src/HOL/UNITY/UNITY_tactics.ML
author hoelzl
Thu Sep 02 10:14:32 2010 +0200 (2010-09-02)
changeset 39072 1030b1a166ef
parent 37936 1e4c5015a72e
child 42767 e6d920bea7a6
permissions -rw-r--r--
Add lessThan_Suc_eq_insert_0
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(*  Title:      HOL/UNITY/UNITY_tactics.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   2003  University of Cambridge
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Specialized UNITY tactics.
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*)
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(*Combines two invariance ASSUMPTIONS into one.  USEFUL??*)
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val Always_Int_tac = dtac @{thm Always_Int_I} THEN' assume_tac THEN' etac @{thm Always_thin}
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(*Combines a list of invariance THEOREMS into one.*)
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val Always_Int_rule = foldr1 (fn (th1,th2) => [th1,th2] MRS @{thm Always_Int_I})
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(*Proves "co" properties when the program is specified.  Any use of invariants
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  (from weak constrains) must have been done already.*)
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fun constrains_tac(cs,ss) i =
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   SELECT_GOAL
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      (EVERY [REPEAT (Always_Int_tac 1),
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              (*reduce the fancy safety properties to "constrains"*)
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              REPEAT (etac @{thm Always_ConstrainsI} 1
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                      ORELSE
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                      resolve_tac [@{thm StableI}, @{thm stableI},
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                                   @{thm constrains_imp_Constrains}] 1),
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              (*for safety, the totalize operator can be ignored*)
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              simp_tac (HOL_ss addsimps
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                         [@{thm mk_total_program_def}, @{thm totalize_constrains_iff}]) 1,
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              rtac @{thm constrainsI} 1,
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              full_simp_tac ss 1,
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              REPEAT (FIRSTGOAL (etac disjE)),
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              ALLGOALS (clarify_tac cs),
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              ALLGOALS (asm_full_simp_tac ss)]) i;
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(*proves "ensures/leadsTo" properties when the program is specified*)
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fun ensures_tac(cs,ss) sact =
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    SELECT_GOAL
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      (EVERY [REPEAT (Always_Int_tac 1),
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              etac @{thm Always_LeadsTo_Basis} 1
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                  ORELSE   (*subgoal may involve LeadsTo, leadsTo or ensures*)
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                  REPEAT (ares_tac [@{thm LeadsTo_Basis}, @{thm leadsTo_Basis},
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                                    @{thm EnsuresI}, @{thm ensuresI}] 1),
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              (*now there are two subgoals: co & transient*)
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              simp_tac (ss addsimps [@{thm mk_total_program_def}]) 2,
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              res_inst_tac (Simplifier.the_context ss)
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                [(("act", 0), sact)] @{thm totalize_transientI} 2
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              ORELSE res_inst_tac (Simplifier.the_context ss)
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                [(("act", 0), sact)] @{thm transientI} 2,
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                 (*simplify the command's domain*)
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              simp_tac (ss addsimps [@{thm Domain_def}]) 3,
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              constrains_tac (cs,ss) 1,
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              ALLGOALS (clarify_tac cs),
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              ALLGOALS (asm_lr_simp_tac ss)]);
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(*Composition equivalences, from Lift_prog*)
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fun make_o_equivs th =
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    [th,
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     th RS @{thm o_equiv_assoc} |> simplify (HOL_ss addsimps [@{thm o_assoc}]),
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     th RS @{thm o_equiv_apply} |> simplify (HOL_ss addsimps [@{thm o_def}, @{thm sub_def}])];
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Simplifier.change_simpset (fn ss => ss
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  addsimps (make_o_equivs @{thm fst_o_funPair} @ make_o_equivs @{thm snd_o_funPair})
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  addsimps (make_o_equivs @{thm fst_o_lift_map} @ make_o_equivs @{thm snd_o_lift_map}));