diff -r f04b33ce250f -r a4dc62a46ee4 indrule.ML --- a/indrule.ML Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,184 +0,0 @@ -(* Title: HOL/indrule.ML - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1994 University of Cambridge - -Induction rule module -- for Inductive/Coinductive Definitions - -Proves a strong induction rule and a mutual induction rule -*) - -signature INDRULE = - sig - val induct : thm (*main induction rule*) - val mutual_induct : thm (*mutual induction rule*) - end; - - -functor Indrule_Fun - (structure Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end and - Intr_elim: INTR_ELIM) : INDRULE = -struct -open Logic Ind_Syntax Inductive Intr_elim; - -val sign = sign_of thy; - -val (Const(_,recT),rec_params) = strip_comb (hd rec_tms); - -val elem_type = dest_setT (body_type recT); -val domTs = summands(elem_type); -val big_rec_name = space_implode "_" rec_names; -val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params); - -val _ = writeln " Proving the induction rules..."; - -(*** Prove the main induction rule ***) - -val pred_name = "P"; (*name for predicate variables*) - -val big_rec_def::part_rec_defs = Intr_elim.defs; - -(*Used to express induction rules: adds induction hypotheses. - ind_alist = [(rec_tm1,pred1),...] -- associates predicates with rec ops - prem is a premise of an intr rule*) -fun add_induct_prem ind_alist (prem as Const("Trueprop",_) $ - (Const("op :",_)$t$X), iprems) = - (case gen_assoc (op aconv) (ind_alist, X) of - Some pred => prem :: mk_Trueprop (pred $ t) :: iprems - | None => (*possibly membership in M(rec_tm), for M monotone*) - let fun mk_sb (rec_tm,pred) = - (case binder_types (fastype_of pred) of - [T] => (rec_tm, - Int_const T $ rec_tm $ (Collect_const T $ pred)) - | _ => error - "Bug: add_induct_prem called with non-unary predicate") - in subst_free (map mk_sb ind_alist) prem :: iprems end) - | add_induct_prem ind_alist (prem,iprems) = prem :: iprems; - -(*Make a premise of the induction rule.*) -fun induct_prem ind_alist intr = - let val quantfrees = map dest_Free (term_frees intr \\ rec_params) - val iprems = foldr (add_induct_prem ind_alist) - (strip_imp_prems intr,[]) - val (t,X) = rule_concl intr - val (Some pred) = gen_assoc (op aconv) (ind_alist, X) - val concl = mk_Trueprop (pred $ t) - in list_all_free (quantfrees, list_implies (iprems,concl)) end - handle Bind => error"Recursion term not found in conclusion"; - -(*Avoids backtracking by delivering the correct premise to each goal*) -fun ind_tac [] 0 = all_tac - | ind_tac(prem::prems) i = - DEPTH_SOLVE_1 (ares_tac [Part_eqI, prem, refl] i) THEN - ind_tac prems (i-1); - -val pred = Free(pred_name, elem_type --> boolT); - -val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) intr_tms; - -val quant_induct = - prove_goalw_cterm part_rec_defs - (cterm_of sign (list_implies (ind_prems, - mk_Trueprop (mk_all_imp(big_rec_tm,pred))))) - (fn prems => - [rtac (impI RS allI) 1, - etac raw_induct 1, - REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE, disjE] - ORELSE' hyp_subst_tac)), - REPEAT (FIRSTGOAL (eresolve_tac [PartE, CollectE])), - ind_tac (rev prems) (length prems)]) - handle e => print_sign_exn sign e; - -(*** Prove the simultaneous induction rule ***) - -(*Make distinct predicates for each inductive set. - Splits cartesian products in domT, IF nested to the right! *) - -(*Given a recursive set and its domain, return the "split" predicate - and a conclusion for the simultaneous induction rule*) -fun mk_predpair (rec_tm,domT) = - let val rec_name = (#1 o dest_Const o head_of) rec_tm - val T = factors domT ---> boolT - val pfree = Free(pred_name ^ "_" ^ rec_name, T) - val frees = mk_frees "za" (binder_types T) - val qconcl = - foldr mk_all (frees, - imp $ (mk_mem (foldr1 mk_Pair frees, rec_tm)) - $ (list_comb (pfree,frees))) - in (ap_split boolT pfree (binder_types T), - qconcl) - end; - -val (preds,qconcls) = split_list (map mk_predpair (rec_tms~~domTs)); - -(*Used to form simultaneous induction lemma*) -fun mk_rec_imp (rec_tm,pred) = - imp $ (mk_mem (Bound 0, rec_tm)) $ (pred $ Bound 0); - -(*To instantiate the main induction rule*) -val induct_concl = - mk_Trueprop(mk_all_imp(big_rec_tm, - Abs("z", elem_type, - fold_bal (app conj) - (map mk_rec_imp (rec_tms~~preds))))) -and mutual_induct_concl = mk_Trueprop(fold_bal (app conj) qconcls); - -val lemma = (*makes the link between the two induction rules*) - prove_goalw_cterm part_rec_defs - (cterm_of sign (mk_implies (induct_concl,mutual_induct_concl))) - (fn prems => - [cut_facts_tac prems 1, - REPEAT (eresolve_tac [asm_rl, conjE, PartE, mp] 1 - ORELSE resolve_tac [allI, impI, conjI, Part_eqI, refl] 1 - ORELSE dresolve_tac [spec, mp, splitD] 1)]) - handle e => print_sign_exn sign e; - -(*Mutual induction follows by freeness of Inl/Inr.*) - -(*Removes Collects caused by M-operators in the intro rules*) -val cmonos = [subset_refl RS Int_Collect_mono] RL monos RLN (2,[rev_subsetD]); - -(*Avoids backtracking by delivering the correct premise to each goal*) -fun mutual_ind_tac [] 0 = all_tac - | mutual_ind_tac(prem::prems) i = - DETERM - (SELECT_GOAL - ((*unpackage and use "prem" in the corresponding place*) - REPEAT (FIRSTGOAL - (etac conjE ORELSE' eq_mp_tac ORELSE' - ares_tac [impI, conjI])) - (*prem is not allowed in the REPEAT, lest it loop!*) - THEN TRYALL (rtac prem) - THEN REPEAT - (FIRSTGOAL (ares_tac [impI] ORELSE' - eresolve_tac (mp::cmonos))) - (*prove remaining goals by contradiction*) - THEN rewrite_goals_tac (con_defs@part_rec_defs) - THEN DEPTH_SOLVE (eresolve_tac (PartE :: sumprod_free_SEs) 1)) - i) - THEN mutual_ind_tac prems (i-1); - -val mutual_induct_split = - prove_goalw_cterm [] - (cterm_of sign - (list_implies (map (induct_prem (rec_tms~~preds)) intr_tms, - mutual_induct_concl))) - (fn prems => - [rtac (quant_induct RS lemma) 1, - mutual_ind_tac (rev prems) (length prems)]) - handle e => print_sign_exn sign e; - -(*Attempts to remove all occurrences of split*) -val split_tac = - REPEAT (SOMEGOAL (FIRST' [rtac splitI, - dtac splitD, - etac splitE, - bound_hyp_subst_tac])) - THEN prune_params_tac; - -(*strip quantifier*) -val induct = standard (quant_induct RS spec RSN (2,rev_mp)); - -val mutual_induct = rule_by_tactic split_tac mutual_induct_split; - -end;