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Quelle inductive_package.ML Sprache: SML |
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(* Title: ZF/Tools/inductive_package.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory Fixedpoint definition module -- for Inductive/Coinductive Definitions The functor will be instantiated for normal sums/products (inductive defs) and non-standard sums/products (coinductive defs) Sums are used only for mutual recursion; Products are used only to derive "streamlined" induction rules for relations *) type inductive_result = {defs : thm list, (*definitions made in thy*) bnd_mono : thm, (*monotonicity for the lfp definition*) dom_subset : thm, (*inclusion of recursive set in dom*) intrs : thm list, (*introduction rules*) elim : thm, (*case analysis theorem*) induct : thm, (*main induction rule*) mutual_induct : thm}; (*mutual induction rule*) (*Functor's result signature*) signature INDUCTIVE_PACKAGE = sig (*Insert definitions for the recursive sets, which must *already* be declared as constants in parent theory!*) val add_inductive_i: bool -> term list * term -> ((binding * term) * attribute list) list -> thm list * thm list * thm list * thm list -> theory -> theory * inductive_result val add_inductive: string list * string -> ((binding * string) * Token.src list) list -> (Facts.ref * Token.src list) list * (Facts.ref * Token.src list) list * (Facts.ref * Token.src list) list * (Facts.ref * Token.src list) list -> theory -> theory * inductive_result end; (*Declares functions to add fixedpoint/constructor defs to a theory. Recursive sets must *already* be declared as constants.*) functor Add_inductive_def_Fun (structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool) : INDUCTIVE_PACKAGE = struct val co_prefix = if coind then "co" else ""; (* utils *) (*make distinct individual variables a1, a2, a3, ..., an. *) fun mk_frees a [] = [] | mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts; (* add_inductive(_i) *) (*internal version, accepting terms*) fun add_inductive_i verbose (rec_tms, dom_sum) raw_intr_specs (monos, con_defs, type_intrs, type_elims) thy0 = let val ctxt0 = Proof_Context.init_global thy0; val intr_specs = map (apfst (apfst Binding.name_of)) raw_intr_specs; val (intr_names, intr_tms) = split_list (map fst intr_specs); val case_names = Rule_Cases.case_names intr_names; (*recT and rec_params should agree for all mutually recursive components*) val rec_hds = map head_of rec_tms; val dummy = rec_hds |> forall (fn t => is_Const t orelse error ("Recursive set not previously declared as constant: " ^ Syntax.string_of_term ctxt0 t)); (*Now we know they are all Consts, so get their names, type and params*) val rec_names = map dest_Const_name rec_hds and (Const(_,recT),rec_params) = strip_comb (hd rec_tms); val rec_base_names = map Long_Name.base_name rec_names; val dummy = rec_base_names |> forall (fn a => Symbol_Pos.is_identifier a orelse error ("Base name of recursive set not an identifier: " ^ a)); local (*Checking the introduction rules*) val intr_sets = map (#2 o Ind_Syntax.rule_concl_msg thy0) intr_tms; fun intr_ok set = case head_of set of Const(a,recT) => member (op =) rec_names a | _ => false; in val dummy = intr_sets |> forall (fn t => intr_ok t orelse error ("Conclusion of rule does not name a recursive set: " ^ Syntax.string_of_term ctxt0 t)); end; val dummy = rec_params |> forall (fn t => is_Free t orelse error ("Param in recursion term not a free variable: " ^ Syntax.string_of_term ctxt0 t)); (*** Construct the fixedpoint definition ***) val mk_variant = singleton (Name.variant_list (List.foldr Misc_Legacy.add_term_names [] val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w"; fun dest_tprop \<^Const_>\<open>Trueprop for P\<close> = P | dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^ Syntax.string_of_term ctxt0 Q); (*Makes a disjunct from an introduction rule*) fun fp_part intr = (*quantify over rule's free vars except parameters*) let val prems = map dest_tprop (Logic.strip_imp_prems intr) val dummy = List.app (fn rec_hd => List.app (Ind_Syntax.chk_prem rec_hd) prems) rec_hds val exfrees = subtract (op =) rec_params (Misc_Legacy.term_frees intr) val zeq = FOLogic.mk_eq (Free(z', \<^Type>\ in fold_rev (FOLogic.mk_exists o Term.dest_Free) exfrees (Balanced_Tree.make FOLogic.mk_conj (zeq::prems)) end; (*The Part(A,h) terms -- compose injections to make h*) fun mk_Part (Bound 0) = Free(X', \<^Type>\ | mk_Part h = \<^Const>\<open>Part\<close> $ Free(X', \<^Type>\ (*Access to balanced disjoint sums via injections*) val parts = map mk_Part (Balanced_Tree.accesses {left = fn t => Su.inl $ t, right = fn t => Su.inr $ t, init = Bound 0} (length rec_tms)); (*replace each set by the corresponding Part(A,h)*) val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms; val fp_abs = absfree (X', \<^Type>\ (Ind_Syntax.mk_Collect (z', dom_sum, Balanced_Tree.make FOLogic.mk_disj part_intrs)); val fp_rhs = Fp.oper $ dom_sum $ fp_abs val dummy = List.app (fn rec_hd => (Logic.occs (rec_hd, fp_rhs) andalso error "Illegal occurrence of recursion operator"; ())) rec_hds; (*** Make the new theory ***) (*A key definition: If no mutual recursion then it equals the one recursive set. If mutual recursion then it differs from all the recursive sets. *) val big_rec_base_name = space_implode "_" rec_base_names; val big_rec_name = Proof_Context.intern_const ctxt0 big_rec_base_name; val _ = if verbose then writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name) else (); (*Big_rec... is the union of the mutually recursive sets*) val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params); (*The individual sets must already be declared*) val axpairs = map Misc_Legacy.mk_defpair ((big_rec_tm, fp_rhs) :: (case parts of [_] => [] (*no mutual recursion*) | _ => rec_tms ~~ (*define the sets as Parts*) map (subst_atomic [(Free (X', \<^Type>\ (*tracing: print the fixedpoint definition*) val dummy = if !Ind_Syntax.trace then writeln (cat_lines (map (Syntax.string_of_term ctxt0 o #2) axpairs)) else () (*add definitions of the inductive sets*) val thy1 = thy0 |> Sign.add_path big_rec_base_name |> fold (snd oo Global_Theory.add_def o apfst Binding.name) axpairs; (*fetch fp definitions from the theory*) val big_rec_def::part_rec_defs = map (Misc_Legacy.get_def thy1) (case rec_names of [_] => rec_names | _ => big_rec_base_name::rec_names); (********) val dummy = writeln " Proving monotonicity..."; val bnd_mono0 = Goal.prove_global thy1 [] [] (\<^make_judgment> (Fp.bnd_mono $ dom_sum $ fp_abs)) (fn {context = ctxt, ...} => EVERY [resolve_tac ctxt [@{thm Collect_subset} RS @{thm bnd_monoI}] 1, REPEAT (ares_tac ctxt (@{thms basic_monos} @ monos) 1)]); val dom_subset0 = Drule.export_without_context (big_rec_def RS Fp.subs); val ([bnd_mono, dom_subset], thy2) = thy1 |> Global_Theory.add_thms [((Binding.name "bnd_mono", bnd_mono0), []), ((Binding.name "dom_subset", dom_subset0), [])]; val unfold = Drule.export_without_context ([big_rec_def, bnd_mono] MRS Fp.Tarski); (********) val dummy = writeln " Proving the introduction rules..."; (*Mutual recursion? Helps to derive subset rules for the individual sets.*) val Part_trans = case rec_names of [_] => asm_rl | _ => Drule.export_without_context (@{thm Part_subset} RS @{thm subset_trans}); (*To type-check recursive occurrences of the inductive sets, possibly enclosed in some monotonic operator M.*) val rec_typechecks = [dom_subset] RL (asm_rl :: ([Part_trans] RL monos)) RL [@{thm subsetD}]; (*Type-checking is hardest aspect of proof; disjIn selects the correct disjunct after unfolding*) fun intro_tacsf disjIn ctxt = [DETERM (stac ctxt unfold 1), REPEAT (resolve_tac ctxt [@{thm Part_eqI}, @{thm CollectI}] 1), (*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*) resolve_tac ctxt [disjIn] 2, (*Not ares_tac, since refl must be tried before equality assumptions; backtracking may occur if the premises have extra variables!*) DEPTH_SOLVE_1 (resolve_tac ctxt [@{thm refl}, @{thm exI}, @{thm conjI}] 2 APPEND assume_tac (*Now solve the equations like Tcons(a,f) = Inl(?b4)*) rewrite_goals_tac ctxt con_defs, REPEAT (resolve_tac ctxt @{thms refl} 2), (*Typechecking; this can fail*) if !Ind_Syntax.trace then print_tac ctxt "The type-checking subgoal:" else all_tac, REPEAT (FIRSTGOAL (dresolve_tac ctxt rec_typechecks ORELSE' eresolve_tac ctxt (asm_rl :: @{thm PartE} :: @{thm SigmaE2} :: type_elims) ORELSE' hyp_subst_tac ctxt)), if !Ind_Syntax.trace then print_tac ctxt "The subgoal after monos, type_elims:" else all_tac, DEPTH_SOLVE (swap_res_tac ctxt (@{thm SigmaI} :: @{thm subsetI} :: type_intrs) 1)]; (*combines disjI1 and disjI2 to get the corresponding nested disjunct...*) val mk_disj_rls = Balanced_Tree.accesses {left = fn rl => rl RS @{thm disjI1}, right = fn rl => rl RS @{thm disjI2}, init = @{thm asm_rl}}; val intrs0 = (intr_tms, map intro_tacsf (mk_disj_rls (length intr_tms))) |> ListPair.map (fn (t, tacs) => Goal.prove_global thy2 [] [] t (fn {context = ctxt, ...} => EVERY (rewrite_goals_tac ctxt part_rec_defs :: tacs ctxt))); val ([intrs], thy3) = thy2 |> Global_Theory.add_thmss [((Binding.name "intros", intrs0), [])]; val ctxt3 = Proof_Context.init_global thy3; (********) val dummy = writeln " Proving the elimination rule..."; (*Breaks down logical connectives in the monotonic function*) fun basic_elim_tac ctxt = REPEAT (SOMEGOAL (eresolve_tac ctxt (Ind_Syntax.elim_rls @ Su.free_SEs) ORELSE' bound_hyp_subst_tac ctxt)) THEN prune_params_tac ctxt (*Mutual recursion: collapse references to Part(D,h)*) THEN (PRIMITIVE (fold_rule ctxt part_rec_defs)); (*Elimination*) val (elim, thy4) = thy3 |> Global_Theory.add_thm ((Binding.name "elim", rule_by_tactic ctxt3 (basic_elim_tac ctxt3) (unfold RS Ind_Syntax.equals_CollectD)), [] val elim' = Thm.trim_context elim; val ctxt4 = Proof_Context.init_global thy4; (*Applies freeness of the given constructors, which *must* be unfolded by the given defs. Cannot simply use the local con_defs because con_defs=[] for inference systems. Proposition A should have the form t:Si where Si is an inductive set*) fun make_cases ctxt A = rule_by_tactic ctxt (basic_elim_tac ctxt THEN ALLGOALS (asm_full_simp_tac ctxt) THEN basic_elim_tac ctxt) (Thm.assume A RS Thm.transfer' ctxt elim') |> Drule.export_without_context_open; fun induction_rules raw_induct = let val dummy = writeln " Proving the induction rule..."; (*** Prove the main induction rule ***) val pred_name = "P"; (*name for predicate variables*) (*Used to make induction rules; 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_>\<open>Trueprop for \<^Const_>\<open>mem for t X\< (case AList.lookup (op aconv) ind_alist X of SOME pred => prem :: \<^make_judgment> (pred $ t) :: iprems | NONE => (*possibly membership in M(rec_tm), for M monotone*) let fun mk_sb (rec_tm,pred) = (rec_tm, \<^Const>\<open>Collect\<close> $ rec_tm $ pred) 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 xs = subtract (op =) rec_params (Misc_Legacy.term_frees intr) val iprems = List.foldr (add_induct_prem ind_alist) [] (Logic.strip_imp_prems intr) val (t,X) = Ind_Syntax.rule_concl intr val (SOME pred) = AList.lookup (op aconv) ind_alist X val concl = \<^make_judgment> (pred $ t) in fold_rev Logic.all xs (Logic.list_implies (iprems,concl)) end handle Bind => error"Recursion term not found in conclusion"; (*Minimizes backtracking by delivering the correct premise to each goal. Intro rules with extra Vars in premises still cause some backtracking *) fun ind_tac _ [] 0 = all_tac | ind_tac ctxt (prem::prems) i = DEPTH_SOLVE_1 (ares_tac ctxt [prem, @{thm refl}] i) THEN ind_tac ctxt prems (i-1); val pred = Free(pred_name, \<^Type>\<open>i\<close> --> \<^Type>\<open>o\<close>); val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) intr_tms; val dummy = if ! Ind_Syntax.trace then writeln (cat_lines (["ind_prems:"] @ map (Syntax.string_of_term ctxt4) ind_prems @ ["raw_induct:", Thm.string_of_thm ctxt4 raw_induct])) else (); (*We use a MINIMAL simpset. Even FOL_ss contains too many simpules. If the premises get simplified, then the proofs could fail.*) val min_ss = empty_simpset ctxt4 |> Simplifier.set_mksimps (fn ctxt => map mk_eq o ZF_atomize o Variable.gen_all ctxt) |> Simplifier.set_unsafe_solver (mk_solver "minimal" (fn ctxt => resolve_tac ctxt (triv_rls @ Simplifier.prems_of ctxt) ORELSE' assume_tac ctxt ORELSE' eresolve_tac ctxt @{thms FalseE})); val quant_induct = Goal.prove_global thy4 [] ind_prems (\<^make_judgment> (Ind_Syntax.mk_all_imp (big_rec_tm, pred))) (fn {context = ctxt, prems} => EVERY [rewrite_goals_tac ctxt part_rec_defs, resolve_tac ctxt [@{thm impI} RS @{thm allI}] 1, DETERM (eresolve_tac ctxt [raw_induct] 1), (*Push Part inside Collect*) full_simp_tac (min_ss |> Simplifier.add_simp @{thm Part_Collect}) 1, (*This CollectE and disjE separates out the introduction rules*) REPEAT (FIRSTGOAL (eresolve_tac ctxt [@{thm CollectE}, @{thm disjE}])), (*Now break down the individual cases. No disjE here in case some premise involves disjunction.*) REPEAT (FIRSTGOAL (eresolve_tac ctxt [@{thm CollectE}, @{thm exE}, @{thm conjE}] ORELSE' (bound_hyp_subst_tac ctxt))), ind_tac ctxt (rev (map (rewrite_rule ctxt part_rec_defs) prems)) (length prems)]); val dummy = if ! Ind_Syntax.trace then writeln ("quant_induct:\n" ^ Thm.string_of_thm ctxt4 quant_induct) else (); (*** Prove the simultaneous induction rule ***) (*Make distinct predicates for each inductive set*) (*The components of the element type, several if it is a product*) val elem_type = CP.pseudo_type dom_sum; val elem_factors = CP.factors elem_type; val elem_frees = mk_frees "za" elem_factors; val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees; (*Given a recursive set and its domain, return the "fsplit" predicate and a conclusion for the simultaneous induction rule. NOTE. This will not work for mutually recursive predicates. Previously a summand 'domt' was also an argument, but this required the domain of mutual recursion to invariably be a disjoint sum.*) fun mk_predpair rec_tm = let val rec_name = dest_Const_name (head_of rec_tm) val pfree = Free(pred_name ^ "_" ^ Long_Name.base_name rec_name, elem_factors ---> \<^Type>\<open>o\<close>) val qconcl = fold_rev (FOLogic.mk_all o Term.dest_Free) elem_frees \<^Const>\<open>imp for \<^Const>\<open>mem for elem_tuple rec_tm\<close> \<open>list_comb (pfree, e in (CP.ap_split elem_type \<^Type>\<open>o\<close> pfree, qconcl) end; val (preds,qconcls) = split_list (map mk_predpair rec_tms); (*Used to form simultaneous induction lemma*) fun mk_rec_imp (rec_tm,pred) = \<^Const>\<open>imp for \<^Const>\<open>mem for \<open>Bound 0\<close> rec_tm\<close> \<open>pred $ Bound (*To instantiate the main induction rule*) val induct_concl = \<^make_judgment> (Ind_Syntax.mk_all_imp (big_rec_tm, Abs("z", \<^Type>\<open>i\<close>, Balanced_Tree.make FOLogic.mk_conj (ListPair.map mk_rec_imp (rec_tms, preds))))) and mutual_induct_concl = \<^make_judgment> (Balanced_Tree.make FOLogic.mk_conj qconcls); val dummy = if !Ind_Syntax.trace then (writeln ("induct_concl = " ^ Syntax.string_of_term ctxt4 induct_concl); writeln ("mutual_induct_concl = " ^ Syntax.string_of_term ctxt4 mutual_induct_concl)) else (); fun lemma_tac ctxt = FIRST' [eresolve_tac ctxt [@{thm asm_rl}, @{thm conjE}, @{thm PartE}, @{thm mp}] resolve_tac ctxt [@{thm allI}, @{thm impI}, @{thm conjI}, @{thm Part_eqI}], dresolve_tac ctxt [@{thm spec}, @{thm mp}, Pr.fsplitD]]; val need_mutual = length rec_names > 1; val lemma = (*makes the link between the two induction rules*) if need_mutual then (writeln " Proving the mutual induction rule..."; Goal.prove_global thy4 [] [] (Logic.mk_implies (induct_concl, mutual_induct_concl)) (fn {context = ctxt, ...} => EVERY [rewrite_goals_tac ctxt part_rec_defs, REPEAT (rewrite_goals_tac ctxt [Pr.split_eq] THEN lemma_tac ctxt 1)])) else (writeln " [ No mutual induction rule needed ]"; @{thm TrueI}); val dummy = if ! Ind_Syntax.trace then writeln ("lemma: " ^ Thm.string_of_thm ctxt4 lemma) else (); (*Mutual induction follows by freeness of Inl/Inr.*) (*Simplification largely reduces the mutual induction rule to the standard rule*) val mut_ss = min_ss |> Simplifier.add_simps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff]; val all_defs = con_defs @ part_rec_defs; (*Removes Collects caused by M-operators in the intro rules. It is very hard to simplify list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))}) where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}). Instead the following rules extract the relevant conjunct. *) val cmonos = [@{thm subset_refl} RS @{thm Collect_mono}] RL monos RLN (2,[@{thm rev_subsetD}]); (*Minimizes backtracking by delivering the correct premise to each goal*) fun mutual_ind_tac _ [] 0 = all_tac | mutual_ind_tac ctxt (prem::prems) i = DETERM (SELECT_GOAL ( (*Simplify the assumptions and goal by unfolding Part and using freeness of the Sum constructors; proves all but one conjunct by contradiction*) rewrite_goals_tac ctxt all_defs THEN simp_tac (mut_ss |> Simplifier.add_simp @{thm Part_iff}) 1 THEN IF_UNSOLVED (*simp_tac may have finished it off!*) ((*simplify assumptions*) (*some risk of excessive simplification here -- might have to identify the bare minimum set of rewrites*) full_simp_tac (mut_ss |> Simplifier.add_simps (@{thms conj_simps} @ @{thms imp_simps} @ @{thms quant_simp THEN (*unpackage and use "prem" in the corresponding place*) REPEAT (resolve_tac ctxt @{thms impI} 1) THEN resolve_tac ctxt [rewrite_rule ctxt all_defs prem] 1 THEN (*prem must not be REPEATed below: could loop!*) DEPTH_SOLVE (FIRSTGOAL (ares_tac ctxt [@{thm impI}] ORELSE' eresolve_tac ctxt (@{thm conjE} :: @{thm mp} :: cmonos)))) ) i) THEN mutual_ind_tac ctxt prems (i-1); val mutual_induct_fsplit = if need_mutual then Goal.prove_global thy4 [] (map (induct_prem (rec_tms~~preds)) intr_tms) mutual_induct_concl (fn {context = ctxt, prems} => EVERY [resolve_tac ctxt [quant_induct RS lemma] 1, mutual_ind_tac ctxt (rev prems) (length prems)]) else @{thm TrueI}; (** Uncurrying the predicate in the ordinary induction rule **) (*instantiate the variable to a tuple, if it is non-trivial, in order to allow the predicate to be "opened up". The name "x.1" comes from the "RS spec" !*) val inst = case elem_frees of [_] => I | _ => Drule.instantiate_normalize (TVars.empty, Vars.make1 ((("x", 1), \<^Type>\<open>i\<close>), Thm.global_cterm_of thy4 elem_tuple)); (*strip quantifier and the implication*) val induct0 = inst (quant_induct RS @{thm spec} RSN (2, @{thm rev_mp})); val \<^Const_>\<open>Trueprop for \<open>pred_var $ _\<close>\<close> = Thm.concl_of induct0 val induct0 = CP.split_rule_var ctxt4 (pred_var, elem_type --> \<^Type>\<open>o\<close>, induct0) |> Drule.export_without_context and mutual_induct = CP.remove_split ctxt4 mutual_induct_fsplit val ([induct, mutual_induct], thy5) = thy4 |> Global_Theory.add_thms [((Binding.name (co_prefix ^ "induct"), induct0), [case_names, Induct.induct_pred big_rec_name]), ((Binding.name "mutual_induct", mutual_induct), [case_names])]; in ((induct, mutual_induct), thy5) end; (*of induction_rules*) val raw_induct = Drule.export_without_context ([big_rec_def, bnd_mono] MRS Fp.induct) val ((induct, mutual_induct), thy5) = if not coind then induction_rules raw_induct else thy4 |> Global_Theory.add_thms [((Binding.name (co_prefix ^ "induct"), raw_induct), [])] |> apfst (hd #> pair @{thm TrueI}); val (([cases], [defs]), thy6) = thy5 |> IndCases.declare big_rec_name make_cases |> Global_Theory.add_thms [((Binding.name "cases", elim), [case_names, Induct.cases_pred big_rec_name])] ||>> (Global_Theory.add_thmss o map Thm.no_attributes) [(Binding.name "defs", big_rec_def :: part_rec_defs)]; val (named_intrs, thy7) = thy6 |> Global_Theory.add_thms ((map Binding.name intr_names ~~ intrs) ~~ map #2 intr_specs) ||> Sign.parent_path; in (thy7, {defs = defs, bnd_mono = bnd_mono, dom_subset = dom_subset, intrs = named_intrs, elim = cases, induct = induct, mutual_induct = mutual_induct}) end; (*source version*) fun add_inductive (srec_tms, sdom_sum) intr_srcs (raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy = let val ctxt = Proof_Context.init_global thy; val read_terms = map (Syntax.parse_term ctxt #> Type.constraint \<^Type>\<open>i\<close>) #> Syntax.check_terms ctxt; val intr_atts = map (map (Attrib.attribute_cmd ctxt) o snd) intr_srcs; val sintrs = map fst intr_srcs ~~ intr_atts; val rec_tms = read_terms srec_tms; val dom_sum = singleton read_terms sdom_sum; val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs); val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs; val monos = Attrib.eval_thms ctxt raw_monos; val con_defs = Attrib.eval_thms ctxt raw_con_defs; val type_intrs = Attrib.eval_thms ctxt raw_type_intrs; val type_elims = Attrib.eval_thms ctxt raw_type_elims; in thy |> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_e end; (* outer syntax *) fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) = #1 o add_inductive doms (map (fn ((x, y), z) => ((x, z), y)) intrs) (monos, con_defs, type_intrs, type_elims); val ind_decl = (\<^keyword>\<open>domains\<close> |-- Parse.!!! (Parse.enum1 "+" Parse.term -- ((\<^keyword>\<open>\<subseteq>\<close> || \<^keyword>\<open><=\<close>) |-- Parse.term))) -- (\<^keyword>\<open>intros\<close> |-- Parse.!!! (Scan.repeat1 (Parse_Spec.opt_thm_name ":" -- Parse.prop))) -- Scan.optional (\<^keyword>\<open>monos\<close> |-- Parse.!!! Parse.thms1) [] -- Scan.optional (\<^keyword>\<open>con_defs\<close> |-- Parse.!!! Parse.thms1) [] -- Scan.optional (\<^keyword>\<open>type_intros\<close> |-- Parse.!!! Parse.thms1) [] -- Scan.optional (\<^keyword>\<open>type_elims\<close> |-- Parse.!!! Parse.thms1) [] >> (Toplevel.theory o mk_ind); val _ = Outer_Syntax.command (if coind then \<^command_keyword>\<open>coinductive\<close> else \<^command_keyword>\<open>ind ("define " ^ co_prefix ^ "inductive sets") ind_decl; end; ¤ Dauer der Verarbeitung: 0.4 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28