diff -r 02c51ca9c531 -r d17c0b34d5c8 doc-src/TutorialI/CodeGen/document/CodeGen.tex --- a/doc-src/TutorialI/CodeGen/document/CodeGen.tex Fri Aug 04 23:02:11 2000 +0200 +++ b/doc-src/TutorialI/CodeGen/document/CodeGen.tex Sun Aug 06 15:26:53 2000 +0200 @@ -10,10 +10,10 @@ a fixed set of binary operations: instead the expression contains the appropriate function itself.% \end{isamarkuptext}% -\isacommand{types}~'v~binop~=~{"}'v~{\isasymRightarrow}~'v~{\isasymRightarrow}~'v{"}\isanewline -\isacommand{datatype}~('a,'v)expr~=~Cex~'v\isanewline -~~~~~~~~~~~~~~~~~~~~~|~Vex~'a\isanewline -~~~~~~~~~~~~~~~~~~~~~|~Bex~{"}'v~binop{"}~~{"}('a,'v)expr{"}~~{"}('a,'v)expr{"}% +\isacommand{types}\ 'v\ binop\ =\ {"}'v\ {\isasymRightarrow}\ 'v\ {\isasymRightarrow}\ 'v{"}\isanewline +\isacommand{datatype}\ ('a,'v)expr\ =\ Cex\ 'v\isanewline +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\ Vex\ 'a\isanewline +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\ Bex\ {"}'v\ binop{"}\ \ {"}('a,'v)expr{"}\ \ {"}('a,'v)expr{"}% \begin{isamarkuptext}% \noindent The three constructors represent constants, variables and the application of @@ -22,20 +22,20 @@ The value of an expression w.r.t.\ an environment that maps variables to values is easily defined:% \end{isamarkuptext}% -\isacommand{consts}~value~::~{"}('a,'v)expr~{\isasymRightarrow}~('a~{\isasymRightarrow}~'v)~{\isasymRightarrow}~'v{"}\isanewline +\isacommand{consts}\ value\ ::\ {"}('a,'v)expr\ {\isasymRightarrow}\ ('a\ {\isasymRightarrow}\ 'v)\ {\isasymRightarrow}\ 'v{"}\isanewline \isacommand{primrec}\isanewline -{"}value~(Cex~v)~env~=~v{"}\isanewline -{"}value~(Vex~a)~env~=~env~a{"}\isanewline -{"}value~(Bex~f~e1~e2)~env~=~f~(value~e1~env)~(value~e2~env){"}% +{"}value\ (Cex\ v)\ env\ =\ v{"}\isanewline +{"}value\ (Vex\ a)\ env\ =\ env\ a{"}\isanewline +{"}value\ (Bex\ f\ e1\ e2)\ env\ =\ f\ (value\ e1\ env)\ (value\ e2\ env){"}% \begin{isamarkuptext}% The stack machine has three instructions: load a constant value onto the stack, load the contents of a certain address onto the stack, and apply a binary operation to the two topmost elements of the stack, replacing them by the result. As for \isa{expr}, addresses and values are type parameters:% \end{isamarkuptext}% -\isacommand{datatype}~('a,'v)~instr~=~Const~'v\isanewline -~~~~~~~~~~~~~~~~~~~~~~~|~Load~'a\isanewline -~~~~~~~~~~~~~~~~~~~~~~~|~Apply~{"}'v~binop{"}% +\isacommand{datatype}\ ('a,'v)\ instr\ =\ Const\ 'v\isanewline +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\ Load\ 'a\isanewline +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\ Apply\ {"}'v\ binop{"}% \begin{isamarkuptext}% The execution of the stack machine is modelled by a function \isa{exec} that takes a list of instructions, a store (modelled as a @@ -44,13 +44,13 @@ and returns the stack at the end of the execution---the store remains unchanged:% \end{isamarkuptext}% -\isacommand{consts}~exec~::~{"}('a,'v)instr~list~{\isasymRightarrow}~('a{\isasymRightarrow}'v)~{\isasymRightarrow}~'v~list~{\isasymRightarrow}~'v~list{"}\isanewline +\isacommand{consts}\ exec\ ::\ {"}('a,'v)instr\ list\ {\isasymRightarrow}\ ('a{\isasymRightarrow}'v)\ {\isasymRightarrow}\ 'v\ list\ {\isasymRightarrow}\ 'v\ list{"}\isanewline \isacommand{primrec}\isanewline -{"}exec~[]~s~vs~=~vs{"}\isanewline -{"}exec~(i\#is)~s~vs~=~(case~i~of\isanewline -~~~~Const~v~~{\isasymRightarrow}~exec~is~s~(v\#vs)\isanewline -~~|~Load~a~~~{\isasymRightarrow}~exec~is~s~((s~a)\#vs)\isanewline -~~|~Apply~f~~{\isasymRightarrow}~exec~is~s~((f~(hd~vs)~(hd(tl~vs)))\#(tl(tl~vs)))){"}% +{"}exec\ []\ s\ vs\ =\ vs{"}\isanewline +{"}exec\ (i\#is)\ s\ vs\ =\ (case\ i\ of\isanewline +\ \ \ \ Const\ v\ \ {\isasymRightarrow}\ exec\ is\ s\ (v\#vs)\isanewline +\ \ |\ Load\ a\ \ \ {\isasymRightarrow}\ exec\ is\ s\ ((s\ a)\#vs)\isanewline +\ \ |\ Apply\ f\ \ {\isasymRightarrow}\ exec\ is\ s\ ((f\ (hd\ vs)\ (hd(tl\ vs)))\#(tl(tl\ vs)))){"}% \begin{isamarkuptext}% \noindent Recall that \isa{hd} and \isa{tl} @@ -64,29 +64,29 @@ The compiler is a function from expressions to a list of instructions. Its definition is pretty much obvious:% \end{isamarkuptext}% -\isacommand{consts}~comp~::~{"}('a,'v)expr~{\isasymRightarrow}~('a,'v)instr~list{"}\isanewline +\isacommand{consts}\ comp\ ::\ {"}('a,'v)expr\ {\isasymRightarrow}\ ('a,'v)instr\ list{"}\isanewline \isacommand{primrec}\isanewline -{"}comp~(Cex~v)~~~~~~~=~[Const~v]{"}\isanewline -{"}comp~(Vex~a)~~~~~~~=~[Load~a]{"}\isanewline -{"}comp~(Bex~f~e1~e2)~=~(comp~e2)~@~(comp~e1)~@~[Apply~f]{"}% +{"}comp\ (Cex\ v)\ \ \ \ \ \ \ =\ [Const\ v]{"}\isanewline +{"}comp\ (Vex\ a)\ \ \ \ \ \ \ =\ [Load\ a]{"}\isanewline +{"}comp\ (Bex\ f\ e1\ e2)\ =\ (comp\ e2)\ @\ (comp\ e1)\ @\ [Apply\ f]{"}% \begin{isamarkuptext}% Now we have to prove the correctness of the compiler, i.e.\ that the execution of a compiled expression results in the value of the expression:% \end{isamarkuptext}% -\isacommand{theorem}~{"}exec~(comp~e)~s~[]~=~[value~e~s]{"}% +\isacommand{theorem}\ {"}exec\ (comp\ e)\ s\ []\ =\ [value\ e\ s]{"}% \begin{isamarkuptext}% \noindent This theorem needs to be generalized to% \end{isamarkuptext}% -\isacommand{theorem}~{"}{\isasymforall}vs.~exec~(comp~e)~s~vs~=~(value~e~s)~\#~vs{"}% +\isacommand{theorem}\ {"}{\isasymforall}vs.\ exec\ (comp\ e)\ s\ vs\ =\ (value\ e\ s)\ \#\ vs{"}% \begin{isamarkuptxt}% \noindent which is proved by induction on \isa{e} followed by simplification, once we have the following lemma about executing the concatenation of two instruction sequences:% \end{isamarkuptxt}% -\isacommand{lemma}~exec\_app[simp]:\isanewline -~~{"}{\isasymforall}vs.~exec~(xs@ys)~s~vs~=~exec~ys~s~(exec~xs~s~vs){"}% +\isacommand{lemma}\ exec\_app[simp]:\isanewline +\ \ {"}{\isasymforall}vs.\ exec\ (xs@ys)\ s\ vs\ =\ exec\ ys\ s\ (exec\ xs\ s\ vs){"}% \begin{isamarkuptxt}% \noindent This requires induction on \isa{xs} and ordinary simplification for the @@ -94,14 +94,14 @@ that contains two \isa{case}-expressions over instructions. Thus we add automatic case splitting as well, which finishes the proof:% \end{isamarkuptxt}% -\isacommand{by}(induct\_tac~xs,~simp,~simp~split:~instr.split)% +\isacommand{by}(induct\_tac\ xs,\ simp,\ simp\ split:\ instr.split)% \begin{isamarkuptext}% \noindent Note that because \isaindex{auto} performs simplification, it can also be modified in the same way \isa{simp} can. Thus the proof can be rewritten as% \end{isamarkuptext}% -\isacommand{by}(induct\_tac~xs,~auto~split:~instr.split)% +\isacommand{by}(induct\_tac\ xs,\ auto\ split:\ instr.split)% \begin{isamarkuptext}% \noindent Although this is more compact, it is less clear for the reader of the proof.