src/HOL/UNITY/UNITY_tactics.ML

document "type_sys" option

(*  Title:      HOL/UNITY/UNITY_tactics.ML
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   2003  University of Cambridge

Specialized UNITY tactics.
*)

(*Combines two invariance ASSUMPTIONS into one.  USEFUL??*)
val Always_Int_tac = dtac @{thm Always_Int_I} THEN' assume_tac THEN' etac @{thm Always_thin}

(*Combines a list of invariance THEOREMS into one.*)
val Always_Int_rule = foldr1 (fn (th1,th2) => [th1,th2] MRS @{thm Always_Int_I})

(*Proves "co" properties when the program is specified.  Any use of invariants
  (from weak constrains) must have been done already.*)
fun constrains_tac(cs,ss) i =
   SELECT_GOAL
      (EVERY [REPEAT (Always_Int_tac 1),
              (*reduce the fancy safety properties to "constrains"*)
              REPEAT (etac @{thm Always_ConstrainsI} 1
                      ORELSE
                      resolve_tac [@{thm StableI}, @{thm stableI},
                                   @{thm constrains_imp_Constrains}] 1),
              (*for safety, the totalize operator can be ignored*)
              simp_tac (HOL_ss addsimps
                         [@{thm mk_total_program_def}, @{thm totalize_constrains_iff}]) 1,
              rtac @{thm constrainsI} 1,
              full_simp_tac ss 1,
              REPEAT (FIRSTGOAL (etac disjE)),
              ALLGOALS (clarify_tac cs),
              ALLGOALS (asm_full_simp_tac ss)]) i;

(*proves "ensures/leadsTo" properties when the program is specified*)
fun ensures_tac(cs,ss) sact =
    SELECT_GOAL
      (EVERY [REPEAT (Always_Int_tac 1),
              etac @{thm Always_LeadsTo_Basis} 1
                  ORELSE   (*subgoal may involve LeadsTo, leadsTo or ensures*)
                  REPEAT (ares_tac [@{thm LeadsTo_Basis}, @{thm leadsTo_Basis},
                                    @{thm EnsuresI}, @{thm ensuresI}] 1),
              (*now there are two subgoals: co & transient*)
              simp_tac (ss addsimps [@{thm mk_total_program_def}]) 2,
              res_inst_tac (Simplifier.the_context ss)
                [(("act", 0), sact)] @{thm totalize_transientI} 2
              ORELSE res_inst_tac (Simplifier.the_context ss)
                [(("act", 0), sact)] @{thm transientI} 2,
                 (*simplify the command's domain*)
              simp_tac (ss addsimps [@{thm Domain_def}]) 3,
              constrains_tac (cs,ss) 1,
              ALLGOALS (clarify_tac cs),
              ALLGOALS (asm_lr_simp_tac ss)]);


(*Composition equivalences, from Lift_prog*)

fun make_o_equivs th =
    [th,
     th RS @{thm o_equiv_assoc} |> simplify (HOL_ss addsimps [@{thm o_assoc}]),
     th RS @{thm o_equiv_apply} |> simplify (HOL_ss addsimps [@{thm o_def}, @{thm sub_def}])];

Simplifier.change_simpset (fn ss => ss
  addsimps (make_o_equivs @{thm fst_o_funPair} @ make_o_equivs @{thm snd_o_funPair})
  addsimps (make_o_equivs @{thm fst_o_lift_map} @ make_o_equivs @{thm snd_o_lift_map}));