diff -r 42671298f037 -r 313a24b66a8d doc-src/TutorialI/Misc/document/case_exprs.tex --- a/doc-src/TutorialI/Misc/document/case_exprs.tex Sun Nov 07 23:32:26 2010 +0100 +++ b/doc-src/TutorialI/Misc/document/case_exprs.tex Mon Nov 08 00:00:47 2010 +0100 @@ -1,6 +1,6 @@ % \begin{isabellebody}% -\def\isabellecontext{case{\isacharunderscore}exprs}% +\def\isabellecontext{case{\isaliteral{5F}{\isacharunderscore}}exprs}% % \isadelimtheory % @@ -21,22 +21,22 @@ HOL also features \isa{case}-expressions for analyzing elements of a datatype. For example, \begin{isabelle}% -\ \ \ \ \ case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ y% +\ \ \ \ \ case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ y% \end{isabelle} -evaluates to \isa{{\isacharbrackleft}{\isacharbrackright}} if \isa{xs} is \isa{{\isacharbrackleft}{\isacharbrackright}} and to \isa{y} if -\isa{xs} is \isa{y\ {\isacharhash}\ ys}. (Since the result in both branches must be of -the same type, it follows that \isa{y} is of type \isa{{\isacharprime}a\ list} and hence -that \isa{xs} is of type \isa{{\isacharprime}a\ list\ list}.) +evaluates to \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} if \isa{xs} is \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and to \isa{y} if +\isa{xs} is \isa{y\ {\isaliteral{23}{\isacharhash}}\ ys}. (Since the result in both branches must be of +the same type, it follows that \isa{y} is of type \isa{{\isaliteral{27}{\isacharprime}}a\ list} and hence +that \isa{xs} is of type \isa{{\isaliteral{27}{\isacharprime}}a\ list\ list}.) In general, case expressions are of the form \[ \begin{array}{c} -\isa{case}~e~\isa{of}\ pattern@1~\isa{{\isasymRightarrow}}~e@1\ \isa{{\isacharbar}}\ \dots\ - \isa{{\isacharbar}}~pattern@m~\isa{{\isasymRightarrow}}~e@m +\isa{case}~e~\isa{of}\ pattern@1~\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}}~e@1\ \isa{{\isaliteral{7C}{\isacharbar}}}\ \dots\ + \isa{{\isaliteral{7C}{\isacharbar}}}~pattern@m~\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}}~e@m \end{array} \] Like in functional programming, patterns are expressions consisting of -datatype constructors (e.g. \isa{{\isacharbrackleft}{\isacharbrackright}} and \isa{{\isacharhash}}) +datatype constructors (e.g. \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and \isa{{\isaliteral{23}{\isacharhash}}}) and variables, including the wildcard ``\verb$_$''. Not all cases need to be covered and the order of cases matters. However, one is well-advised not to wallow in complex patterns because @@ -68,7 +68,7 @@ \end{isamarkuptext}% \isamarkuptrue% \isacommand{lemma}\isamarkupfalse% -\ {\isachardoublequoteopen}{\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y{\isacharhash}ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline +\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y{\isaliteral{23}{\isacharhash}}ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline % \isadelimproof % @@ -76,20 +76,20 @@ % \isatagproof \isacommand{apply}\isamarkupfalse% -{\isacharparenleft}case{\isacharunderscore}tac\ xs{\isacharparenright}% +{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}% \begin{isamarkuptxt}% \noindent results in the proof state \begin{isabelle}% -\ {\isadigit{1}}{\isachardot}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ {\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs\isanewline -\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline -\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }xs\ {\isacharequal}\ a\ {\isacharhash}\ list\ {\isasymLongrightarrow}\ {\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs% +\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs\isanewline +\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline +\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }xs\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs% \end{isabelle} which is solved automatically:% \end{isamarkuptxt}% \isamarkuptrue% \isacommand{apply}\isamarkupfalse% -{\isacharparenleft}auto{\isacharparenright}% +{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}% \endisatagproof {\isafoldproof}% % @@ -107,11 +107,11 @@ Induction is only allowed on free (or \isasymAnd-bound) variables that should not occur among the assumptions of the subgoal; see \S\ref{sec:ind-var-in-prems} for details. Case distinction - (\isa{case{\isacharunderscore}tac}) works for arbitrary terms, which need to be - quoted if they are non-atomic. However, apart from \isa{{\isasymAnd}}-bound + (\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}) works for arbitrary terms, which need to be + quoted if they are non-atomic. However, apart from \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}-bound variables, the terms must not contain variables that are bound outside. - For example, given the goal \isa{{\isasymforall}xs{\isachardot}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymor}\ {\isacharparenleft}{\isasymexists}y\ ys{\isachardot}\ xs\ {\isacharequal}\ y\ {\isacharhash}\ ys{\isacharparenright}}, - \isa{case{\isacharunderscore}tac\ xs} will not work as expected because Isabelle interprets + For example, given the goal \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}xs{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}y\ ys{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}}, + \isa{case{\isaliteral{5F}{\isacharunderscore}}tac\ xs} will not work as expected because Isabelle interprets the \isa{xs} as a new free variable distinct from the bound \isa{xs} in the goal. \end{warn}%