(* Title: HOL/Tools/datatype_package.ML ID: $Id: datatype_package.ML,v 1.181 2007/10/11 14:05:23 wenzelm Exp $ Author: Stefan Berghofer, TU Muenchen Datatype package for Isabelle/HOL. *) signature BASIC_DATATYPE_PACKAGE = sig val induct_tac : string -> int -> tactic val induct_thm_tac : thm -> string -> int -> tactic val case_tac : string -> int -> tactic val distinct_simproc : simproc end; signature DATATYPE_PACKAGE = sig include BASIC_DATATYPE_PACKAGE val quiet_mode : bool ref val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix * (bstring * typ list * mixfix) list) list -> theory -> {distinct : thm list list, inject : thm list list, exhaustion : thm list, rec_thms : thm list, case_thms : thm list list, split_thms : (thm * thm) list, induction : thm, simps : thm list} * theory val add_datatype : bool -> string list -> (string list * bstring * mixfix * (bstring * string list * mixfix) list) list -> theory -> {distinct : thm list list, inject : thm list list, exhaustion : thm list, rec_thms : thm list, case_thms : thm list list, split_thms : (thm * thm) list, induction : thm, simps : thm list} * theory val rep_datatype_i : string list option -> (thm list * attribute list) list list -> (thm list * attribute list) list list -> (thm list * attribute list) -> theory -> {distinct : thm list list, inject : thm list list, exhaustion : thm list, rec_thms : thm list, case_thms : thm list list, split_thms : (thm * thm) list, induction : thm, simps : thm list} * theory val rep_datatype : string list option -> (thmref * Attrib.src list) list list -> (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> theory -> {distinct : thm list list, inject : thm list list, exhaustion : thm list, rec_thms : thm list, case_thms : thm list list, split_thms : (thm * thm) list, induction : thm, simps : thm list} * theory val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table val get_datatype : theory -> string -> DatatypeAux.datatype_info option val the_datatype : theory -> string -> DatatypeAux.datatype_info val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option val get_datatype_spec : theory -> string -> ((string * sort) list * (string * typ list) list) option val get_datatype_constrs : theory -> string -> (string * typ) list option val interpretation: (string list -> theory -> theory) -> theory -> theory val print_datatypes : theory -> unit val make_case : Proof.context -> bool -> string list -> term -> (term * term) list -> term * (term * (int * bool)) list val strip_case: Proof.context -> bool -> term -> (term * (term * term) list) option val setup: theory -> theory end; structure DatatypePackage : DATATYPE_PACKAGE = struct open DatatypeAux; val quiet_mode = quiet_mode; (* theory data *) structure DatatypesData = TheoryDataFun ( type T = {types: datatype_info Symtab.table, constrs: datatype_info Symtab.table, cases: datatype_info Symtab.table}; val empty = {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; val copy = I; val extend = I; fun merge _ ({types = types1, constrs = constrs1, cases = cases1}, {types = types2, constrs = constrs2, cases = cases2}) = {types = Symtab.merge (K true) (types1, types2), constrs = Symtab.merge (K true) (constrs1, constrs2), cases = Symtab.merge (K true) (cases1, cases2)}; ); val get_datatypes = #types o DatatypesData.get; val map_datatypes = DatatypesData.map; fun print_datatypes thy = Pretty.writeln (Pretty.strs ("datatypes:" :: map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy)))); (** theory information about datatypes **) fun put_dt_infos (dt_infos : (string * datatype_info) list) = map_datatypes (fn {types, constrs, cases} => {types = fold Symtab.update dt_infos types, constrs = fold Symtab.update (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst) (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs, cases = fold Symtab.update (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos) cases}); val get_datatype = Symtab.lookup o get_datatypes; fun the_datatype thy name = (case get_datatype thy name of SOME info => info | NONE => error ("Unknown datatype " ^ quote name)); val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get; val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get; fun get_datatype_descr thy dtco = get_datatype thy dtco |> Option.map (fn info as { descr, index, ... } => (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index))); fun get_datatype_spec thy dtco = let fun mk_cons typ_of_dtyp (co, tys) = (co, map typ_of_dtyp tys); fun mk_dtyp ({ sorts = raw_sorts, descr, ... } : DatatypeAux.datatype_info, (dtys, cos)) = let val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) o DatatypeAux.dest_DtTFree) dtys; val typ_of_dtyp = DatatypeAux.typ_of_dtyp descr sorts; val tys = map typ_of_dtyp dtys; in (sorts, map (mk_cons typ_of_dtyp) cos) end; in Option.map mk_dtyp (get_datatype_descr thy dtco) end; fun get_datatype_constrs thy dtco = case get_datatype_spec thy dtco of SOME (sorts, cos) => let fun subst (v, sort) = TVar ((v, 0), sort); fun subst_ty (TFree v) = subst v | subst_ty ty = ty; val dty = Type (dtco, map subst sorts); fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty); in SOME (map mk_co cos) end | NONE => NONE; fun find_tname var Bi = let val frees = map dest_Free (term_frees Bi) val params = rename_wrt_term Bi (Logic.strip_params Bi); in case AList.lookup (op =) (frees @ params) var of NONE => error ("No such variable in subgoal: " ^ quote var) | SOME(Type (tn, _)) => tn | _ => error ("Cannot determine type of " ^ quote var) end; fun infer_tname state i aterm = let val sign = Thm.theory_of_thm state; val (_, _, Bi, _) = Thm.dest_state (state, i) val params = Logic.strip_params Bi; (*params of subgoal i*) val params = rev (rename_wrt_term Bi params); (*as they are printed*) val (types, sorts) = types_sorts state; fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm) | types' ixn = types ixn; val ([ct], _) = Thm.read_def_cterms (sign, types', sorts) [] false [(aterm, dummyT)]; in case #T (rep_cterm ct) of Type (tn, _) => tn | _ => error ("Cannot determine type of " ^ quote aterm) end; (*Warn if the (induction) variable occurs Free among the premises, which usually signals a mistake. But calls the tactic either way!*) fun occs_in_prems tacf vars = SUBGOAL (fn (Bi, i) => (if exists (fn (a, _) => member (op =) vars a) (fold Term.add_frees (#2 (strip_context Bi)) []) then warning "Induction variable occurs also among premises!" else (); tacf i)); (* generic induction tactic for datatypes *) local fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x) | prep_var _ = NONE; fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*) let val vs = Induct.vars_of concl in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end; in fun gen_induct_tac inst_tac (varss, opt_rule) i state = SUBGOAL (fn (Bi,_) => let val (rule, rule_name) = case opt_rule of SOME r => (r, "Induction rule") | NONE => let val tn = find_tname (hd (map_filter I (flat varss))) Bi val thy = Thm.theory_of_thm state in (#induction (the_datatype thy tn), "Induction rule for type " ^ tn) end val concls = HOLogic.dest_concls (Thm.concl_of rule); val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths => error (rule_name ^ " has different numbers of variables"); in occs_in_prems (inst_tac insts rule) (map #2 insts) i end) i state; fun induct_tac s = gen_induct_tac Tactic.res_inst_tac' (map (single o SOME) (Syntax.read_idents s), NONE); fun induct_thm_tac th s = gen_induct_tac Tactic.res_inst_tac' ([map SOME (Syntax.read_idents s)], SOME th); end; (* generic case tactic for datatypes *) fun case_inst_tac inst_tac t rule i state = let val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule)))); in inst_tac [(ixn, t)] rule i state end; fun gen_case_tac inst_tac (t, SOME rule) i state = case_inst_tac inst_tac t rule i state | gen_case_tac inst_tac (t, NONE) i state = let val tn = infer_tname state i t in if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state else case_inst_tac inst_tac t (#exhaustion (the_datatype (Thm.theory_of_thm state) tn)) i state end handle THM _ => Seq.empty; fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE); (** Isar tactic emulations **) local val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":"); val opt_rule = Scan.option (rule_spec |-- Attrib.thm); val varss = Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name)))); val inst_tac = RuleInsts.bires_inst_tac false; fun induct_meth ctxt (varss, opt_rule) = gen_induct_tac (inst_tac ctxt) (varss, opt_rule); fun case_meth ctxt (varss, opt_rule) = gen_case_tac (inst_tac ctxt) (varss, opt_rule); in val tactic_emulations = [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth, "induct_tac emulation (dynamic instantiation)"), ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth, "case_tac emulation (dynamic instantiation)")]; end; (** induct method setup **) (* case names *) local fun dt_recs (DtTFree _) = [] | dt_recs (DtType (_, dts)) = maps dt_recs dts | dt_recs (DtRec i) = [i]; fun dt_cases (descr: descr) (_, args, constrs) = let fun the_bname i = Sign.base_name (#1 (the (AList.lookup (op =) descr i))); val bnames = map the_bname (distinct (op =) (maps dt_recs args)); in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end; fun induct_cases descr = DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr)); fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i)); in fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); fun mk_case_names_exhausts descr new = map (RuleCases.case_names o exhaust_cases descr o #1) (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); end; fun add_rules simps case_thms rec_thms inject distinct weak_case_congs cong_att = PureThy.add_thmss [(("simps", simps), []), (("", flat case_thms @ flat distinct @ rec_thms), [Simplifier.simp_add]), (("", rec_thms), [RecfunCodegen.add_default]), (("", flat inject), [iff_add]), (("", map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]), (("", weak_case_congs), [cong_att])] #> snd; (* add_cases_induct *) fun add_cases_induct infos induction thy = let val inducts = ProjectRule.projections (ProofContext.init thy) induction; fun named_rules (name, {index, exhaustion, ...}: datatype_info) = [(("", nth inducts index), [Induct.induct_type name]), (("", exhaustion), [Induct.cases_type name])]; fun unnamed_rule i = (("", nth inducts i), [PureThy.kind_internal, Induct.induct_type ""]); in thy |> PureThy.add_thms (maps named_rules infos @ map unnamed_rule (length infos upto length inducts - 1)) |> snd |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd end; (**** simplification procedure for showing distinctness of constructors ****) fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T) | stripT p = p; fun stripC (i, f $ x) = stripC (i + 1, f) | stripC p = p; val distinctN = "constr_distinct"; exception ConstrDistinct of term; fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) = (case (stripC (0, t1), stripC (0, t2)) of ((i, Const (cname1, T1)), (j, Const (cname2, T2))) => (case (stripT (0, T1), stripT (0, T2)) of ((i', Type (tname1, _)), (j', Type (tname2, _))) => if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then (case (get_datatype_descr thy) tname1 of SOME (_, (_, constrs)) => let val cnames = map fst constrs in if cname1 mem cnames andalso cname2 mem cnames then let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT)); val eq_ct = cterm_of thy eq_t; val Datatype_thy = ThyInfo.the_theory "Datatype" thy; val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] = map (get_thm Datatype_thy o Name) ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"] in (case (#distinct (the_datatype thy tname1)) of QuickAndDirty => SOME (Thm.invoke_oracle Datatype_thy distinctN (thy, ConstrDistinct eq_t)) | FewConstrs thms => SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1, atac 2, resolve_tac thms 1, etac FalseE 1]))) | ManyConstrs (thm, simpset) => SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1, full_simp_tac (Simplifier.inherit_context ss simpset) 1, REPEAT (dresolve_tac [In0_inject, In1_inject] 1), eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1, etac FalseE 1])))) end else NONE end | NONE => NONE) else NONE | _ => NONE) | _ => NONE) | distinct_proc _ _ _ = NONE; val distinct_simproc = Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc; val dist_ss = HOL_ss addsimprocs [distinct_simproc]; val simproc_setup = Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #> (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy)); (**** translation rules for case ****) fun make_case ctxt = DatatypeCase.make_case (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt; fun strip_case ctxt = DatatypeCase.strip_case (datatype_of_case (ProofContext.theory_of ctxt)); fun add_case_tr' case_names thy = Sign.add_advanced_trfuns ([], [], map (fn case_name => let val case_name' = Sign.const_syntax_name thy case_name in (case_name', DatatypeCase.case_tr' datatype_of_case case_name') end) case_names, []) thy; val trfun_setup = Sign.add_advanced_trfuns ([], [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)], [], []); (* prepare types *) fun read_typ sign ((Ts, sorts), str) = let val T = Type.no_tvars (Sign.read_def_typ (sign, AList.lookup (op =) (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg in (Ts @ [T], add_typ_tfrees (T, sorts)) end; fun cert_typ sign ((Ts, sorts), raw_T) = let val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle TYPE (msg, _, _) => error msg; val sorts' = add_typ_tfrees (T, sorts) in (Ts @ [T], case duplicates (op =) (map fst sorts') of [] => sorts' | dups => error ("Inconsistent sort constraints for " ^ commas dups)) end; (**** make datatype info ****) fun make_dt_info head_len descr sorts induct reccomb_names rec_thms (((((((((i, (_, (tname, _, _))), case_name), case_thms), exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) = (tname, {index = i, head_len = head_len, descr = descr, sorts = sorts, rec_names = reccomb_names, rec_rewrites = rec_thms, case_name = case_name, case_rewrites = case_thms, induction = induct, exhaustion = exhaustion_thm, distinct = distinct_thm, inject = inject, nchotomy = nchotomy, case_cong = case_cong, weak_case_cong = weak_case_cong}); (********************* axiomatic introduction of datatypes ********************) fun add_axiom label t atts thy = thy |> PureThy.add_axioms_i [((label, t), atts)]; fun add_axioms label ts atts thy = thy |> PureThy.add_axiomss_i [((label, ts), atts)]; fun add_and_get_axioms_atts label tnames ts attss = fold_map (fn (tname, (atts, t)) => fn thy => thy |> Sign.add_path tname |> add_axiom label t atts ||> Sign.parent_path |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts)); fun add_and_get_axioms label tnames ts = add_and_get_axioms_atts label tnames ts (replicate (length tnames) []); fun add_and_get_axiomss label tnames tss = fold_map (fn (tname, ts) => fn thy => thy |> Sign.add_path tname |> add_axioms label ts [] ||> Sign.parent_path |-> (fn [ax] => pair ax)) (tnames ~~ tss); fun gen_specify_consts add args thy = let val specs = map (fn (c, T, mx) => Const (Sign.full_name thy (Syntax.const_name c mx), T)) args; in thy |> add args |> Theory.add_finals_i false specs end; val specify_consts = gen_specify_consts Sign.add_consts_i; val specify_consts_authentic = gen_specify_consts (fold (snd oo Sign.declare_const [])); structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =); val interpretation = DatatypeInterpretation.interpretation; fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info case_names_induct case_names_exhausts thy = let val descr' = flat descr; val recTs = get_rec_types descr' sorts; val used = map fst (fold Term.add_tfreesT recTs []); val newTs = Library.take (length (hd descr), recTs); (**** declare new types and constants ****) val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr); val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') => map (fn ((_, cargs), (cname, mx)) => (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx)) (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax); val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used; val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; val reccomb_names = if length descr' = 1 then [big_reccomb_name] else (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) (1 upto (length descr'))); val freeT = TFree (Name.variant used "'t", HOLogic.typeS); val case_fn_Ts = map (fn (i, (_, _, constrs)) => map (fn (_, cargs) => let val Ts = map (typ_of_dtyp descr' sorts) cargs in Ts ---> freeT end) constrs) (hd descr); val case_names = map (fn s => (s ^ "_case")) new_type_names; val thy2' = thy (** new types **) |> fold2 (fn (name, mx) => fn tvs => TypedefPackage.add_typedecls [(name, tvs, mx)]) types_syntax tyvars |> add_path flat_names (space_implode "_" new_type_names) (** primrec combinators **) |> specify_consts (map (fn ((name, T), T') => (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts)) (** case combinators **) |> specify_consts_authentic (map (fn ((name, T), Ts) => (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts)); val reccomb_names' = map (Sign.full_name thy2') reccomb_names; val case_names' = map (Sign.full_name thy2') case_names; val thy2 = thy2' (** constructors **) |> parent_path flat_names |> fold (fn ((((_, (_, _, constrs)), T), tname), constr_syntax') => add_path flat_names tname #> specify_consts (map (fn ((_, cargs), (cname, mx)) => (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx)) (constrs ~~ constr_syntax')) #> parent_path flat_names) (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax); (**** introduction of axioms ****) val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2; val ((([induct], [rec_thms]), inject), thy3) = thy2 |> Sign.add_path (space_implode "_" new_type_names) |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct] ||>> add_axioms "recs" rec_axs [] ||> Sign.parent_path ||>> add_and_get_axiomss "inject" new_type_names (DatatypeProp.make_injs descr sorts); val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3; val exhaust_ts = DatatypeProp.make_casedists descr sorts; val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names exhaust_ts (map single case_names_exhausts) thy4; val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5; val (split_ts, split_asm_ts) = ListPair.unzip (DatatypeProp.make_splits new_type_names descr sorts thy6); val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6; val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names split_asm_ts thy7; val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names (DatatypeProp.make_nchotomys descr sorts) thy8; val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9; val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10; val dt_infos = map (make_dt_info (length (hd descr)) descr' sorts induct reccomb_names' rec_thms) ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~ exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); val simps = flat (distinct @ inject @ case_thms) @ rec_thms; val split_thms = split ~~ split_asm; val thy12 = thy11 |> add_case_tr' case_names' |> Sign.add_path (space_implode "_" new_type_names) |> add_rules simps case_thms rec_thms inject distinct weak_case_congs Simplifier.cong_add |> put_dt_infos dt_infos |> add_cases_induct dt_infos induct |> Sign.parent_path |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |> DatatypeInterpretation.data (map fst dt_infos); in ({distinct = distinct, inject = inject, exhaustion = exhaustion, rec_thms = rec_thms, case_thms = case_thms, split_thms = split_thms, induction = induct, simps = simps}, thy12) end; (******************* definitional introduction of datatypes *******************) fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info case_names_induct case_names_exhausts thy = let val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |> DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts types_syntax constr_syntax case_names_induct; val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy2; val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms flat_names new_type_names descr sorts dt_info inject dist_rewrites (Simplifier.theory_context thy3 dist_ss) induct thy3; val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms flat_names new_type_names descr sorts reccomb_names rec_thms thy4; val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names descr sorts inject dist_rewrites casedist_thms case_thms thy6; val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names descr sorts casedist_thms thy7; val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names descr sorts nchotomys case_thms thy8; val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names descr sorts thy9; val dt_infos = map (make_dt_info (length (hd descr)) (flat descr) sorts induct reccomb_names rec_thms) ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~ casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); val simps = flat (distinct @ inject @ case_thms) @ rec_thms; val thy12 = thy10 |> add_case_tr' case_names |> Sign.add_path (space_implode "_" new_type_names) |> add_rules simps case_thms rec_thms inject distinct weak_case_congs (Simplifier.attrib (op addcongs)) |> put_dt_infos dt_infos |> add_cases_induct dt_infos induct |> Sign.parent_path |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |> DatatypeInterpretation.data (map fst dt_infos); in ({distinct = distinct, inject = inject, exhaustion = casedist_thms, rec_thms = rec_thms, case_thms = case_thms, split_thms = split_thms, induction = induct, simps = simps}, thy12) end; (*********************** declare existing type as datatype *********************) fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 = let val (((distinct, inject), [induction]), thy1) = thy0 |> fold_map apply_theorems raw_distinct ||>> fold_map apply_theorems raw_inject ||>> apply_theorems [raw_induction]; val ((_, [induction']), _) = Variable.importT_thms [induction] (Variable.thm_context induction); fun err t = error ("Ill-formed predicate in induction rule: " ^ Sign.string_of_term thy1 t); fun get_typ (t as _ $ Var (_, Type (tname, Ts))) = ((tname, map dest_TFree Ts) handle TERM _ => err t) | get_typ t = err t; val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction'))); val new_type_names = getOpt (alt_names, map fst dtnames); fun get_constr t = (case Logic.strip_assums_concl t of _ $ (_ $ t') => (case head_of t' of Const (cname, cT) => (case strip_type cT of (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts)) | _ => err t) | _ => err t) | _ => err t); fun make_dt_spec [] _ _ = [] | make_dt_spec ((tname, tvs)::dtnames') i constrs = let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs in (i, (tname, map DtTFree tvs, map snd constrs')):: (make_dt_spec dtnames' (i + 1) constrs'') end; val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction')); val sorts = add_term_tfrees (concl_of induction', []); val dt_info = get_datatypes thy1; val (case_names_induct, case_names_exhausts) = (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames)); val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); val (casedist_thms, thy2) = thy1 |> DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction case_names_exhausts; val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms false new_type_names [descr] sorts dt_info inject distinct (Simplifier.theory_context thy2 dist_ss) induction thy2; val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false new_type_names [descr] sorts reccomb_names rec_thms thy3; val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4; val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names [descr] sorts casedist_thms thy5; val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names [descr] sorts nchotomys case_thms thy6; val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names [descr] sorts thy7; val ((_, [induction']), thy10) = thy8 |> store_thmss "inject" new_type_names inject ||>> store_thmss "distinct" new_type_names distinct ||> Sign.add_path (space_implode "_" new_type_names) ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])]; val dt_infos = map (make_dt_info (length descr) descr sorts induction' reccomb_names rec_thms) ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~ map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); val simps = flat (distinct @ inject @ case_thms) @ rec_thms; val thy11 = thy10 |> add_case_tr' case_names |> add_rules simps case_thms rec_thms inject distinct weak_case_congs (Simplifier.attrib (op addcongs)) |> put_dt_infos dt_infos |> add_cases_induct dt_infos induction' |> Sign.parent_path |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |> DatatypeInterpretation.data (map fst dt_infos); in ({distinct = distinct, inject = inject, exhaustion = casedist_thms, rec_thms = rec_thms, case_thms = case_thms, split_thms = split_thms, induction = induction', simps = simps}, thy11) end; val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems; val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i; (******************************** add datatype ********************************) fun gen_add_datatype prep_typ err flat_names new_type_names dts thy = let val _ = Theory.requires thy "Datatype" "datatype definitions"; (* this theory is used just for parsing *) val tmp_thy = thy |> Theory.copy |> Sign.add_types (map (fn (tvs, tname, mx, _) => (tname, length tvs, mx)) dts); val (tyvars, _, _, _)::_ = dts; val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) => let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx) in (case duplicates (op =) tvs of [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx)) else error ("Mutually recursive datatypes must have same type parameters") | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^ " : " ^ commas dups)) end) dts); val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of [] => () | dups => error ("Duplicate datatypes: " ^ commas dups)); fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) = let fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') = let val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs); val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of [] => () | vs => error ("Extra type variables on rhs: " ^ commas vs)) in (constrs @ [((if flat_names then Sign.full_name tmp_thy else Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'), map (dtyp_of_typ new_dts) cargs')], constr_syntax' @ [(cname, mx')], sorts'') end handle ERROR msg => cat_error msg ("The error above occured in constructor " ^ cname ^ " of datatype " ^ tname); val (constrs', constr_syntax', sorts') = fold prep_constr constrs ([], [], sorts) in case duplicates (op =) (map fst constrs') of [] => (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx), map DtTFree tvs, constrs'))], constr_syntax @ [constr_syntax'], sorts', i + 1) | dups => error ("Duplicate constructors " ^ commas dups ^ " in datatype " ^ tname) end; val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0); val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts')); val dt_info = get_datatypes thy; val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i; val _ = check_nonempty descr handle (exn as Datatype_Empty s) => if err then error ("Nonemptiness check failed for datatype " ^ s) else raise exn; val descr' = flat descr; val case_names_induct = mk_case_names_induct descr'; val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts); in (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def) flat_names new_type_names descr sorts types_syntax constr_syntax dt_info case_names_induct case_names_exhausts thy end; val add_datatype_i = gen_add_datatype cert_typ; val add_datatype = gen_add_datatype read_typ true; (** package setup **) (* setup theory *) val setup = DatatypeProp.distinctness_limit_setup #> Method.add_methods tactic_emulations #> simproc_setup #> trfun_setup #> DatatypeInterpretation.init; (* outer syntax *) local structure P = OuterParse and K = OuterKeyword in val _ = OuterSyntax.keywords ["distinct", "inject", "induction"]; val datatype_decl = Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix -- (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix)); fun mk_datatype args = let val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args; val specs = map (fn ((((_, vs), t), mx), cons) => (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; in snd o add_datatype false names specs end; val _ = OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); val rep_datatype_decl = Scan.option (Scan.repeat1 P.name) -- Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] -- Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] -- (P.$$$ "induction" |-- P.!!! SpecParse.xthm); fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind; val _ = OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype)); end; end; structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage; open BasicDatatypePackage;