diff -r eacce1cd716a -r 05fc32a23b8b doc-src/TutorialI/CodeGen/document/CodeGen.tex --- a/doc-src/TutorialI/CodeGen/document/CodeGen.tex Tue Aug 16 13:42:21 2005 +0200 +++ b/doc-src/TutorialI/CodeGen/document/CodeGen.tex Tue Aug 16 13:42:23 2005 +0200 @@ -1,7 +1,20 @@ % \begin{isabellebody}% \def\isabellecontext{CodeGen}% -\isamarkupfalse% +% +\isadelimtheory +% +\endisadelimtheory +% +\isatagtheory +% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +\isamarkuptrue% % \isamarkupsection{Case Study: Compiling Expressions% } @@ -18,12 +31,12 @@ a fixed set of binary operations: instead the expression contains the appropriate function itself.% \end{isamarkuptext}% -\isamarkuptrue% +\isamarkupfalse% \isacommand{types}\ {\isacharprime}v\ binop\ {\isacharequal}\ {\isachardoublequote}{\isacharprime}v\ {\isasymRightarrow}\ {\isacharprime}v\ {\isasymRightarrow}\ {\isacharprime}v{\isachardoublequote}\isanewline \isamarkupfalse% \isacommand{datatype}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isacharequal}\ Cex\ {\isacharprime}v\isanewline \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Vex\ {\isacharprime}a\isanewline -\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Bex\ {\isachardoublequote}{\isacharprime}v\ binop{\isachardoublequote}\ \ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequote}\ \ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequote}\isamarkupfalse% +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Bex\ {\isachardoublequote}{\isacharprime}v\ binop{\isachardoublequote}\ \ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequote}\ \ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequote}\isamarkuptrue% % \begin{isamarkuptext}% \noindent @@ -33,13 +46,13 @@ The value of an expression with respect to an environment that maps variables to values is easily defined:% \end{isamarkuptext}% -\isamarkuptrue% +\isamarkupfalse% \isacommand{consts}\ value\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}v{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}v{\isachardoublequote}\isanewline \isamarkupfalse% \isacommand{primrec}\isanewline {\isachardoublequote}value\ {\isacharparenleft}Cex\ v{\isacharparenright}\ env\ {\isacharequal}\ v{\isachardoublequote}\isanewline {\isachardoublequote}value\ {\isacharparenleft}Vex\ a{\isacharparenright}\ env\ {\isacharequal}\ env\ a{\isachardoublequote}\isanewline -{\isachardoublequote}value\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ f\ {\isacharparenleft}value\ e{\isadigit{1}}\ env{\isacharparenright}\ {\isacharparenleft}value\ e{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequote}\isamarkupfalse% +{\isachardoublequote}value\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ f\ {\isacharparenleft}value\ e{\isadigit{1}}\ env{\isacharparenright}\ {\isacharparenleft}value\ e{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequote}\isamarkuptrue% % \begin{isamarkuptext}% The stack machine has three instructions: load a constant value onto the @@ -47,10 +60,10 @@ 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}% -\isamarkuptrue% +\isamarkupfalse% \isacommand{datatype}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}\ instr\ {\isacharequal}\ Const\ {\isacharprime}v\isanewline \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Load\ {\isacharprime}a\isanewline -\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Apply\ {\isachardoublequote}{\isacharprime}v\ binop{\isachardoublequote}\isamarkupfalse% +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Apply\ {\isachardoublequote}{\isacharprime}v\ binop{\isachardoublequote}\isamarkuptrue% % \begin{isamarkuptext}% The execution of the stack machine is modelled by a function @@ -60,7 +73,7 @@ and returns the stack at the end of the execution --- the store remains unchanged:% \end{isamarkuptext}% -\isamarkuptrue% +\isamarkupfalse% \isacommand{consts}\ exec\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}instr\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isasymRightarrow}{\isacharprime}v{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}v\ list\ {\isasymRightarrow}\ {\isacharprime}v\ list{\isachardoublequote}\isanewline \isamarkupfalse% \isacommand{primrec}\isanewline @@ -68,7 +81,7 @@ {\isachardoublequote}exec\ {\isacharparenleft}i{\isacharhash}is{\isacharparenright}\ s\ vs\ {\isacharequal}\ {\isacharparenleft}case\ i\ of\isanewline \ \ \ \ Const\ v\ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}v{\isacharhash}vs{\isacharparenright}\isanewline \ \ {\isacharbar}\ Load\ a\ \ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}{\isacharparenleft}s\ a{\isacharparenright}{\isacharhash}vs{\isacharparenright}\isanewline -\ \ {\isacharbar}\ Apply\ f\ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}{\isacharparenleft}f\ {\isacharparenleft}hd\ vs{\isacharparenright}\ {\isacharparenleft}hd{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharhash}{\isacharparenleft}tl{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkupfalse% +\ \ {\isacharbar}\ Apply\ f\ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}{\isacharparenleft}f\ {\isacharparenleft}hd\ vs{\isacharparenright}\ {\isacharparenleft}hd{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharhash}{\isacharparenleft}tl{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkuptrue% % \begin{isamarkuptext}% \noindent @@ -83,28 +96,46 @@ The compiler is a function from expressions to a list of instructions. Its definition is obvious:% \end{isamarkuptext}% -\isamarkuptrue% +\isamarkupfalse% \isacommand{consts}\ comp\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}instr\ list{\isachardoublequote}\isanewline \isamarkupfalse% \isacommand{primrec}\isanewline {\isachardoublequote}comp\ {\isacharparenleft}Cex\ v{\isacharparenright}\ \ \ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}Const\ v{\isacharbrackright}{\isachardoublequote}\isanewline {\isachardoublequote}comp\ {\isacharparenleft}Vex\ a{\isacharparenright}\ \ \ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}Load\ a{\isacharbrackright}{\isachardoublequote}\isanewline -{\isachardoublequote}comp\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}comp\ e{\isadigit{2}}{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}comp\ e{\isadigit{1}}{\isacharparenright}\ {\isacharat}\ {\isacharbrackleft}Apply\ f{\isacharbrackright}{\isachardoublequote}\isamarkupfalse% +{\isachardoublequote}comp\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}comp\ e{\isadigit{2}}{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}comp\ e{\isadigit{1}}{\isacharparenright}\ {\isacharat}\ {\isacharbrackleft}Apply\ f{\isacharbrackright}{\isachardoublequote}\isamarkuptrue% % \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}% +\isamarkupfalse% +\isacommand{theorem}\ {\isachardoublequote}exec\ {\isacharparenleft}comp\ e{\isacharparenright}\ s\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}value\ e\ s{\isacharbrackright}{\isachardoublequote}% +\isadelimproof +% +\endisadelimproof +% +\isatagproof +% +\endisatagproof +{\isafoldproof}% +% +\isadelimproof +% +\endisadelimproof \isamarkuptrue% -\isacommand{theorem}\ {\isachardoublequote}exec\ {\isacharparenleft}comp\ e{\isacharparenright}\ s\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}value\ e\ s{\isacharbrackright}{\isachardoublequote}\isamarkupfalse% -\isamarkupfalse% % \begin{isamarkuptext}% \noindent This theorem needs to be generalized:% \end{isamarkuptext}% +\isamarkupfalse% +\isacommand{theorem}\ {\isachardoublequote}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}comp\ e{\isacharparenright}\ s\ vs\ {\isacharequal}\ {\isacharparenleft}value\ e\ s{\isacharparenright}\ {\isacharhash}\ vs{\isachardoublequote}% +\isadelimproof +% +\endisadelimproof +% +\isatagproof \isamarkuptrue% -\isacommand{theorem}\ {\isachardoublequote}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}comp\ e{\isacharparenright}\ s\ vs\ {\isacharequal}\ {\isacharparenleft}value\ e\ s{\isacharparenright}\ {\isacharhash}\ vs{\isachardoublequote}\isamarkupfalse% % \begin{isamarkuptxt}% \noindent @@ -112,10 +143,22 @@ First, we must prove a lemma about executing the concatenation of two instruction sequences:% \end{isamarkuptxt}% -\isamarkuptrue% +% +\endisatagproof +{\isafoldproof}% +% +\isadelimproof +% +\endisadelimproof \isamarkupfalse% \isacommand{lemma}\ exec{\isacharunderscore}app{\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\isanewline -\ \ {\isachardoublequote}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}xs{\isacharat}ys{\isacharparenright}\ s\ vs\ {\isacharequal}\ exec\ ys\ s\ {\isacharparenleft}exec\ xs\ s\ vs{\isacharparenright}{\isachardoublequote}\isamarkupfalse% +\ \ {\isachardoublequote}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}xs{\isacharat}ys{\isacharparenright}\ s\ vs\ {\isacharequal}\ exec\ ys\ s\ {\isacharparenleft}exec\ xs\ s\ vs{\isacharparenright}{\isachardoublequote}% +\isadelimproof +% +\endisadelimproof +% +\isatagproof +\isamarkuptrue% % \begin{isamarkuptxt}% \noindent @@ -124,9 +167,15 @@ that contains two \isa{case}-expressions over instructions. Thus we add automatic case splitting, which finishes the proof:% \end{isamarkuptxt}% +\isamarkupfalse% +\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharcomma}\ simp\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}% +\endisatagproof +{\isafoldproof}% +% +\isadelimproof +% +\endisadelimproof \isamarkuptrue% -\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharcomma}\ simp\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}\isamarkupfalse% -\isamarkupfalse% % \begin{isamarkuptext}% \noindent @@ -134,11 +183,21 @@ be modified in the same way as \isa{simp}. Thus the proof can be rewritten as% \end{isamarkuptext}% -\isamarkuptrue% -\isamarkupfalse% +% +\isadelimproof +% +\endisadelimproof +% +\isatagproof \isamarkupfalse% -\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharunderscore}all\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}\isamarkupfalse% -\isamarkupfalse% +\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharunderscore}all\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}% +\endisatagproof +{\isafoldproof}% +% +\isadelimproof +% +\endisadelimproof +\isamarkuptrue% % \begin{isamarkuptext}% \noindent @@ -150,10 +209,32 @@ its instance.% \index{compiling expressions example|)}% \end{isamarkuptext}% -\isamarkuptrue% -\isamarkupfalse% -\isamarkupfalse% -\isamarkupfalse% +% +\isadelimproof +% +\endisadelimproof +% +\isatagproof +% +\endisatagproof +{\isafoldproof}% +% +\isadelimproof +% +\endisadelimproof +% +\isadelimtheory +% +\endisadelimtheory +% +\isatagtheory +% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory \end{isabellebody}% %%% Local Variables: %%% mode: latex