author | wenzelm |
Sat, 04 Dec 2010 14:59:25 +0100 | |
changeset 40957 | f840361f8e69 |
parent 40929 | 7ff03a5e044f |
child 41423 | 25df154b8ffc |
permissions | -rw-r--r-- |
(* Title: HOL/Tools/Datatype/datatype_data.ML Author: Stefan Berghofer, TU Muenchen Datatype package: bookkeeping; interpretation of existing types as datatypes. *) signature DATATYPE_DATA = sig include DATATYPE_COMMON val derive_datatype_props : config -> string list -> string list option -> descr list -> (string * sort) list -> thm -> thm list list -> thm list list -> theory -> string list * theory val rep_datatype : config -> (string list -> Proof.context -> Proof.context) -> string list option -> term list -> theory -> Proof.state val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state val get_info : theory -> string -> info option val the_info : theory -> string -> info val the_descr : theory -> string list -> descr * (string * sort) list * string list * string * (string list * string list) * (typ list * typ list) val the_spec : theory -> string -> (string * sort) list * (string * typ list) list val all_distincts : theory -> typ list -> thm list list val get_constrs : theory -> string -> (string * typ) list option val get_all : theory -> info Symtab.table val info_of_constr : theory -> string * typ -> info option val info_of_case : theory -> string -> info option val interpretation : (config -> string list -> theory -> theory) -> theory -> theory val make_case : Proof.context -> Datatype_Case.config -> string list -> term -> (term * term) list -> term * (term * (int * bool)) list val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option val read_typ: theory -> string -> (string * sort) list -> typ * (string * sort) list val cert_typ: theory -> typ -> (string * sort) list -> typ * (string * sort) list val mk_case_names_induct: descr -> attribute val setup: theory -> theory end; structure Datatype_Data: DATATYPE_DATA = struct open Datatype_Aux; (** theory data **) (* data management *) structure DatatypesData = Theory_Data ( type T = {types: info Symtab.table, constrs: (string * info) list Symtab.table, cases: info Symtab.table}; val empty = {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; val extend = I; fun merge ({types = types1, constrs = constrs1, cases = cases1}, {types = types2, constrs = constrs2, cases = cases2}) : T = {types = Symtab.merge (K true) (types1, types2), constrs = Symtab.join (K (AList.merge (op =) (K true))) (constrs1, constrs2), cases = Symtab.merge (K true) (cases1, cases2)}; ); val get_all = #types o DatatypesData.get; val get_info = Symtab.lookup o get_all; fun the_info thy name = (case get_info thy name of SOME info => info | NONE => error ("Unknown datatype " ^ quote name)); fun info_of_constr thy (c, T) = let val tab = Symtab.lookup_list ((#constrs o DatatypesData.get) thy) c; val hint = case body_type T of Type (tyco, _) => SOME tyco | _ => NONE; val default = if null tab then NONE else SOME (snd (Library.last_elem tab)) (*conservative wrt. overloaded constructors*); in case hint of NONE => default | SOME tyco => case AList.lookup (op =) tab tyco of NONE => default (*permissive*) | SOME info => SOME info end; val info_of_case = Symtab.lookup o #cases o DatatypesData.get; fun register (dt_infos : (string * info) list) = DatatypesData.map (fn {types, constrs, cases} => {types = types |> fold Symtab.update dt_infos, constrs = constrs |> fold (fn (constr, dtname_info) => Symtab.map_default (constr, []) (cons dtname_info)) (maps (fn (dtname, info as {descr, index, ...}) => map (rpair (dtname, info) o fst) (#3 (the (AList.lookup op = descr index)))) dt_infos), cases = cases |> fold Symtab.update (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)}); (* complex queries *) fun the_spec thy dtco = let val { descr, index, sorts = raw_sorts, ... } = the_info thy dtco; val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index; val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) o Datatype_Aux.dest_DtTFree) dtys; val cos = map (fn (co, tys) => (co, map (Datatype_Aux.typ_of_dtyp descr sorts) tys)) raw_cos; in (sorts, cos) end; fun the_descr thy (raw_tycos as raw_tyco :: _) = let val info = the_info thy raw_tyco; val descr = #descr info; val SOME (_, dtys, _) = AList.lookup (op =) descr (#index info); val vs = map ((fn v => (v, (the o AList.lookup (op =) (#sorts info)) v)) o dest_DtTFree) dtys; fun is_DtTFree (DtTFree _) = true | is_DtTFree _ = false val k = find_index (fn (_, (_, dTs, _)) => not (forall is_DtTFree dTs)) descr; val protoTs as (dataTs, _) = chop k descr |> (pairself o map) (fn (_, (tyco, dTs, _)) => (tyco, map (typ_of_dtyp descr vs) dTs)); val tycos = map fst dataTs; val _ = if eq_set (op =) (tycos, raw_tycos) then () else error ("Type constructors " ^ commas (map quote raw_tycos) ^ " do not belong exhaustively to one mutual recursive datatype"); val (Ts, Us) = (pairself o map) Type protoTs; val names = map Long_Name.base_name (the_default tycos (#alt_names info)); val (auxnames, _) = Name.make_context names |> fold_map (yield_singleton Name.variants o name_of_typ) Us; val prefix = space_implode "_" names; in (descr, vs, tycos, prefix, (names, auxnames), (Ts, Us)) end; fun all_distincts thy Ts = let fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts | add_tycos _ = I; val tycos = fold add_tycos Ts []; in map_filter (Option.map #distinct o get_info thy) tycos end; fun get_constrs thy dtco = case try (the_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; (** various auxiliary **) (* prepare datatype specifications *) fun read_typ thy str sorts = let val ctxt = ProofContext.init_global thy |> fold (Variable.declare_typ o TFree) sorts; val T = Syntax.read_typ ctxt str; in (T, Term.add_tfreesT T sorts) end; fun cert_typ sign raw_T sorts = let val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle TYPE (msg, _, _) => error msg; val sorts' = Term.add_tfreesT T sorts; val _ = case duplicates (op =) (map fst sorts') of [] => () | dups => error ("Inconsistent sort constraints for " ^ commas dups) in (T, sorts') end; (* 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 = Long_Name.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 "_" (Long_Name.base_name c :: bnames)) constrs end; fun induct_cases descr = Datatype_Prop.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 = Rule_Cases.case_names (induct_cases descr); fun mk_case_names_exhausts descr new = map (Rule_Cases.case_names o exhaust_cases descr o #1) (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); end; (* translation rules for case *) fun make_case ctxt = Datatype_Case.make_case (info_of_constr (ProofContext.theory_of ctxt)) ctxt; fun strip_case ctxt = Datatype_Case.strip_case (info_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' = Syntax.mark_const case_name in (case_name', Datatype_Case.case_tr' info_of_case case_name') end) case_names, []) thy; val trfun_setup = Sign.add_advanced_trfuns ([], [(@{syntax_const "_case_syntax"}, Datatype_Case.case_tr true info_of_constr)], [], []); (** document antiquotation **) val _ = Thy_Output.antiquotation "datatype" (Args.type_name true) (fn {source = src, context = ctxt, ...} => fn dtco => let val thy = ProofContext.theory_of ctxt; val (vs, cos) = the_spec thy dtco; val ty = Type (dtco, map TFree vs); val pretty_typ_bracket = Syntax.pretty_typ (Config.put Syntax.pretty_priority (Syntax.max_pri + 1) ctxt); fun pretty_constr (co, tys) = Pretty.block (Pretty.breaks (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) :: map pretty_typ_bracket tys)); val pretty_datatype = Pretty.block (Pretty.command "datatype" :: Pretty.brk 1 :: Syntax.pretty_typ ctxt ty :: Pretty.str " =" :: Pretty.brk 1 :: flat (separate [Pretty.brk 1, Pretty.str "| "] (map (single o pretty_constr) cos))); in Thy_Output.output ctxt (Thy_Output.maybe_pretty_source (K (K pretty_datatype)) ctxt src [()]) end); (** abstract theory extensions relative to a datatype characterisation **) structure Datatype_Interpretation = Interpretation (type T = config * string list val eq: T * T -> bool = eq_snd op =); fun interpretation f = Datatype_Interpretation.interpretation (uncurry f); fun make_dt_info alt_names descr sorts induct inducts rec_names rec_rewrites (index, (((((((((((_, (tname, _, _))), inject), distinct), exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong), (split, split_asm))) = (tname, {index = index, alt_names = alt_names, descr = descr, sorts = sorts, inject = inject, distinct = distinct, induct = induct, inducts = inducts, exhaust = exhaust, nchotomy = nchotomy, rec_names = rec_names, rec_rewrites = rec_rewrites, case_name = case_name, case_rewrites = case_rewrites, case_cong = case_cong, weak_case_cong = weak_case_cong, split = split, split_asm = split_asm}); fun derive_datatype_props config dt_names alt_names descr sorts induct inject distinct thy1 = let val thy2 = thy1 |> Theory.checkpoint; val flat_descr = flat descr; val new_type_names = map Long_Name.base_name (the_default dt_names alt_names); val _ = message config ("Deriving properties for datatype(s) " ^ commas_quote new_type_names); val (exhaust, thy3) = Datatype_Abs_Proofs.prove_casedist_thms config new_type_names descr sorts induct (mk_case_names_exhausts flat_descr dt_names) thy2; val (nchotomys, thy4) = Datatype_Abs_Proofs.prove_nchotomys config new_type_names descr sorts exhaust thy3; val ((rec_names, rec_rewrites), thy5) = Datatype_Abs_Proofs.prove_primrec_thms config new_type_names descr sorts (#inject o the o Symtab.lookup (get_all thy4)) inject (distinct, all_distincts thy2 (get_rec_types flat_descr sorts)) induct thy4; val ((case_rewrites, case_names), thy6) = Datatype_Abs_Proofs.prove_case_thms config new_type_names descr sorts rec_names rec_rewrites thy5; val (case_congs, thy7) = Datatype_Abs_Proofs.prove_case_congs new_type_names descr sorts nchotomys case_rewrites thy6; val (weak_case_congs, thy8) = Datatype_Abs_Proofs.prove_weak_case_congs new_type_names descr sorts thy7; val (splits, thy9) = Datatype_Abs_Proofs.prove_split_thms config new_type_names descr sorts inject distinct exhaust case_rewrites thy8; val inducts = Project_Rule.projections (ProofContext.init_global thy2) induct; val dt_infos = map_index (make_dt_info alt_names flat_descr sorts induct inducts rec_names rec_rewrites) (hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~ case_names ~~ case_rewrites ~~ case_congs ~~ weak_case_congs ~~ splits); val dt_names = map fst dt_infos; val prfx = Binding.qualify true (space_implode "_" new_type_names); val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites; val named_rules = flat (map_index (fn (index, tname) => [((Binding.empty, [nth inducts index]), [Induct.induct_type tname]), ((Binding.empty, [nth exhaust index]), [Induct.cases_type tname])]) dt_names); val unnamed_rules = map (fn induct => ((Binding.empty, [induct]), [Rule_Cases.inner_rule, Induct.induct_type ""])) (drop (length dt_names) inducts); in thy9 |> Global_Theory.add_thmss ([((prfx (Binding.name "simps"), simps), []), ((prfx (Binding.name "inducts"), inducts), []), ((prfx (Binding.name "splits"), maps (fn (x, y) => [x, y]) splits), []), ((Binding.empty, flat case_rewrites @ flat distinct @ rec_rewrites), [Simplifier.simp_add]), ((Binding.empty, rec_rewrites), [Code.add_default_eqn_attribute]), ((Binding.empty, flat inject), [iff_add]), ((Binding.empty, map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]), ((Binding.empty, weak_case_congs), [Simplifier.attrib (op addcongs)]), ((Binding.empty, flat (distinct @ inject)), [Induct.induct_simp_add])] @ named_rules @ unnamed_rules) |> snd |> add_case_tr' case_names |> register dt_infos |> Datatype_Interpretation.data (config, dt_names) |> pair dt_names end; (** declare existing type as datatype **) fun prove_rep_datatype config dt_names alt_names descr sorts raw_inject half_distinct raw_induct thy1 = let val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; val new_type_names = map Long_Name.base_name (the_default dt_names alt_names); val prfx = Binding.qualify true (space_implode "_" new_type_names); val (((inject, distinct), [induct]), thy2) = thy1 |> store_thmss "inject" new_type_names raw_inject ||>> store_thmss "distinct" new_type_names raw_distinct ||>> Global_Theory.add_thms [((prfx (Binding.name "induct"), raw_induct), [mk_case_names_induct descr])]; in thy2 |> derive_datatype_props config dt_names alt_names [descr] sorts induct inject distinct end; fun gen_rep_datatype prep_term config after_qed alt_names raw_ts thy = let fun constr_of_term (Const (c, T)) = (c, T) | constr_of_term t = error ("Not a constant: " ^ Syntax.string_of_term_global thy t); fun no_constr (c, T) = error ("Bad constructor: " ^ Sign.extern_const thy c ^ "::" ^ Syntax.string_of_typ_global thy T); fun type_of_constr (cT as (_, T)) = let val frees = OldTerm.typ_tfrees T; val (tyco, vs) = (apsnd o map) dest_TFree (dest_Type (body_type T)) handle TYPE _ => no_constr cT val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); val _ = if length frees <> length vs then no_constr cT else (); in (tyco, (vs, cT)) end; val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); val _ = case map_filter (fn (tyco, _) => if Symtab.defined (get_all thy) tyco then SOME tyco else NONE) raw_cs of [] => () | tycos => error ("Type(s) " ^ commas (map quote tycos) ^ " already represented inductivly"); val raw_vss = maps (map (map snd o fst) o snd) raw_cs; val ms = case distinct (op =) (map length raw_vss) of [n] => 0 upto n - 1 | _ => error ("Different types in given constructors"); fun inter_sort m = map (fn xs => nth xs m) raw_vss |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy)) val sorts = map inter_sort ms; val vs = Name.names Name.context Name.aT sorts; fun norm_constr (raw_vs, (c, T)) = (c, map_atyps (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); val cs = map (apsnd (map norm_constr)) raw_cs; val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) o binder_types; val dt_names = map fst cs; fun mk_spec (i, (tyco, constr)) = (i, (tyco, map (DtTFree o fst) vs, (map o apsnd) dtyps_of_typ constr)) val descr = map_index mk_spec cs; val injs = Datatype_Prop.make_injs [descr] vs; val half_distincts = map snd (Datatype_Prop.make_distincts [descr] vs); val ind = Datatype_Prop.make_ind [descr] vs; val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; fun after_qed' raw_thms = let val [[[raw_induct]], raw_inject, half_distinct] = unflat rules (map Drule.zero_var_indexes_list raw_thms); (*FIXME somehow dubious*) in ProofContext.background_theory_result (prove_rep_datatype config dt_names alt_names descr vs raw_inject half_distinct raw_induct) #-> after_qed end; in thy |> ProofContext.init_global |> Proof.theorem NONE after_qed' ((map o map) (rpair []) (flat rules)) end; val rep_datatype = gen_rep_datatype Sign.cert_term; val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global default_config (K I); (** package setup **) (* setup theory *) val setup = trfun_setup #> Datatype_Interpretation.init; (* outer syntax *) val _ = Outer_Syntax.command "rep_datatype" "represent existing types inductively" Keyword.thy_goal (Scan.option (Parse.$$$ "(" |-- Scan.repeat1 Parse.name --| Parse.$$$ ")") -- Scan.repeat1 Parse.term >> (fn (alt_names, ts) => Toplevel.print o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts))); end;