--- a/hws/hw09.tex	Tue Nov 28 11:45:48 2023 +0000
+++ b/hws/hw09.tex	Sat Dec 02 21:37:04 2023 +0000
@@ -13,7 +13,17 @@
 \begin{enumerate}
 \item Describe what is meant by \emph{eliminating tail
       recursion}? When can this optimization be applied and
-      why is it of benefit?
+    why is it of benefit?
+
+    \solution{ Tail-call optimisation replaces a recursive call (in
+      tail-call position) by a jump to the beginning of a function.
+      In this way a recursion is replaced by a loop. This saves stack
+      space because no new stack space needs to be allocated when a
+      function is called recursively.
+
+      Tail-call optimisation can be applied when the recursive call is
+    the last instruction that is run in the function.}
+    
 
 \item A programming language has arithmetic expression. For an
   arithmetic expression the compiler of this language produces the
@@ -34,6 +44,10 @@
   Give the arithmetic expression that produced this code.  Make sure
   you give all necessary parentheses.
 
+  \solution{
+    $1 + ((2 * 3) + (4 - 3))$
+  }
+
 \item Describe what the following JVM instructions do!
 
   
@@ -45,6 +59,11 @@
 if_icmpge label
 \end{lstlisting}
 
+\solution{
+(1) load the constant 3 onto the stack. (2) load the 4th local variable onto the stack. (3) store the top of the stack into the 2nd local variable (deleting the top element from the stack) (4) tests whether the top of the stack is equal to zero (if yes, then jump to label; delete top of the stack) (5) compares the top 2 elements of the stack whether they are greater or equal (if yes jump to label; delete two topmost elements from the stack) 
+  }
+
+
 \item What does the following JVM function calculate?
 
 \begin{lstlisting}[language=JVMIS2,numbers=none]    
@@ -78,6 +97,8 @@
 .end method  
 \end{lstlisting}
 
+\solution{ Fibonacci function..students should be able to read what the instructions do on the stack).}
+
 \item What does the following LLVM function calculate? Give the
   corresponding arithmetic expression .
 
@@ -93,10 +114,22 @@
 }
 \end{lstlisting}
 
-\item As an optimisation technique, a compiler might want to detect `dead code' and
-  not generate anything for this code. Why does this optimisation technique have the
-  potential of speeding up the run-time of a program? (Hint: On what kind of CPUs are programs
-  run nowadays?)
+\solution{ $a^2+a*2*b + b^2$
+  }
+
+
+\item As an optimisation technique, a compiler might want to detect
+  `dead code' and not generate anything for this code. Why does this
+  optimisation technique have the potential of speeding up the
+  run-time of a program? (Hint: On what kind of CPUs are programs run
+  nowadays?)
+
+  \solution{ Modern CPUs use predictive branching (guessing which
+    code-branch is run) and use the cache extensively...any code that
+    isn't in the program helps with guessing the right branch and does
+    not occupy anything in the cache. So in effect the code will run
+    faster.  }
+  
 
 \item In an earlier question, we analysed the advantages of having a lexer-phase
   before running the parser (having a lexer is definitely a good thing to have). But you
@@ -112,9 +145,20 @@
 
   What is wrong with implementing a lexer in this way?
 
+  \solution { There is no problem in terms of which strings are
+    matched (the grammar can be defined such that it matches exactly
+    the same strings. However, CFG do not obey the POSIX rules,
+    meaning they cannot implement ``how regular expressions matc a
+    string'' (for example longest match rule; rule priority).  }
+  
+
 \item What is the difference between a parse tree and an abstract
   syntax tree? Give some simple examples for each of them.
 
+  \solution { Parse-trees follow the grammar rules, therefore the
+    inner nodes correspond to the non-terminal symbols in CFGs. ASTs
+    represent the tree-structure of the programs. }
+
 \item What are the two main features of code in
   static single assignment form (SSA)?