src/HOL/Tools/record_package.ML

+(*  Title:      HOL/Tools/record_package.ML
+    ID:         $Id$
+    Author:     Wolfgang Naraschewski and Markus Wenzel, TU Muenchen
+
+Extensible records with structural subtyping in HOL.
+
+TODO:
+  - record_info: tr' funs;
+  - trfuns for record types;
+  - field types: typedef;
+  - make selector types as general as possible (no!?);
+*)
+
+signature RECORD_PACKAGE =
+sig
+  val print_records: theory -> unit
+  val add_record: (string list * bstring) -> string option
+    -> (bstring * string) list -> theory -> theory
+  val add_record_i: (string list * bstring) -> (typ list * string) option
+    -> (bstring * typ) list -> theory -> theory
+  val setup: (theory -> theory) list
+end;
+
+structure RecordPackage: RECORD_PACKAGE =
+struct
+
+
+(*** syntax operations ***)
+
+(** names **)
+
+(* name components *)
+
+val moreN = "more";
+val schemeN = "_scheme";
+val fieldN = "_field";
+val field_typeN = "_field_type";
+val fstN = "_val";
+val sndN = "_more";
+val updateN = "_update";
+val makeN = "make";
+val make_schemeN = "make_scheme";
+
+
+(* suffixes *)
+
+fun suffix sfx s = s ^ sfx;
+
+fun unsuffix sfx s =
+  let
+    val cs = explode s;
+    val prfx_len = size s - size sfx;
+  in
+    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
+      implode (take (prfx_len, cs))
+    else raise LIST "unsuffix"
+  end;
+
+
+
+(** tuple operations **)
+
+(* more type class *)
+
+val moreS = ["more"];
+
+
+(* types *)
+
+fun mk_fieldT ((c, T), U) = Type (suffix field_typeN c, [T, U]);
+
+fun dest_fieldT (typ as Type (c_field_type, [T, U])) =
+      (case try (unsuffix field_typeN) c_field_type of
+        None => raise TYPE ("dest_fieldT", [typ], [])
+      | Some c => ((c, T), U))
+  | dest_fieldT typ = raise TYPE ("dest_fieldT", [typ], []);
+
+
+(* constructors *)
+
+fun mk_fieldC U (c, T) = (suffix fieldN c, T --> U --> mk_fieldT ((c, T), U));
+
+fun mk_field ((c, t), u) =
+  let val T = fastype_of t and U = fastype_of u
+  in Const (suffix fieldN c, [T, U] ---> mk_fieldT ((c, T), U)) $ t $ u end;
+
+
+(* destructors *)
+
+fun mk_fstC U (c, T) = (suffix fstN c, mk_fieldT ((c, T), U) --> T);
+fun mk_sndC U (c, T) = (suffix sndN c, mk_fieldT ((c, T), U) --> U);
+
+fun dest_field fst_or_snd p =
+  let
+    val pT = fastype_of p;
+    val ((c, T), U) = dest_fieldT pT;
+    val (destN, destT) = if fst_or_snd then (fstN, T) else (sndN, U);
+  in Const (suffix destN c, pT --> destT) $ p end;
+
+val mk_fst = dest_field true;
+val mk_snd = dest_field false;
+
+
+
+(** record operations **)
+
+(* types *)
+
+val mk_recordT = foldr mk_fieldT;
+
+fun dest_recordT T =
+  (case try dest_fieldT T of
+    None => ([], T)
+  | Some (c_T, U) => apfst (cons c_T) (dest_recordT U));
+
+fun find_fieldT c rT =
+  (case assoc (fst (dest_recordT rT), c) of
+    None => raise TYPE ("find_field: " ^ c, [rT], [])
+  | Some T => T);
+
+
+(* constructors *)
+
+val mk_record = foldr mk_field;
+
+
+(* selectors *)
+
+fun mk_selC rT (c, T) = (c, rT --> T);
+
+fun mk_sel c r =
+  let val rT = fastype_of r
+  in Const (mk_selC rT (c, find_fieldT c rT)) $ r end;
+
+
+(* updates *)
+
+fun mk_updateC rT (c, T) = (suffix updateN c, T --> rT --> rT);
+
+fun mk_update c x r =
+  let val rT = fastype_of r
+  in Const (mk_updateC rT (c, find_fieldT c rT)) $ x $ r end;
+
+
+
+(** concrete syntax for records **)
+
+(* parse translations *)
+
+fun field_tr (Const ("_field", _) $ Free (name, _) $ arg) =
+      Syntax.const (suffix fieldN name) $ arg
+  | field_tr t = raise TERM ("field_tr", [t]);
+
+fun fields_tr (Const ("_fields", _) $ field $ fields) =
+      field_tr field :: fields_tr fields
+  | fields_tr field = [field_tr field];
+
+fun record_tr (*"_record"*) [fields] =
+      foldr (op $) (fields_tr fields, HOLogic.unit)
+  | record_tr (*"_record"*) ts = raise TERM ("record_tr", ts);
+
+fun record_scheme_tr (*"_record_scheme"*) [fields, more] =
+      foldr (op $) (fields_tr fields, more)
+  | record_scheme_tr (*"_record_scheme"*) ts = raise TERM ("record_scheme_tr", ts);
+
+
+(* print translations *)		(* FIXME tune, activate *)
+
+(* FIXME ... :: tms *)
+fun fields_tr' (tm as Const (name_field, _) $ arg $ more) =
+      (case try (unsuffix fieldN) name_field of
+        Some name =>
+          apfst (cons (Syntax.const "_field" $ Syntax.free name $ arg)) (fields_tr' more)
+      | None => ([], tm))
+  | fields_tr' tm = ([], tm);
+
+fun record_tr' tm =
+  let
+    val mk_fields = foldr (fn (field, fields) => Syntax.const "_fields" $ field $ fields);
+    val (fields, more) = fields_tr' tm;
+  in
+    if HOLogic.is_unit more then
+      Syntax.const "_record" $ mk_fields (split_last fields)
+    else Syntax.const "_record_scheme" $ mk_fields (fields, more)
+  end;
+
+fun field_tr' name [arg, more] = record_tr' (Syntax.const name $ arg $ more)
+  | field_tr' _ _ = raise Match;
+
+
+
+(*** extend theory by record definition ***)
+
+(** record info **)
+
+(* type record_info and parent_info *)
+
+type record_info =
+ {args: (string * sort) list,
+  parent: (typ list * string) option,
+  fields: (string * typ) list,
+  simps: tthm list};
+
+type parent_info =
+ {name: string,
+  fields: (string * typ) list,
+  simps: tthm list};
+
+
+(* theory data *)
+
+val recordsK = "HOL/records";
+exception Records of record_info Symtab.table;
+
+fun print_records thy = Display.print_data thy recordsK;
+
+local
+  val empty = Records Symtab.empty;
+
+  fun prep_ext (x as Records _) = x;
+
+  fun merge (Records tab1, Records tab2) =
+    Records (Symtab.merge (K true) (tab1, tab2));
+
+  fun print sg (Records tab) =
+    let
+      val prt_typ = Sign.pretty_typ sg;
+      val ext_const = Sign.cond_extern sg Sign.constK;
+
+      fun pretty_parent None = []
+        | pretty_parent (Some (Ts, name)) =
+            [Pretty.block [prt_typ (Type (name, Ts)), Pretty.str " +"]];
+
+      fun pretty_field (c, T) = Pretty.block
+        [Pretty.str (ext_const c), Pretty.str " ::", Pretty.brk 1, Pretty.quote (prt_typ T)];
+
+      fun pretty_record (name, {args, parent, fields, simps = _}) = Pretty.block (Pretty.fbreaks
+        (Pretty.block [prt_typ (Type (name, map TFree args)), Pretty.str " = "] ::
+          pretty_parent parent @ map pretty_field fields));
+    in
+      seq (Pretty.writeln o pretty_record) (Symtab.dest tab)
+    end;
+in
+  val record_thy_data = (recordsK, (empty, prep_ext, merge, print));
+end;
+
+
+(* get and put records *)
+
+fun get_records thy =
+  (case Theory.get_data thy recordsK of
+    Records tab => tab
+  | _ => type_error recordsK);
+
+fun get_record thy name = Symtab.lookup (get_records thy, name);
+
+
+fun put_records tab thy =
+  Theory.put_data (recordsK, Records tab) thy;
+
+fun put_new_record name info thy =
+  thy |> put_records
+    (Symtab.update_new ((name, info), get_records thy)
+      handle Symtab.DUP _ => error ("Duplicate definition of record " ^ quote name));
+
+
+(* parent records *)
+
+fun inst_record thy (types, name) =
+  let
+    val sign = Theory.sign_of thy;
+    fun err msg = error (msg ^ " parent record " ^ quote name);
+
+    val {args, parent, fields, simps} =
+      (case get_record thy name of Some info => info | None => err "Unknown");
+
+    fun bad_inst ((x, S), T) =
+      if Sign.of_sort sign (T, S) then None else Some x
+    val bads = mapfilter bad_inst (args ~~ types);
+
+    val inst = map fst args ~~ types;
+    val subst = Term.map_type_tfree (fn (x, _) => the (assoc (inst, x)));
+  in
+    if length types <> length args then
+      err "Bad number of arguments for"
+    else if not (null bads) then
+      err ("Ill-sorted instantiation of " ^ commas bads ^ " in")
+    else (apsome (apfst (map subst)) parent, map (apsnd subst) fields, simps)
+  end;
+
+fun add_parents thy (None, parents) = parents
+  | add_parents thy (Some (types, name), parents) =
+      let val (pparent, pfields, psimps) = inst_record thy (types, name)
+      in add_parents thy (pparent, {name = name, fields = pfields, simps = psimps} :: parents) end;
+
+
+
+(** record theorems **)
+
+(* proof by simplification *)
+
+fun prove_simp thy opt_ss simps =
+  let val ss = if_none opt_ss HOL_basic_ss addsimps simps in
+    fn goal => Goals.prove_goalw_cterm [] (Thm.cterm_of (sign_of thy) goal)
+      (K [ALLGOALS (Simplifier.simp_tac ss)])
+  end;
+
+
+
+(** internal theory extender **)
+
+(*do the actual record definition, assuming that all arguments are
+  well-formed*)
+
+fun record_definition (args, bname) parent (parents: parent_info list) bfields thy =
+  let
+    val sign = Theory.sign_of thy;
+    val full = Sign.full_name_path sign bname;
+
+
+    (* input *)
+
+    val alphas = map fst args;
+    val name = Sign.full_name sign bname;		(* FIXME !? *)
+    val parent_fields = flat (map #fields parents);
+    val fields = map (apfst full) bfields;
+
+    val all_fields = parent_fields @ fields;
+    val all_types = map snd all_fields;
+
+
+    (* term / type components *)
+
+    val zeta = variant alphas "'z";
+    val moreT = TFree (zeta, moreS);
+
+    val xs = variantlist (map fst bfields, []);
+    val vars = map2 Free (xs, map snd fields);
+    val more = Free (variant xs moreN, moreT);
+
+    val rec_schemeT = mk_recordT (all_fields, moreT);
+    val recT = mk_recordT (all_fields, HOLogic.unitT);
+
+    (* FIXME tune *)
+    val make_schemeT = all_types ---> moreT --> rec_schemeT;
+    val make_scheme = Const (full make_schemeN, make_schemeT);
+    val makeT = all_types ---> recT;
+    val make = Const (full makeN, makeT);
+
+    val parent_more = funpow (length parent_fields) mk_snd;
+
+
+    (* prepare type definitions *)
+
+    (*field types*)
+    fun mk_fieldT_spec ((c, T), a) =
+      (suffix field_typeN c, [a, zeta],
+        HOLogic.mk_prodT (TFree (a, HOLogic.termS), moreT), Syntax.NoSyn);
+    val fieldT_specs = map2 mk_fieldT_spec (bfields, alphas);
+
+    (*record types*)
+    val recordT_specs =
+      [(suffix schemeN bname, alphas @ [zeta], rec_schemeT, Syntax.NoSyn),
+        (bname, alphas, recT, Syntax.NoSyn)];
+
+
+    (* prepare declarations *)
+
+    val field_decls = map (mk_fieldC moreT) fields;
+    val dest_decls = map (mk_fstC moreT) fields @ map (mk_sndC moreT) fields;
+    val sel_decls = map (mk_selC rec_schemeT) fields;
+    val update_decls = map (mk_updateC rec_schemeT) fields;
+    val make_decls = [(make_schemeN, make_schemeT), (makeN, makeT)];
+
+
+    (* prepare definitions *)
+
+    (*field constructors*)
+    fun mk_field_spec ((c, _), v) =
+      Logic.mk_defpair (mk_field ((c, v), more), HOLogic.mk_prod (v, more));
+    val field_specs = map2 mk_field_spec (fields, vars);
+
+    (*field destructors*)
+    fun mk_dest_spec dest dest' (c, T) =
+      let
+        val p = Free ("p",  mk_fieldT ((c, T), moreT));
+        val p' = Free ("p",  HOLogic.mk_prodT (T, moreT));  (*Note: field types are abbreviations*)
+      in Logic.mk_defpair (dest p, dest' p') end;
+    val dest_specs =
+      map (mk_dest_spec mk_fst HOLogic.mk_fst) fields @
+      map (mk_dest_spec mk_snd HOLogic.mk_snd) fields;
+
+    (*field selectors*)		(* FIXME tune *)
+    fun mk_sel_specs _ [] specs = rev specs
+      | mk_sel_specs prfx ((c, T) :: fs) specs =
+          let
+            val prfx' = prfx @ [(c, T)];
+            val r = Free ("r", mk_recordT (prfx' @ fs, moreT));
+            val spec = Logic.mk_defpair (mk_sel c r, mk_fst (funpow (length prfx) mk_snd r));
+          in mk_sel_specs prfx' fs (spec :: specs) end;
+    val sel_specs = mk_sel_specs parent_fields fields [];
+
+    (*updates*)
+    val update_specs = [];	(* FIXME *)
+
+    (*makes*)
+    val make_specs =
+      map Logic.mk_defpair
+        [(list_comb (make_scheme, vars) $ more, mk_record (map fst fields ~~ vars, more)),
+          (list_comb (make, vars), mk_record (map fst fields ~~ vars, HOLogic.unit))];
+
+
+    (* 1st stage: defs_thy *)
+
+    val defs_thy =
+      thy
+      |> Theory.add_path bname
+      |> Theory.add_tyabbrs_i (fieldT_specs @ recordT_specs)
+      |> (Theory.add_consts_i o map (Syntax.no_syn o apfst Sign.base_name))
+        (field_decls @ dest_decls @ sel_decls @ update_decls @ make_decls)
+      |> (PureThy.add_defs_i o map Attribute.none)
+        (field_specs @ dest_specs @ sel_specs @ update_specs @ make_specs);
+
+    local fun get_defs specs = map (PureThy.get_tthm defs_thy o fst) specs in
+      val make_defs = get_defs make_specs;
+      val field_defs = get_defs field_specs;
+      val sel_defs = get_defs sel_specs;
+      val update_defs = get_defs update_specs;
+    end;
+
+
+    (* 2nd stage: thms_thy *)
+
+    val thms_thy =
+      defs_thy
+      |> (PureThy.add_tthmss o map Attribute.none)
+        [("make_defs", make_defs),
+          ("field_defs", field_defs),
+          ("sel_defs", sel_defs),
+          ("update_defs", update_defs)]
+(*    |> record_theorems FIXME *)
+
+
+    (* 3rd stage: final_thy *)
+
+    val final_thy =
+      thms_thy
+      |> put_new_record name
+        {args = args, parent = parent, fields = fields, simps = [] (* FIXME *)}
+      |> Theory.parent_path;
+
+  in final_thy end;
+
+
+
+(** theory extender interface **)
+
+(*do all preparations and error checks here, deferring the real work
+  to record_definition above*)
+
+
+(* prepare arguments *)
+
+(*Note: read_raw_typ avoids expanding type abbreviations*)
+fun read_raw_parent sign s =
+  (case Sign.read_raw_typ (sign, K None) s handle TYPE (msg, _, _) => error msg of
+    Type (name, Ts) => (Ts, name)
+  | _ => error ("Bad parent record specification: " ^ quote s));
+
+fun read_typ sign (env, s) =
+  let
+    fun def_type (x, ~1) = assoc (env, x)
+      | def_type _ = None;
+    val T = Type.no_tvars (Sign.read_typ (sign, def_type) s) handle TYPE (msg, _, _) => error msg;
+  in (Term.add_typ_tfrees (T, env), T) end;
+
+fun cert_typ sign (env, raw_T) =
+  let val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle TYPE (msg, _, _) => error msg
+  in (Term.add_typ_tfrees (T, env), T) end;
+
+
+(* add_record *)
+
+fun gen_add_record prep_typ prep_raw_parent (params, bname) raw_parent raw_fields thy =
+  let
+    val _ = Theory.require thy "Record" "record definitions";
+    val sign = Theory.sign_of thy;
+
+
+    (* parents *)
+
+    fun prep_inst T = snd (cert_typ sign ([], T));
+
+    val parent = apsome (apfst (map prep_inst) o prep_raw_parent sign) raw_parent
+      handle ERROR => error ("The error(s) above in parent record specification");
+    val parents = add_parents thy (parent, []);
+
+    val init_env =
+      (case parent of
+        None => []
+      | Some (types, _) => foldr Term.add_typ_tfrees (types, []));
+
+
+    (* fields *)
+
+    fun prep_fields (env, []) = (env, [])
+      | prep_fields (env, (c, raw_T) :: fs) =
+          let
+            val (env', T) = prep_typ sign (env, raw_T) handle ERROR =>
+              error ("The error(s) above occured in field " ^ quote c);
+            val (env'', fs') = prep_fields (env', fs);
+      in (env'', (c, T) :: fs') end;
+
+    val (envir, bfields) = prep_fields (init_env, raw_fields);
+    val envir_names = map fst envir;
+
+
+    (* args *)
+
+    val defaultS = Sign.defaultS sign;
+    val args = map (fn x => (x, if_none (assoc (envir, x)) defaultS)) params;
+
+
+    (* errors *)
+
+    val err_dup_parms =
+      (case duplicates params of
+        [] => []
+      | dups => ["Duplicate parameters " ^ commas params]);
+
+    val err_extra_frees =
+      (case gen_rems (op =) (envir_names, params) of
+        [] => []
+      | extras => ["Extraneous free type variables " ^ commas extras]);
+
+    val err_no_fields = if null bfields then ["No fields"] else [];
+
+    val err_dup_fields =
+      (case duplicates (map fst bfields) of
+        [] => []
+      | dups => ["Duplicate fields " ^ commas_quote dups]);
+
+    val err_dup_sorts =
+      (case duplicates envir_names of
+        [] => []
+      | dups => ["Inconsistent sort constraints for " ^ commas dups]);
+
+    val errs =
+      err_dup_parms @ err_extra_frees @ err_no_fields @ err_dup_fields @ err_dup_sorts;
+  in
+    if null errs then ()
+    else error (cat_lines errs);
+
+    writeln ("Defining record " ^ quote bname ^ " ...");
+    thy |> record_definition (args, bname) parent parents bfields
+  end
+  handle ERROR => error ("Failed to define record " ^ quote bname);
+
+val add_record = gen_add_record read_typ read_raw_parent;
+val add_record_i = gen_add_record cert_typ (K I);
+
+
+
+(** setup theory **)
+
+val setup =
+ [Theory.init_data [record_thy_data],
+  Theory.add_trfuns
+    ([], [("_record", record_tr), ("_record_scheme", record_scheme_tr)], [], [])];
+
+
+end;