diff -r 17098171d46a -r 6f79647cf536 src/HOL/TLA/Memory/Memory.ML --- a/src/HOL/TLA/Memory/Memory.ML Fri Dec 01 17:22:33 2006 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,126 +0,0 @@ -(* - File: Memory.ML - ID: $Id$ - Author: Stephan Merz - Copyright: 1997 University of Munich - - RPC-Memory example: Memory specification (theorems and proofs) -*) - -val RM_action_defs = - [MInit_def, PInit_def, RdRequest_def, WrRequest_def, MemInv_def, - GoodRead_def, BadRead_def, ReadInner_def, Read_def, - GoodWrite_def, BadWrite_def, WriteInner_def, Write_def, - MemReturn_def, RNext_def]; - -val UM_action_defs = RM_action_defs @ [MemFail_def, UNext_def]; - -val RM_temp_defs = [RPSpec_def, MSpec_def, IRSpec_def]; -val UM_temp_defs = [UPSpec_def, MSpec_def, IUSpec_def]; - -val mem_css = (claset(), simpset()); - -(* -------------------- Proofs ---------------------------------------------- *) - -(* The reliable memory is an implementation of the unreliable one *) -Goal "|- IRSpec ch mm rs --> IUSpec ch mm rs"; -by (force_tac (temp_css addsimps2 ([UNext_def,UPSpec_def,IUSpec_def] @ RM_temp_defs) - addSEs2 [STL4E,squareE]) 1); -qed "ReliableImplementsUnReliable"; - -(* The memory spec implies the memory invariant *) -Goal "|- MSpec ch mm rs l --> [](MemInv mm l)"; -by (auto_inv_tac (simpset() addsimps RM_temp_defs @ RM_action_defs) 1); -qed "MemoryInvariant"; - -(* The invariant is trivial for non-locations *) -Goal "|- #l ~: #MemLoc --> [](MemInv mm l)"; -by (auto_tac (temp_css addsimps2 [MemInv_def] addSIs2 [necT])); -qed "NonMemLocInvariant"; - -Goal "|- (ALL l. #l : #MemLoc --> MSpec ch mm rs l) --> (ALL l. [](MemInv mm l))"; -by (step_tac temp_cs 1); -by (case_tac "l : MemLoc" 1); -by (auto_tac (temp_css addSEs2 [MemoryInvariant,NonMemLocInvariant])); -qed "MemoryInvariantAll"; - -(* The memory engages in an action for process p only if there is an - unanswered call from p. - We need this only for the reliable memory. -*) - -Goal "|- ~$(Calling ch p) --> ~ RNext ch mm rs p"; -by (auto_tac (mem_css addsimps2 (Return_def::RM_action_defs))); -qed "Memoryidle"; - -(* Enabledness conditions *) - -Goal "|- MemReturn ch rs p --> _(rtrner ch ! p, rs!p)"; -by (force_tac (mem_css addsimps2 [MemReturn_def,angle_def]) 1); -qed "MemReturn_change"; - -Goal "!!p. basevars (rtrner ch ! p, rs!p) ==> \ -\ |- Calling ch p & (rs!p ~= #NotAResult) \ -\ --> Enabled (_(rtrner ch ! p, rs!p))"; -by (action_simp_tac (simpset()) [MemReturn_change RSN (2,enabled_mono)] [] 1); -by (action_simp_tac (simpset() addsimps [MemReturn_def,Return_def,rtrner_def]) - [exI] [base_enabled,Pair_inject] 1); -qed "MemReturn_enabled"; - -Goal "!!p. basevars (rtrner ch ! p, rs!p) ==> \ -\ |- Calling ch p & (arg = #(read l)) --> Enabled (ReadInner ch mm rs p l)"; -by (case_tac "l : MemLoc" 1); -by (ALLGOALS - (force_tac (mem_css addsimps2 [ReadInner_def,GoodRead_def, - BadRead_def,RdRequest_def] - addSIs2 [exI] addSEs2 [base_enabled]))); -qed "ReadInner_enabled"; - -Goal "!!p. basevars (mm!l, rtrner ch ! p, rs!p) ==> \ -\ |- Calling ch p & (arg = #(write l v)) \ -\ --> Enabled (WriteInner ch mm rs p l v)"; -by (case_tac "l:MemLoc & v:MemVal" 1); -by (ALLGOALS - (force_tac (mem_css addsimps2 [WriteInner_def,GoodWrite_def, - BadWrite_def,WrRequest_def] - addSIs2 [exI] addSEs2 [base_enabled]))); -qed "WriteInner_enabled"; - -Goal "|- Read ch mm rs p & (!l. $(MemInv mm l)) --> (rs!p)` ~= #NotAResult"; -by (force_tac (mem_css addsimps2 - [Read_def,ReadInner_def,GoodRead_def,BadRead_def,MemInv_def]) 1); -qed "ReadResult"; - -Goal "|- Write ch mm rs p l --> (rs!p)` ~= #NotAResult"; -by (auto_tac (mem_css addsimps2 ([Write_def,WriteInner_def,GoodWrite_def,BadWrite_def]))); -qed "WriteResult"; - -Goal "|- (ALL l. $MemInv mm l) & MemReturn ch rs p \ -\ --> ~ Read ch mm rs p & (ALL l. ~ Write ch mm rs p l)"; -by (auto_tac (mem_css addsimps2 [MemReturn_def] addSDs2 [WriteResult, ReadResult])); -qed "ReturnNotReadWrite"; - -Goal "|- (rs!p = #NotAResult) & (!l. MemInv mm l) \ -\ & Enabled (Read ch mm rs p | (? l. Write ch mm rs p l)) \ -\ --> Enabled (_(rtrner ch ! p, rs!p))"; -by (force_tac (mem_css addsimps2 [RNext_def,angle_def] - addSEs2 [enabled_mono2] - addDs2 [ReadResult, WriteResult]) 1); -qed "RWRNext_enabled"; - - -(* Combine previous lemmas: the memory can make a visible step if there is an - outstanding call for which no result has been produced. -*) -Goal "!!p. !l. basevars (mm!l, rtrner ch!p, rs!p) ==> \ -\ |- (rs!p = #NotAResult) & Calling ch p & (!l. MemInv mm l) \ -\ --> Enabled (_(rtrner ch ! p, rs!p))"; -by (auto_tac (mem_css addsimps2 [enabled_disj] addSIs2 [RWRNext_enabled])); -by (case_tac "arg(ch w p)" 1); - by (action_simp_tac (simpset()addsimps[Read_def,enabled_ex]) - [ReadInner_enabled,exI] [] 1); - by (force_tac (mem_css addDs2 [base_pair]) 1); -by (etac contrapos_np 1); -by (action_simp_tac (simpset() addsimps [Write_def,enabled_ex]) - [WriteInner_enabled,exI] [] 1); -qed "RNext_enabled";