diff -r a5f5b9336007 -r 1cde7bf45858 Separation_Algebra/Sep_Tactics.thy~ --- a/Separation_Algebra/Sep_Tactics.thy~ Sat Sep 13 10:07:14 2014 +0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,161 +0,0 @@ -(* Authors: Gerwin Klein and Rafal Kolanski, 2012 - Maintainers: Gerwin Klein - Rafal Kolanski -*) - -header "Separation Logic Tactics" - -theory Sep_Tactics -imports Separation_Algebra -begin - -ML_file "sep_tactics.ML" - -text {* A number of proof methods to assist with reasoning about separation logic. *} - - -section {* Selection (move-to-front) tactics *} - -ML {* - fun sep_select_method n ctxt = - Method.SIMPLE_METHOD' (sep_select_tac ctxt n); - fun sep_select_asm_method n ctxt = - Method.SIMPLE_METHOD' (sep_select_asm_tac ctxt n); -*} - -method_setup sep_select = {* - Scan.lift Parse.int >> sep_select_method -*} "Select nth separation conjunct in conclusion" - -method_setup sep_select_asm = {* - Scan.lift Parse.int >> sep_select_asm_method -*} "Select nth separation conjunct in assumptions" - - -section {* Substitution *} - -ML {* - fun sep_subst_method ctxt occs thms = - SIMPLE_METHOD' (sep_subst_tac ctxt occs thms); - fun sep_subst_asm_method ctxt occs thms = - SIMPLE_METHOD' (sep_subst_asm_tac ctxt occs thms); - - val sep_subst_parser = - Args.mode "asm" - -- Scan.lift (Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) - -- Attrib.thms; -*} - -method_setup "sep_subst" = {* - sep_subst_parser >> - (fn ((asm, occs), thms) => fn ctxt => - (if asm then sep_subst_asm_method else sep_subst_method) ctxt occs thms) -*} -"single-step substitution after solving one separation logic assumption" - - -section {* Forward Reasoning *} - -ML {* - fun sep_drule_method thms ctxt = SIMPLE_METHOD' (sep_dtac ctxt thms); - fun sep_frule_method thms ctxt = SIMPLE_METHOD' (sep_ftac ctxt thms); -*} - -method_setup "sep_drule" = {* - Attrib.thms >> sep_drule_method -*} "drule after separating conjunction reordering" - -method_setup "sep_frule" = {* - Attrib.thms >> sep_frule_method -*} "frule after separating conjunction reordering" - - -section {* Backward Reasoning *} - -ML {* - fun sep_rule_method thms ctxt = SIMPLE_METHOD' (sep_rtac ctxt thms) -*} - -method_setup "sep_rule" = {* - Attrib.thms >> sep_rule_method -*} "applies rule after separating conjunction reordering" - - -section {* Cancellation of Common Conjuncts via Elimination Rules *} - -ML {* - structure SepCancel_Rules = Named_Thms ( - val name = @{binding "sep_cancel"}; - val description = "sep_cancel rules"; - ); -*} -setup SepCancel_Rules.setup - -text {* - The basic @{text sep_cancel_tac} is minimal. It only eliminates - erule-derivable conjuncts between an assumption and the conclusion. - - To have a more useful tactic, we augment it with more logic, to proceed as - follows: - \begin{itemize} - \item try discharge the goal first using @{text tac} - \item if that fails, invoke @{text sep_cancel_tac} - \item if @{text sep_cancel_tac} succeeds - \begin{itemize} - \item try to finish off with tac (but ok if that fails) - \item try to finish off with @{term sep_true} (but ok if that fails) - \end{itemize} - \end{itemize} - *} - -ML {* - fun sep_cancel_smart_tac ctxt tac = - let fun TRY' tac = tac ORELSE' (K all_tac) - in - tac - ORELSE' (sep_cancel_tac ctxt tac - THEN' TRY' tac - THEN' TRY' (rtac @{thm TrueI})) - ORELSE' (etac @{thm sep_conj_sep_emptyE} - THEN' sep_cancel_tac ctxt tac - THEN' TRY' tac - THEN' TRY' (rtac @{thm TrueI})) - end; - - fun sep_cancel_smart_tac_rules ctxt etacs = - sep_cancel_smart_tac ctxt (FIRST' ([atac] @ etacs)); - - fun sep_cancel_method ctxt = - let - val etacs = map etac (SepCancel_Rules.get ctxt); - in - SIMPLE_METHOD' (sep_cancel_smart_tac_rules ctxt etacs) - end; - - val sep_cancel_syntax = Method.sections [ - Args.add -- Args.colon >> K (I, SepCancel_Rules.add)]; -*} - -method_setup sep_cancel = {* - sep_cancel_syntax >> K sep_cancel_method -*} "Separating conjunction conjunct cancellation" - -text {* - As above, but use blast with a depth limit to figure out where cancellation - can be done. *} - -ML {* - fun sep_cancel_blast_method ctxt = - let - val rules = SepCancel_Rules.get ctxt; - val tac = Blast.depth_tac (ctxt addIs rules) 10; - in - SIMPLE_METHOD' (sep_cancel_smart_tac ctxt tac) - end; -*} - -method_setup sep_cancel_blast = {* - sep_cancel_syntax >> K sep_cancel_blast_method -*} "Separating conjunction conjunct cancellation using blast" - -end