diff -r 378bdbce68e6 -r 35809287ab23 doc-src/IsarRef/Thy/document/Quick_Reference.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/IsarRef/Thy/document/Quick_Reference.tex Sat May 03 13:26:08 2008 +0200 @@ -0,0 +1,278 @@ +% +\begin{isabellebody}% +\def\isabellecontext{Quick{\isacharunderscore}Reference}% +% +\isadelimtheory +\isanewline +\isanewline +% +\endisadelimtheory +% +\isatagtheory +\isacommand{theory}\isamarkupfalse% +\ Quick{\isacharunderscore}Reference\isanewline +\isakeyword{imports}\ Main\isanewline +\isakeyword{begin}% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +% +\isamarkupchapter{Isabelle/Isar quick reference \label{ap:refcard}% +} +\isamarkuptrue% +% +\isamarkupsection{Proof commands% +} +\isamarkuptrue% +% +\isamarkupsubsection{Primitives and basic syntax% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \mbox{\isa{\isacommand{fix}}}~\isa{x} & augment context by \isa{{\isasymAnd}x{\isachardot}\ {\isasymbox}} \\ + \mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & augment context by \isa{{\isasymphi}\ {\isasymLongrightarrow}\ {\isasymbox}} \\ + \mbox{\isa{\isacommand{then}}} & indicate forward chaining of facts \\ + \mbox{\isa{\isacommand{have}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & prove local result \\ + \mbox{\isa{\isacommand{show}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & prove local result, refining some goal \\ + \mbox{\isa{\isacommand{using}}}~\isa{a} & indicate use of additional facts \\ + \mbox{\isa{\isacommand{unfolding}}}~\isa{a} & unfold definitional equations \\ + \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}~\dots~\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}} & indicate proof structure and refinements \\ + \mbox{\isa{\isacommand{{\isacharbraceleft}}}}~\dots~\mbox{\isa{\isacommand{{\isacharbraceright}}}} & indicate explicit blocks \\ + \mbox{\isa{\isacommand{next}}} & switch blocks \\ + \mbox{\isa{\isacommand{note}}}~\isa{a\ {\isacharequal}\ b} & reconsider facts \\ + \mbox{\isa{\isacommand{let}}}~\isa{p\ {\isacharequal}\ t} & abbreviate terms by higher-order matching \\ + \end{tabular} + + \begin{matharray}{rcl} + \isa{theory{\isasymdash}stmt} & = & \mbox{\isa{\isacommand{theorem}}}~\isa{name{\isacharcolon}\ prop\ proof} \Or \mbox{\isa{\isacommand{definition}}}~\dots \Or \dots \\[1ex] + \isa{proof} & = & \isa{prfx\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{proof}}}~\isa{method\ stmt\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{qed}}}~\isa{method} \\ + & \Or & \isa{prfx\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{done}}} \\[1ex] + \isa{prfx} & = & \mbox{\isa{\isacommand{apply}}}~\isa{method} \\ + & \Or & \mbox{\isa{\isacommand{using}}}~\isa{name\isactrlsup {\isacharplus}} \\ + & \Or & \mbox{\isa{\isacommand{unfolding}}}~\isa{name\isactrlsup {\isacharplus}} \\ + \isa{stmt} & = & \mbox{\isa{\isacommand{{\isacharbraceleft}}}}~\isa{stmt\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{{\isacharbraceright}}}} \\ + & \Or & \mbox{\isa{\isacommand{next}}} \\ + & \Or & \mbox{\isa{\isacommand{note}}}~\isa{name\ {\isacharequal}\ name\isactrlsup {\isacharplus}} \\ + & \Or & \mbox{\isa{\isacommand{let}}}~\isa{term\ {\isacharequal}\ term} \\ + & \Or & \mbox{\isa{\isacommand{fix}}}~\isa{var\isactrlsup {\isacharplus}} \\ + & \Or & \mbox{\isa{\isacommand{assume}}}~\isa{name{\isacharcolon}\ prop\isactrlsup {\isacharplus}} \\ + & \Or & \mbox{\isa{\isacommand{then}}}\isa{\isactrlsup {\isacharquery}}~\isa{goal} \\ + \isa{goal} & = & \mbox{\isa{\isacommand{have}}}~\isa{name{\isacharcolon}\ prop\isactrlsup {\isacharplus}\ proof} \\ + & \Or & \mbox{\isa{\isacommand{show}}}~\isa{name{\isacharcolon}\ prop\isactrlsup {\isacharplus}\ proof} \\ + \end{matharray}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Abbreviations and synonyms% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{matharray}{rcl} + \mbox{\isa{\isacommand{by}}}~\isa{m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}} & \equiv & \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}~\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}} \\ + \mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}} & \equiv & \mbox{\isa{\isacommand{by}}}~\isa{rule} \\ + \mbox{\isa{\isacommand{{\isachardot}}}} & \equiv & \mbox{\isa{\isacommand{by}}}~\isa{this} \\ + \mbox{\isa{\isacommand{hence}}} & \equiv & \mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{have}}} \\ + \mbox{\isa{\isacommand{thus}}} & \equiv & \mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{show}}} \\ + \mbox{\isa{\isacommand{from}}}~\isa{a} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{a}~\mbox{\isa{\isacommand{then}}} \\ + \mbox{\isa{\isacommand{with}}}~\isa{a} & \equiv & \mbox{\isa{\isacommand{from}}}~\isa{a\ {\isasymAND}\ this} \\[1ex] + \mbox{\isa{\isacommand{from}}}~\isa{this} & \equiv & \mbox{\isa{\isacommand{then}}} \\ + \mbox{\isa{\isacommand{from}}}~\isa{this}~\mbox{\isa{\isacommand{have}}} & \equiv & \mbox{\isa{\isacommand{hence}}} \\ + \mbox{\isa{\isacommand{from}}}~\isa{this}~\mbox{\isa{\isacommand{show}}} & \equiv & \mbox{\isa{\isacommand{thus}}} \\ + \end{matharray}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Derived elements% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{matharray}{rcl} + \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub {\isadigit{0}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ this} \\ + \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}} \\ + \mbox{\isa{\isacommand{finally}}} & \approx & \mbox{\isa{\isacommand{also}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\[0.5ex] + \mbox{\isa{\isacommand{moreover}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ calculation\ this} \\ + \mbox{\isa{\isacommand{ultimately}}} & \approx & \mbox{\isa{\isacommand{moreover}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\[0.5ex] + \mbox{\isa{\isacommand{presume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & \approx & \mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} \\ + \mbox{\isa{\isacommand{def}}}~\isa{a{\isacharcolon}\ x\ {\isasymequiv}\ t} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ x\ {\isasymequiv}\ t} \\ + \mbox{\isa{\isacommand{obtain}}}~\isa{x\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}} & \approx & \dots~\mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} \\ + \mbox{\isa{\isacommand{case}}}~\isa{c} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{c{\isacharcolon}\ {\isasymphi}} \\ + \mbox{\isa{\isacommand{sorry}}} & \approx & \mbox{\isa{\isacommand{by}}}~\isa{cheating} \\ + \end{matharray}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Diagnostic commands% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \mbox{\isa{\isacommand{pr}}} & print current state \\ + \mbox{\isa{\isacommand{thm}}}~\isa{a} & print fact \\ + \mbox{\isa{\isacommand{term}}}~\isa{t} & print term \\ + \mbox{\isa{\isacommand{prop}}}~\isa{{\isasymphi}} & print meta-level proposition \\ + \mbox{\isa{\isacommand{typ}}}~\isa{{\isasymtau}} & print meta-level type \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsection{Proof methods% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex] + \mbox{\isa{assumption}} & apply some assumption \\ + \mbox{\isa{this}} & apply current facts \\ + \mbox{\isa{rule}}~\isa{a} & apply some rule \\ + \mbox{\isa{rule}} & apply standard rule (default for \mbox{\isa{\isacommand{proof}}}) \\ + \mbox{\isa{contradiction}} & apply \isa{{\isasymnot}} elimination rule (any order) \\ + \mbox{\isa{cases}}~\isa{t} & case analysis (provides cases) \\ + \mbox{\isa{induct}}~\isa{x} & proof by induction (provides cases) \\[2ex] + + \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex] + \mbox{\isa{{\isacharminus}}} & no rules \\ + \mbox{\isa{intro}}~\isa{a} & introduction rules \\ + \mbox{\isa{intro{\isacharunderscore}classes}} & class introduction rules \\ + \mbox{\isa{elim}}~\isa{a} & elimination rules \\ + \mbox{\isa{unfold}}~\isa{a} & definitional rewrite rules \\[2ex] + + \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex] + \mbox{\isa{iprover}} & intuitionistic proof search \\ + \mbox{\isa{blast}}, \mbox{\isa{fast}} & Classical Reasoner \\ + \mbox{\isa{simp}}, \mbox{\isa{simp{\isacharunderscore}all}} & Simplifier (+ Splitter) \\ + \mbox{\isa{auto}}, \mbox{\isa{force}} & Simplifier + Classical Reasoner \\ + \mbox{\isa{arith}} & Arithmetic procedures \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsection{Attributes% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \multicolumn{2}{l}{\textbf{Operations}} \\[0.5ex] + \mbox{\isa{OF}}~\isa{a} & rule resolved with facts (skipping ``\isa{{\isacharunderscore}}'') \\ + \mbox{\isa{of}}~\isa{t} & rule instantiated with terms (skipping ``\isa{{\isacharunderscore}}'') \\ + \mbox{\isa{where}}~\isa{x\ {\isacharequal}\ t} & rule instantiated with terms, by variable name \\ + \mbox{\isa{symmetric}} & resolution with symmetry rule \\ + \mbox{\isa{THEN}}~\isa{b} & resolution with another rule \\ + \mbox{\isa{rule{\isacharunderscore}format}} & result put into standard rule format \\ + \mbox{\isa{elim{\isacharunderscore}format}} & destruct rule turned into elimination rule format \\[1ex] + + \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex] + \mbox{\isa{simp}} & Simplifier rule \\ + \mbox{\isa{intro}}, \mbox{\isa{elim}}, \mbox{\isa{dest}} & Pure or Classical Reasoner rule \\ + \mbox{\isa{iff}} & Simplifier + Classical Reasoner rule \\ + \mbox{\isa{split}} & case split rule \\ + \mbox{\isa{trans}} & transitivity rule \\ + \mbox{\isa{sym}} & symmetry rule \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsection{Rule declarations and methods% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{l|lllll} + & \mbox{\isa{rule}} & \mbox{\isa{iprover}} & \mbox{\isa{blast}} & \mbox{\isa{simp}} & \mbox{\isa{auto}} \\ + & & & \mbox{\isa{fast}} & \mbox{\isa{simp{\isacharunderscore}all}} & \mbox{\isa{force}} \\ + \hline + \mbox{\isa{Pure{\isachardot}elim}}\isa{{\isacharbang}} \mbox{\isa{Pure{\isachardot}intro}}\isa{{\isacharbang}} + & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{Pure{\isachardot}elim}} \mbox{\isa{Pure{\isachardot}intro}} + & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{elim}}\isa{{\isacharbang}} \mbox{\isa{intro}}\isa{{\isacharbang}} + & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} \\ + \mbox{\isa{elim}} \mbox{\isa{intro}} + & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} \\ + \mbox{\isa{iff}} + & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{iff}}\isa{{\isacharquery}} + & \isa{{\isasymtimes}} \\ + \mbox{\isa{elim}}\isa{{\isacharquery}} \mbox{\isa{intro}}\isa{{\isacharquery}} + & \isa{{\isasymtimes}} \\ + \mbox{\isa{simp}} + & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{cong}} + & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{split}} + & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsection{Emulating tactic scripts% +} +\isamarkuptrue% +% +\isamarkupsubsection{Commands% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \mbox{\isa{\isacommand{apply}}}~\isa{m} & apply proof method at initial position \\ + \mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}~\isa{m} & apply proof method near terminal position \\ + \mbox{\isa{\isacommand{done}}} & complete proof \\ + \mbox{\isa{\isacommand{defer}}}~\isa{n} & move subgoal to end \\ + \mbox{\isa{\isacommand{prefer}}}~\isa{n} & move subgoal to beginning \\ + \mbox{\isa{\isacommand{back}}} & backtrack last command \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Methods% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{tabular}{ll} + \mbox{\isa{rule{\isacharunderscore}tac}}~\isa{insts} & resolution (with instantiation) \\ + \mbox{\isa{erule{\isacharunderscore}tac}}~\isa{insts} & elim-resolution (with instantiation) \\ + \mbox{\isa{drule{\isacharunderscore}tac}}~\isa{insts} & destruct-resolution (with instantiation) \\ + \mbox{\isa{frule{\isacharunderscore}tac}}~\isa{insts} & forward-resolution (with instantiation) \\ + \mbox{\isa{cut{\isacharunderscore}tac}}~\isa{insts} & insert facts (with instantiation) \\ + \mbox{\isa{thin{\isacharunderscore}tac}}~\isa{{\isasymphi}} & delete assumptions \\ + \mbox{\isa{subgoal{\isacharunderscore}tac}}~\isa{{\isasymphi}} & new claims \\ + \mbox{\isa{rename{\isacharunderscore}tac}}~\isa{x} & rename innermost goal parameters \\ + \mbox{\isa{rotate{\isacharunderscore}tac}}~\isa{n} & rotate assumptions of goal \\ + \mbox{\isa{tactic}}~\isa{text} & arbitrary ML tactic \\ + \mbox{\isa{case{\isacharunderscore}tac}}~\isa{t} & exhaustion (datatypes) \\ + \mbox{\isa{induct{\isacharunderscore}tac}}~\isa{x} & induction (datatypes) \\ + \mbox{\isa{ind{\isacharunderscore}cases}}~\isa{t} & exhaustion + simplification (inductive predicates) \\ + \end{tabular}% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isadelimtheory +% +\endisadelimtheory +% +\isatagtheory +\isacommand{end}\isamarkupfalse% +% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +\isanewline +\end{isabellebody}% +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "root" +%%% End: