(* $Id: Init.ML,v 1.2 2005/09/07 18:22:39 wenzelm Exp $ *) local fun prover s = prove_goal (the_context ()) s (K [force_tac (claset(), simpset() addsimps [Init_def]) 1]) in val const_simps = map (int_rewrite o prover) [ "|- (Init #True) = #True", "|- (Init #False) = #False"] val Init_simps = map (int_rewrite o prover) [ "|- (Init ~F) = (~ Init F)", "|- (Init (P --> Q)) = (Init P --> Init Q)", "|- (Init (P & Q)) = (Init P & Init Q)", "|- (Init (P | Q)) = (Init P | Init Q)", "|- (Init (P = Q)) = ((Init P) = (Init Q))", "|- (Init (!x. F x)) = (!x. (Init F x))", "|- (Init (? x. F x)) = (? x. (Init F x))", "|- (Init (?! x. F x)) = (?! x. (Init F x))" ] end; Addsimps const_simps; Goal "|- (Init $P) = (Init P)"; by (force_tac (claset(), simpset() addsimps [Init_def,fw_act_def,fw_stp_def]) 1); qed "Init_stp_act"; val Init_simps = (int_rewrite Init_stp_act)::Init_simps; bind_thm("Init_stp_act_rev", symmetric(int_rewrite Init_stp_act)); Goal "|- (Init F) = F"; by (force_tac (claset(), simpset() addsimps [Init_def,fw_temp_def]) 1); qed "Init_temp"; val Init_simps = (int_rewrite Init_temp)::Init_simps; (* Trivial instances of the definitions that avoid introducing lambda expressions. *) Goalw [Init_def,fw_stp_def] "(sigma |= Init P) = P (st1 sigma)"; by (rtac refl 1); qed "Init_stp"; Goalw [Init_def,fw_act_def] "(sigma |= Init A) = A (st1 sigma, st2 sigma)"; by (rtac refl 1); qed "Init_act"; val Init_defs = [Init_stp, Init_act, int_use Init_temp];