if n == 0 then 1 else n * fact(n - 1);
+def fact(n) = if n == 0 then 1 
+              else n * fact(n - 1);
+
 write(fact(5))
 \end{lstlisting}
 
-\noindent would be a valid Fun-program. The parser of the
+\noindent is a valid Fun-program. The parser of the
 Fun-language produces abstract syntax trees which in Scala
 can be represented as follows:
 
@@ -210,7 +214,7 @@
    .limit locals ??
    .limit stack ?? 
    ...
-  ireturn
+   ireturn
 .method end  
 \end{lstlisting}
 
@@ -398,12 +402,12 @@
 \code{n} and \code{acc} are referenced inside the function with \pcode{iload 0}
 and \pcode{iload 1} respectively.
 
-The idea of tail-call optimisation is to eliminate the expensive recursive 
-functions call and replace it by a simple jump back to the beginning of the
-function. To make this work we have to change how we communicate the arguments
-to the next level of ``recursion'': we cannot use the stack, but have to load 
-the argument into the corresponding local variables. This gives the following
-code
+The idea of tail-call optimisation is to eliminate the expensive
+recursive functions call and replace it by a simple jump back to the
+beginning of the function. To make this work we have to change how we
+communicate the arguments to the next level of the recursion/iteration:
+we cannot use the stack, but have to load the arguments into the
+corresponding local variables. This gives the following code
 
 \begin{lstlisting}[language=JVMIS, numbers=left, escapeinside={(*@}{@*)}]
 .method public static facT(II)I 
@@ -433,12 +437,11 @@
 \noindent
 In Line 4 we introduce a label for indicating where the start of the
 function is. Important are Lines 17 and 18 where we store the values
-from the stack into local variables. When we then jump back to the 
-beginning of the function (in Line 19) it will look like to the 
-function as if the function had been called the normal way via values
-on the stack. But because of the jump, clearly, no memory on the
-stack is needed. In effect we replaced a recursive call with a simple 
-loop.
+from the stack into local variables. When we then jump back to the
+beginning of the function (in Line 19) it will look to the function as
+if it had been called the normal way via values on the stack. But
+because of the jump, clearly, no memory on the stack is needed. In
+effect we replaced a recursive call with a simple loop.
 
 Can this optimisation always be applied? Unfortunately not. The 
 recursive call needs to be in tail-call position, that is the last




