wenzelm@12191: (* Title: ZF/Tools/inductive_package.ML paulson@6051: ID: $Id$ paulson@6051: Author: Lawrence C Paulson, Cambridge University Computer Laboratory paulson@6051: Copyright 1994 University of Cambridge paulson@6051: paulson@6051: Fixedpoint definition module -- for Inductive/Coinductive Definitions paulson@6051: paulson@6051: The functor will be instantiated for normal sums/products (inductive defs) paulson@6051: and non-standard sums/products (coinductive defs) paulson@6051: paulson@6051: Sums are used only for mutual recursion; paulson@6051: Products are used only to derive "streamlined" induction rules for relations paulson@6051: *) paulson@6051: paulson@6051: type inductive_result = paulson@6051: {defs : thm list, (*definitions made in thy*) paulson@6051: bnd_mono : thm, (*monotonicity for the lfp definition*) paulson@6051: dom_subset : thm, (*inclusion of recursive set in dom*) paulson@6051: intrs : thm list, (*introduction rules*) paulson@6051: elim : thm, (*case analysis theorem*) paulson@6141: mk_cases : string -> thm, (*generates case theorems*) paulson@6051: induct : thm, (*main induction rule*) paulson@6051: mutual_induct : thm}; (*mutual induction rule*) paulson@6051: paulson@6051: paulson@6051: (*Functor's result signature*) paulson@6051: signature INDUCTIVE_PACKAGE = wenzelm@12132: sig paulson@6051: (*Insert definitions for the recursive sets, which paulson@6051: must *already* be declared as constants in parent theory!*) wenzelm@12132: val add_inductive_i: bool -> term list * term -> wenzelm@18728: ((bstring * term) * attribute list) list -> wenzelm@12132: thm list * thm list * thm list * thm list -> theory -> theory * inductive_result wenzelm@12132: val add_inductive: string list * string -> wenzelm@15703: ((bstring * string) * Attrib.src list) list -> wenzelm@15703: (thmref * Attrib.src list) list * (thmref * Attrib.src list) list * wenzelm@15703: (thmref * Attrib.src list) list * (thmref * Attrib.src list) list -> wenzelm@12132: theory -> theory * inductive_result wenzelm@12132: end; paulson@6051: paulson@6051: paulson@6051: (*Declares functions to add fixedpoint/constructor defs to a theory. paulson@6051: Recursive sets must *already* be declared as constants.*) wenzelm@12132: functor Add_inductive_def_Fun wenzelm@12132: (structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool) paulson@6051: : INDUCTIVE_PACKAGE = paulson@6051: struct wenzelm@12183: wenzelm@16855: open Ind_Syntax; paulson@6051: wenzelm@12227: val co_prefix = if coind then "co" else ""; wenzelm@12227: wenzelm@7695: wenzelm@7695: (* utils *) wenzelm@7695: wenzelm@7695: (*make distinct individual variables a1, a2, a3, ..., an. *) wenzelm@7695: fun mk_frees a [] = [] wenzelm@12902: | mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts; wenzelm@7695: wenzelm@7695: wenzelm@7695: (* add_inductive(_i) *) wenzelm@7695: paulson@6051: (*internal version, accepting terms*) wenzelm@12132: fun add_inductive_i verbose (rec_tms, dom_sum) wenzelm@12132: intr_specs (monos, con_defs, type_intrs, type_elims) thy = wenzelm@12132: let wenzelm@12132: val _ = Theory.requires thy "Inductive" "(co)inductive definitions"; paulson@6051: wenzelm@12191: val (intr_names, intr_tms) = split_list (map fst intr_specs); wenzelm@12191: val case_names = RuleCases.case_names intr_names; paulson@6051: paulson@6051: (*recT and rec_params should agree for all mutually recursive components*) paulson@6051: val rec_hds = map head_of rec_tms; paulson@6051: paulson@6051: val dummy = assert_all is_Const rec_hds wenzelm@12132: (fn t => "Recursive set not previously declared as constant: " ^ wenzelm@20342: Sign.string_of_term thy t); paulson@6051: paulson@6051: (*Now we know they are all Consts, so get their names, type and params*) paulson@6051: val rec_names = map (#1 o dest_Const) rec_hds paulson@6051: and (Const(_,recT),rec_params) = strip_comb (hd rec_tms); paulson@6051: paulson@6051: val rec_base_names = map Sign.base_name rec_names; paulson@6051: val dummy = assert_all Syntax.is_identifier rec_base_names paulson@6051: (fn a => "Base name of recursive set not an identifier: " ^ a); paulson@6051: paulson@6051: local (*Checking the introduction rules*) wenzelm@20342: val intr_sets = map (#2 o rule_concl_msg thy) intr_tms; paulson@6051: fun intr_ok set = wenzelm@12132: case head_of set of Const(a,recT) => a mem rec_names | _ => false; paulson@6051: in paulson@6051: val dummy = assert_all intr_ok intr_sets wenzelm@12132: (fn t => "Conclusion of rule does not name a recursive set: " ^ wenzelm@20342: Sign.string_of_term thy t); paulson@6051: end; paulson@6051: paulson@6051: val dummy = assert_all is_Free rec_params paulson@6051: (fn t => "Param in recursion term not a free variable: " ^ wenzelm@20342: Sign.string_of_term thy t); paulson@6051: paulson@6051: (*** Construct the fixedpoint definition ***) wenzelm@20071: val mk_variant = Name.variant (foldr add_term_names [] intr_tms); paulson@6051: paulson@6051: val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w"; paulson@6051: paulson@6051: fun dest_tprop (Const("Trueprop",_) $ P) = P wenzelm@12132: | dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^ wenzelm@20342: Sign.string_of_term thy Q); paulson@6051: paulson@6051: (*Makes a disjunct from an introduction rule*) paulson@6051: fun fp_part intr = (*quantify over rule's free vars except parameters*) wenzelm@16855: let val prems = map dest_tprop (Logic.strip_imp_prems intr) skalberg@15570: val dummy = List.app (fn rec_hd => List.app (chk_prem rec_hd) prems) rec_hds wenzelm@12132: val exfrees = term_frees intr \\ rec_params wenzelm@12132: val zeq = FOLogic.mk_eq (Free(z',iT), #1 (rule_concl intr)) skalberg@15574: in foldr FOLogic.mk_exists wenzelm@23419: (BalancedTree.make FOLogic.mk_conj (zeq::prems)) exfrees paulson@6051: end; paulson@6051: paulson@6051: (*The Part(A,h) terms -- compose injections to make h*) paulson@6051: fun mk_Part (Bound 0) = Free(X',iT) (*no mutual rec, no Part needed*) paulson@6051: | mk_Part h = Part_const $ Free(X',iT) $ Abs(w',iT,h); paulson@6051: paulson@6051: (*Access to balanced disjoint sums via injections*) wenzelm@23419: val parts = map mk_Part wenzelm@23419: (BalancedTree.accesses {left = fn t => Su.inl $ t, right = fn t => Su.inr $ t, init = Bound 0} wenzelm@23419: (length rec_tms)); paulson@6051: paulson@6051: (*replace each set by the corresponding Part(A,h)*) paulson@6051: val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms; paulson@6051: wenzelm@12132: val fp_abs = absfree(X', iT, wenzelm@12132: mk_Collect(z', dom_sum, wenzelm@23419: BalancedTree.make FOLogic.mk_disj part_intrs)); paulson@6051: paulson@6051: val fp_rhs = Fp.oper $ dom_sum $ fp_abs paulson@6051: wenzelm@22567: val dummy = List.app (fn rec_hd => (Logic.occs (rec_hd, fp_rhs) andalso wenzelm@22567: error "Illegal occurrence of recursion operator"; ())) wenzelm@12132: rec_hds; paulson@6051: paulson@6051: (*** Make the new theory ***) paulson@6051: paulson@6051: (*A key definition: paulson@6051: If no mutual recursion then it equals the one recursive set. paulson@6051: If mutual recursion then it differs from all the recursive sets. *) paulson@6051: val big_rec_base_name = space_implode "_" rec_base_names; wenzelm@20342: val big_rec_name = Sign.intern_const thy big_rec_base_name; paulson@6051: wenzelm@12132: wenzelm@21962: val _ = wenzelm@21962: if verbose then wenzelm@21962: writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name) wenzelm@21962: else (); paulson@6051: paulson@6051: (*Big_rec... is the union of the mutually recursive sets*) paulson@6051: val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params); paulson@6051: paulson@6051: (*The individual sets must already be declared*) wenzelm@24255: val axpairs = map PrimitiveDefs.mk_defpair wenzelm@12132: ((big_rec_tm, fp_rhs) :: wenzelm@12132: (case parts of wenzelm@12132: [_] => [] (*no mutual recursion*) wenzelm@12132: | _ => rec_tms ~~ (*define the sets as Parts*) wenzelm@12132: map (subst_atomic [(Free(X',iT),big_rec_tm)]) parts)); paulson@6051: paulson@6051: (*tracing: print the fixedpoint definition*) paulson@6051: val dummy = if !Ind_Syntax.trace then wenzelm@20342: List.app (writeln o Sign.string_of_term thy o #2) axpairs wenzelm@12132: else () paulson@6051: paulson@6051: (*add definitions of the inductive sets*) haftmann@18377: val (_, thy1) = haftmann@18377: thy wenzelm@24712: |> Sign.add_path big_rec_base_name haftmann@18377: |> PureThy.add_defs_i false (map Thm.no_attributes axpairs) paulson@6051: paulson@6051: paulson@6051: (*fetch fp definitions from the theory*) wenzelm@12132: val big_rec_def::part_rec_defs = paulson@6051: map (get_def thy1) wenzelm@12132: (case rec_names of [_] => rec_names wenzelm@12132: | _ => big_rec_base_name::rec_names); paulson@6051: paulson@6051: paulson@6051: (********) paulson@6051: val dummy = writeln " Proving monotonicity..."; paulson@6051: wenzelm@12132: val bnd_mono = wenzelm@20342: Goal.prove_global thy1 [] [] (FOLogic.mk_Trueprop (Fp.bnd_mono $ dom_sum $ fp_abs)) wenzelm@17985: (fn _ => EVERY wenzelm@17985: [rtac (Collect_subset RS bnd_monoI) 1, wenzelm@20046: REPEAT (ares_tac (basic_monos @ monos) 1)]); paulson@6051: paulson@6051: val dom_subset = standard (big_rec_def RS Fp.subs); paulson@6051: paulson@6051: val unfold = standard ([big_rec_def, bnd_mono] MRS Fp.Tarski); paulson@6051: paulson@6051: (********) paulson@6051: val dummy = writeln " Proving the introduction rules..."; paulson@6051: wenzelm@12132: (*Mutual recursion? Helps to derive subset rules for the paulson@6051: individual sets.*) paulson@6051: val Part_trans = paulson@6051: case rec_names of wenzelm@12132: [_] => asm_rl wenzelm@12132: | _ => standard (Part_subset RS subset_trans); paulson@6051: paulson@6051: (*To type-check recursive occurrences of the inductive sets, possibly paulson@6051: enclosed in some monotonic operator M.*) wenzelm@12132: val rec_typechecks = wenzelm@12132: [dom_subset] RL (asm_rl :: ([Part_trans] RL monos)) paulson@6051: RL [subsetD]; paulson@6051: paulson@6051: (*Type-checking is hardest aspect of proof; paulson@6051: disjIn selects the correct disjunct after unfolding*) wenzelm@17985: fun intro_tacsf disjIn = wenzelm@17985: [DETERM (stac unfold 1), paulson@6051: REPEAT (resolve_tac [Part_eqI,CollectI] 1), paulson@6051: (*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*) paulson@6051: rtac disjIn 2, paulson@6051: (*Not ares_tac, since refl must be tried before equality assumptions; paulson@6051: backtracking may occur if the premises have extra variables!*) paulson@6051: DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 2 APPEND assume_tac 2), paulson@6051: (*Now solve the equations like Tcons(a,f) = Inl(?b4)*) paulson@6051: rewrite_goals_tac con_defs, paulson@6051: REPEAT (rtac refl 2), paulson@6051: (*Typechecking; this can fail*) paulson@6172: if !Ind_Syntax.trace then print_tac "The type-checking subgoal:" paulson@6051: else all_tac, paulson@6051: REPEAT (FIRSTGOAL ( dresolve_tac rec_typechecks wenzelm@12132: ORELSE' eresolve_tac (asm_rl::PartE::SigmaE2:: wenzelm@12132: type_elims) wenzelm@12132: ORELSE' hyp_subst_tac)), paulson@6051: if !Ind_Syntax.trace then print_tac "The subgoal after monos, type_elims:" paulson@6051: else all_tac, paulson@6051: DEPTH_SOLVE (swap_res_tac (SigmaI::subsetI::type_intrs) 1)]; paulson@6051: paulson@6051: (*combines disjI1 and disjI2 to get the corresponding nested disjunct...*) wenzelm@23419: val mk_disj_rls = BalancedTree.accesses wenzelm@23419: {left = fn rl => rl RS disjI1, right = fn rl => rl RS disjI2, init = asm_rl}; paulson@6051: wenzelm@17985: val intrs = wenzelm@17985: (intr_tms, map intro_tacsf (mk_disj_rls (length intr_tms))) wenzelm@17985: |> ListPair.map (fn (t, tacs) => wenzelm@20342: Goal.prove_global thy1 [] [] t wenzelm@20046: (fn _ => EVERY (rewrite_goals_tac part_rec_defs :: tacs))) wenzelm@17985: handle MetaSimplifier.SIMPLIFIER (msg, thm) => (print_thm thm; error msg); paulson@6051: paulson@6051: (********) paulson@6051: val dummy = writeln " Proving the elimination rule..."; paulson@6051: paulson@6051: (*Breaks down logical connectives in the monotonic function*) paulson@6051: val basic_elim_tac = paulson@6051: REPEAT (SOMEGOAL (eresolve_tac (Ind_Syntax.elim_rls @ Su.free_SEs) wenzelm@12132: ORELSE' bound_hyp_subst_tac)) paulson@6051: THEN prune_params_tac wenzelm@12132: (*Mutual recursion: collapse references to Part(D,h)*) paulson@6051: THEN fold_tac part_rec_defs; paulson@6051: paulson@6051: (*Elimination*) wenzelm@12132: val elim = rule_by_tactic basic_elim_tac wenzelm@12132: (unfold RS Ind_Syntax.equals_CollectD) paulson@6051: paulson@6051: (*Applies freeness of the given constructors, which *must* be unfolded by wenzelm@12132: the given defs. Cannot simply use the local con_defs because wenzelm@12132: con_defs=[] for inference systems. wenzelm@12175: Proposition A should have the form t:Si where Si is an inductive set*) wenzelm@12175: fun make_cases ss A = wenzelm@12175: rule_by_tactic wenzelm@12175: (basic_elim_tac THEN ALLGOALS (asm_full_simp_tac ss) THEN basic_elim_tac) wenzelm@12175: (Thm.assume A RS elim) wenzelm@12175: |> Drule.standard'; wenzelm@12175: fun mk_cases a = make_cases (*delayed evaluation of body!*) wenzelm@22675: (simpset ()) (Thm.read_cterm (Thm.theory_of_thm elim) (a, propT)); paulson@6051: paulson@6051: fun induction_rules raw_induct thy = paulson@6051: let paulson@6051: val dummy = writeln " Proving the induction rule..."; paulson@6051: paulson@6051: (*** Prove the main induction rule ***) paulson@6051: paulson@6051: val pred_name = "P"; (*name for predicate variables*) paulson@6051: paulson@6051: (*Used to make induction rules; wenzelm@12132: ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops wenzelm@12132: prem is a premise of an intr rule*) wenzelm@12132: fun add_induct_prem ind_alist (prem as Const("Trueprop",_) $ wenzelm@24826: (Const(@{const_name mem},_)$t$X), iprems) = haftmann@17314: (case AList.lookup (op aconv) ind_alist X of skalberg@15531: SOME pred => prem :: FOLogic.mk_Trueprop (pred $ t) :: iprems skalberg@15531: | NONE => (*possibly membership in M(rec_tm), for M monotone*) wenzelm@12132: let fun mk_sb (rec_tm,pred) = wenzelm@12132: (rec_tm, Ind_Syntax.Collect_const$rec_tm$pred) wenzelm@12132: in subst_free (map mk_sb ind_alist) prem :: iprems end) paulson@6051: | add_induct_prem ind_alist (prem,iprems) = prem :: iprems; paulson@6051: paulson@6051: (*Make a premise of the induction rule.*) paulson@6051: fun induct_prem ind_alist intr = paulson@6051: let val quantfrees = map dest_Free (term_frees intr \\ rec_params) skalberg@15574: val iprems = foldr (add_induct_prem ind_alist) [] skalberg@15574: (Logic.strip_imp_prems intr) wenzelm@12132: val (t,X) = Ind_Syntax.rule_concl intr haftmann@17314: val (SOME pred) = AList.lookup (op aconv) ind_alist X wenzelm@12132: val concl = FOLogic.mk_Trueprop (pred $ t) paulson@6051: in list_all_free (quantfrees, Logic.list_implies (iprems,concl)) end paulson@6051: handle Bind => error"Recursion term not found in conclusion"; paulson@6051: paulson@6051: (*Minimizes backtracking by delivering the correct premise to each goal. paulson@6051: Intro rules with extra Vars in premises still cause some backtracking *) paulson@6051: fun ind_tac [] 0 = all_tac wenzelm@12132: | ind_tac(prem::prems) i = paulson@13747: DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN ind_tac prems (i-1); paulson@6051: paulson@6051: val pred = Free(pred_name, Ind_Syntax.iT --> FOLogic.oT); paulson@6051: wenzelm@12132: val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) wenzelm@12132: intr_tms; paulson@6051: wenzelm@12132: val dummy = if !Ind_Syntax.trace then wenzelm@12132: (writeln "ind_prems = "; wenzelm@20342: List.app (writeln o Sign.string_of_term thy1) ind_prems; wenzelm@12132: writeln "raw_induct = "; print_thm raw_induct) wenzelm@12132: else (); paulson@6051: paulson@6051: wenzelm@12132: (*We use a MINIMAL simpset. Even FOL_ss contains too many simpules. paulson@6051: If the premises get simplified, then the proofs could fail.*) wenzelm@17892: val min_ss = Simplifier.theory_context thy empty_ss wenzelm@12725: setmksimps (map mk_eq o ZF_atomize o gen_all) wenzelm@12132: setSolver (mk_solver "minimal" wenzelm@12132: (fn prems => resolve_tac (triv_rls@prems) wenzelm@12132: ORELSE' assume_tac wenzelm@12132: ORELSE' etac FalseE)); paulson@6051: wenzelm@12132: val quant_induct = wenzelm@20342: Goal.prove_global thy1 [] ind_prems wenzelm@17985: (FOLogic.mk_Trueprop (Ind_Syntax.mk_all_imp (big_rec_tm, pred))) wenzelm@17985: (fn prems => EVERY wenzelm@17985: [rewrite_goals_tac part_rec_defs, wenzelm@17985: rtac (impI RS allI) 1, wenzelm@17985: DETERM (etac raw_induct 1), wenzelm@17985: (*Push Part inside Collect*) wenzelm@17985: full_simp_tac (min_ss addsimps [Part_Collect]) 1, wenzelm@17985: (*This CollectE and disjE separates out the introduction rules*) wenzelm@17985: REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])), wenzelm@17985: (*Now break down the individual cases. No disjE here in case wenzelm@17985: some premise involves disjunction.*) wenzelm@17985: REPEAT (FIRSTGOAL (eresolve_tac [CollectE, exE, conjE] wenzelm@17985: ORELSE' bound_hyp_subst_tac)), wenzelm@20046: ind_tac (rev (map (rewrite_rule part_rec_defs) prems)) (length prems)]); paulson@6051: wenzelm@12132: val dummy = if !Ind_Syntax.trace then wenzelm@12132: (writeln "quant_induct = "; print_thm quant_induct) wenzelm@12132: else (); paulson@6051: paulson@6051: paulson@6051: (*** Prove the simultaneous induction rule ***) paulson@6051: paulson@6051: (*Make distinct predicates for each inductive set*) paulson@6051: paulson@6051: (*The components of the element type, several if it is a product*) paulson@6051: val elem_type = CP.pseudo_type dom_sum; paulson@6051: val elem_factors = CP.factors elem_type; paulson@6051: val elem_frees = mk_frees "za" elem_factors; paulson@6051: val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees; paulson@6051: paulson@6051: (*Given a recursive set and its domain, return the "fsplit" predicate paulson@6051: and a conclusion for the simultaneous induction rule. paulson@6051: NOTE. This will not work for mutually recursive predicates. Previously paulson@6051: a summand 'domt' was also an argument, but this required the domain of paulson@6051: mutual recursion to invariably be a disjoint sum.*) wenzelm@12132: fun mk_predpair rec_tm = paulson@6051: let val rec_name = (#1 o dest_Const o head_of) rec_tm wenzelm@12132: val pfree = Free(pred_name ^ "_" ^ Sign.base_name rec_name, wenzelm@12132: elem_factors ---> FOLogic.oT) wenzelm@12132: val qconcl = skalberg@15574: foldr FOLogic.mk_all skalberg@15574: (FOLogic.imp $ wenzelm@12132: (Ind_Syntax.mem_const $ elem_tuple $ rec_tm) skalberg@15574: $ (list_comb (pfree, elem_frees))) elem_frees wenzelm@12132: in (CP.ap_split elem_type FOLogic.oT pfree, wenzelm@12132: qconcl) paulson@6051: end; paulson@6051: paulson@6051: val (preds,qconcls) = split_list (map mk_predpair rec_tms); paulson@6051: paulson@6051: (*Used to form simultaneous induction lemma*) wenzelm@12132: fun mk_rec_imp (rec_tm,pred) = wenzelm@12132: FOLogic.imp $ (Ind_Syntax.mem_const $ Bound 0 $ rec_tm) $ wenzelm@12132: (pred $ Bound 0); paulson@6051: paulson@6051: (*To instantiate the main induction rule*) wenzelm@12132: val induct_concl = wenzelm@12132: FOLogic.mk_Trueprop wenzelm@12132: (Ind_Syntax.mk_all_imp wenzelm@12132: (big_rec_tm, wenzelm@12132: Abs("z", Ind_Syntax.iT, wenzelm@23419: BalancedTree.make FOLogic.mk_conj wenzelm@12132: (ListPair.map mk_rec_imp (rec_tms, preds))))) paulson@6051: and mutual_induct_concl = wenzelm@23419: FOLogic.mk_Trueprop(BalancedTree.make FOLogic.mk_conj qconcls); paulson@6051: wenzelm@12132: val dummy = if !Ind_Syntax.trace then wenzelm@12132: (writeln ("induct_concl = " ^ wenzelm@20342: Sign.string_of_term thy1 induct_concl); wenzelm@12132: writeln ("mutual_induct_concl = " ^ wenzelm@20342: Sign.string_of_term thy1 mutual_induct_concl)) wenzelm@12132: else (); paulson@6051: paulson@6051: paulson@6051: val lemma_tac = FIRST' [eresolve_tac [asm_rl, conjE, PartE, mp], wenzelm@12132: resolve_tac [allI, impI, conjI, Part_eqI], wenzelm@12132: dresolve_tac [spec, mp, Pr.fsplitD]]; paulson@6051: paulson@6051: val need_mutual = length rec_names > 1; paulson@6051: paulson@6051: val lemma = (*makes the link between the two induction rules*) paulson@6051: if need_mutual then wenzelm@12132: (writeln " Proving the mutual induction rule..."; wenzelm@20342: Goal.prove_global thy1 [] [] wenzelm@17985: (Logic.mk_implies (induct_concl, mutual_induct_concl)) wenzelm@17985: (fn _ => EVERY wenzelm@17985: [rewrite_goals_tac part_rec_defs, wenzelm@20046: REPEAT (rewrite_goals_tac [Pr.split_eq] THEN lemma_tac 1)])) wenzelm@17985: else (writeln " [ No mutual induction rule needed ]"; TrueI); paulson@6051: wenzelm@12132: val dummy = if !Ind_Syntax.trace then wenzelm@12132: (writeln "lemma = "; print_thm lemma) wenzelm@12132: else (); paulson@6051: paulson@6051: paulson@6051: (*Mutual induction follows by freeness of Inl/Inr.*) paulson@6051: wenzelm@12132: (*Simplification largely reduces the mutual induction rule to the paulson@6051: standard rule*) wenzelm@12132: val mut_ss = wenzelm@12132: min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff]; paulson@6051: paulson@6051: val all_defs = con_defs @ part_rec_defs; paulson@6051: paulson@6051: (*Removes Collects caused by M-operators in the intro rules. It is very paulson@6051: hard to simplify wenzelm@12132: list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))}) paulson@6051: where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}). paulson@6051: Instead the following rules extract the relevant conjunct. paulson@6051: *) paulson@6051: val cmonos = [subset_refl RS Collect_mono] RL monos wenzelm@12132: RLN (2,[rev_subsetD]); paulson@6051: paulson@6051: (*Minimizes backtracking by delivering the correct premise to each goal*) paulson@6051: fun mutual_ind_tac [] 0 = all_tac wenzelm@12132: | mutual_ind_tac(prem::prems) i = wenzelm@12132: DETERM wenzelm@12132: (SELECT_GOAL wenzelm@12132: ( wenzelm@12132: (*Simplify the assumptions and goal by unfolding Part and wenzelm@12132: using freeness of the Sum constructors; proves all but one wenzelm@12132: conjunct by contradiction*) wenzelm@12132: rewrite_goals_tac all_defs THEN wenzelm@12132: simp_tac (mut_ss addsimps [Part_iff]) 1 THEN wenzelm@12132: IF_UNSOLVED (*simp_tac may have finished it off!*) wenzelm@12132: ((*simplify assumptions*) wenzelm@12132: (*some risk of excessive simplification here -- might have wenzelm@12132: to identify the bare minimum set of rewrites*) wenzelm@12132: full_simp_tac wenzelm@12132: (mut_ss addsimps conj_simps @ imp_simps @ quant_simps) 1 wenzelm@12132: THEN wenzelm@12132: (*unpackage and use "prem" in the corresponding place*) wenzelm@12132: REPEAT (rtac impI 1) THEN wenzelm@12132: rtac (rewrite_rule all_defs prem) 1 THEN wenzelm@12132: (*prem must not be REPEATed below: could loop!*) wenzelm@12132: DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE' wenzelm@12132: eresolve_tac (conjE::mp::cmonos)))) wenzelm@12132: ) i) wenzelm@12132: THEN mutual_ind_tac prems (i-1); paulson@6051: wenzelm@12132: val mutual_induct_fsplit = paulson@6051: if need_mutual then wenzelm@20342: Goal.prove_global thy1 [] (map (induct_prem (rec_tms~~preds)) intr_tms) wenzelm@17985: mutual_induct_concl wenzelm@17985: (fn prems => EVERY wenzelm@17985: [rtac (quant_induct RS lemma) 1, wenzelm@20046: mutual_ind_tac (rev prems) (length prems)]) paulson@6051: else TrueI; paulson@6051: paulson@6051: (** Uncurrying the predicate in the ordinary induction rule **) paulson@6051: paulson@6051: (*instantiate the variable to a tuple, if it is non-trivial, in order to paulson@6051: allow the predicate to be "opened up". paulson@6051: The name "x.1" comes from the "RS spec" !*) wenzelm@12132: val inst = wenzelm@12132: case elem_frees of [_] => I wenzelm@20342: | _ => instantiate ([], [(cterm_of thy1 (Var(("x",1), Ind_Syntax.iT)), wenzelm@20342: cterm_of thy1 elem_tuple)]); paulson@6051: paulson@6051: (*strip quantifier and the implication*) paulson@6051: val induct0 = inst (quant_induct RS spec RSN (2,rev_mp)); paulson@6051: paulson@6051: val Const ("Trueprop", _) $ (pred_var $ _) = concl_of induct0 paulson@6051: wenzelm@12132: val induct = CP.split_rule_var(pred_var, elem_type-->FOLogic.oT, induct0) wenzelm@12132: |> standard paulson@6051: and mutual_induct = CP.remove_split mutual_induct_fsplit wenzelm@8438: haftmann@18377: val ([induct', mutual_induct'], thy') = haftmann@18377: thy wenzelm@18643: |> PureThy.add_thms [((co_prefix ^ "induct", induct), wenzelm@24861: [case_names, Induct.induct_pred big_rec_name]), wenzelm@18643: (("mutual_induct", mutual_induct), [case_names])]; wenzelm@12227: in ((thy', induct'), mutual_induct') paulson@6051: end; (*of induction_rules*) paulson@6051: paulson@6051: val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct) paulson@6051: wenzelm@12227: val ((thy2, induct), mutual_induct) = wenzelm@12227: if not coind then induction_rules raw_induct thy1 haftmann@18377: else haftmann@18377: (thy1 haftmann@18377: |> PureThy.add_thms [((co_prefix ^ "induct", raw_induct), [])] haftmann@18377: |> apfst hd |> Library.swap, TrueI) paulson@6051: and defs = big_rec_def :: part_rec_defs paulson@6051: paulson@6051: haftmann@18377: val (([bnd_mono', dom_subset', elim'], [defs', intrs']), thy3) = wenzelm@8438: thy2 wenzelm@12183: |> IndCases.declare big_rec_name make_cases wenzelm@12132: |> PureThy.add_thms wenzelm@12132: [(("bnd_mono", bnd_mono), []), wenzelm@12132: (("dom_subset", dom_subset), []), wenzelm@24861: (("cases", elim), [case_names, Induct.cases_pred big_rec_name])] haftmann@18377: ||>> (PureThy.add_thmss o map Thm.no_attributes) wenzelm@8438: [("defs", defs), wenzelm@12175: ("intros", intrs)]; haftmann@18377: val (intrs'', thy4) = haftmann@18377: thy3 haftmann@18377: |> PureThy.add_thms ((intr_names ~~ intrs') ~~ map #2 intr_specs) wenzelm@24712: ||> Sign.parent_path; wenzelm@8438: in wenzelm@12132: (thy4, wenzelm@8438: {defs = defs', wenzelm@8438: bnd_mono = bnd_mono', wenzelm@8438: dom_subset = dom_subset', wenzelm@12132: intrs = intrs'', wenzelm@8438: elim = elim', wenzelm@8438: mk_cases = mk_cases, wenzelm@8438: induct = induct, wenzelm@8438: mutual_induct = mutual_induct}) wenzelm@8438: end; paulson@6051: wenzelm@12132: (*source version*) wenzelm@12132: fun add_inductive (srec_tms, sdom_sum) intr_srcs wenzelm@12132: (raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy = wenzelm@12132: let wenzelm@24726: val ctxt = ProofContext.init thy; wenzelm@24726: val read_terms = map (Syntax.parse_term ctxt #> TypeInfer.constrain Ind_Syntax.iT) wenzelm@24726: #> Syntax.check_terms ctxt; wenzelm@24726: wenzelm@18728: val intr_atts = map (map (Attrib.attribute thy) o snd) intr_srcs; wenzelm@17937: val sintrs = map fst intr_srcs ~~ intr_atts; wenzelm@24726: val rec_tms = read_terms srec_tms; wenzelm@24726: val dom_sum = singleton read_terms sdom_sum; wenzelm@24726: val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs); wenzelm@17937: val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs; wenzelm@24726: val monos = Attrib.eval_thms ctxt raw_monos; wenzelm@24726: val con_defs = Attrib.eval_thms ctxt raw_con_defs; wenzelm@24726: val type_intrs = Attrib.eval_thms ctxt raw_type_intrs; wenzelm@24726: val type_elims = Attrib.eval_thms ctxt raw_type_elims; wenzelm@12132: in haftmann@18418: thy wenzelm@24726: |> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_elims) haftmann@18418: end; wenzelm@12132: wenzelm@12132: wenzelm@12132: (* outer syntax *) wenzelm@12132: wenzelm@17057: local structure P = OuterParse and K = OuterKeyword in wenzelm@12132: wenzelm@24867: val _ = OuterSyntax.keywords wenzelm@24867: ["domains", "intros", "monos", "con_defs", "type_intros", "type_elims"]; wenzelm@24867: wenzelm@12132: fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) = wenzelm@12132: #1 o add_inductive doms (map P.triple_swap intrs) (monos, con_defs, type_intrs, type_elims); wenzelm@12132: wenzelm@12132: val ind_decl = wenzelm@12132: (P.$$$ "domains" |-- P.!!! (P.enum1 "+" P.term -- wenzelm@12876: ((P.$$$ "\\" || P.$$$ "<=") |-- P.term))) -- wenzelm@12132: (P.$$$ "intros" |-- wenzelm@22101: P.!!! (Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop))) -- wenzelm@22101: Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) [] -- wenzelm@22101: Scan.optional (P.$$$ "con_defs" |-- P.!!! SpecParse.xthms1) [] -- wenzelm@22101: Scan.optional (P.$$$ "type_intros" |-- P.!!! SpecParse.xthms1) [] -- wenzelm@22101: Scan.optional (P.$$$ "type_elims" |-- P.!!! SpecParse.xthms1) [] wenzelm@12132: >> (Toplevel.theory o mk_ind); wenzelm@12132: wenzelm@24867: val _ = OuterSyntax.command (co_prefix ^ "inductive") wenzelm@12227: ("define " ^ co_prefix ^ "inductive sets") K.thy_decl ind_decl; wenzelm@12132: paulson@6051: end; wenzelm@12132: wenzelm@12132: end; wenzelm@15705: