src/HOL/Tools/datatype_aux.ML
author wenzelm
Mon Sep 05 17:38:18 2005 +0200 (2005-09-05)
changeset 17261 193b84a70ca4
parent 16901 d649ff14096a
child 17412 e26cb20ef0cc
permissions -rw-r--r--
curried_lookup/update;
     1 (*  Title:      HOL/Tools/datatype_aux.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Auxiliary functions for defining datatypes.
     6 *)
     7 
     8 signature DATATYPE_AUX =
     9 sig
    10   val quiet_mode : bool ref
    11   val message : string -> unit
    12   
    13   val foldl1 : ('a * 'a -> 'a) -> 'a list -> 'a
    14 
    15   val add_path : bool -> string -> theory -> theory
    16   val parent_path : bool -> theory -> theory
    17 
    18   val store_thmss : string -> string list -> thm list list -> theory -> theory * thm list list
    19   val store_thms_atts : string -> string list -> theory attribute list list -> thm list
    20     -> theory -> theory * thm list
    21   val store_thms : string -> string list -> thm list -> theory -> theory * thm list
    22 
    23   val split_conj_thm : thm -> thm list
    24   val mk_conj : term list -> term
    25   val mk_disj : term list -> term
    26 
    27   val app_bnds : term -> int -> term
    28 
    29   val cong_tac : int -> tactic
    30   val indtac : thm -> int -> tactic
    31   val exh_tac : (string -> thm) -> int -> tactic
    32 
    33   datatype simproc_dist = QuickAndDirty
    34                         | FewConstrs of thm list
    35                         | ManyConstrs of thm * simpset;
    36 
    37   datatype dtyp =
    38       DtTFree of string
    39     | DtType of string * (dtyp list)
    40     | DtRec of int;
    41   type descr
    42   type datatype_info
    43 
    44   exception Datatype
    45   exception Datatype_Empty of string
    46   val name_of_typ : typ -> string
    47   val dtyp_of_typ : (string * string list) list -> typ -> dtyp
    48   val mk_Free : string -> typ -> int -> term
    49   val is_rec_type : dtyp -> bool
    50   val typ_of_dtyp : descr -> (string * sort) list -> dtyp -> typ
    51   val dest_DtTFree : dtyp -> string
    52   val dest_DtRec : dtyp -> int
    53   val strip_dtyp : dtyp -> dtyp list * dtyp
    54   val body_index : dtyp -> int
    55   val mk_fun_dtyp : dtyp list -> dtyp -> dtyp
    56   val dest_TFree : typ -> string
    57   val get_nonrec_types : descr -> (string * sort) list -> typ list
    58   val get_branching_types : descr -> (string * sort) list -> typ list
    59   val get_arities : descr -> int list
    60   val get_rec_types : descr -> (string * sort) list -> typ list
    61   val check_nonempty : descr list -> unit
    62   val unfold_datatypes : 
    63     Sign.sg -> descr -> (string * sort) list -> datatype_info Symtab.table ->
    64       descr -> int -> descr list * int
    65 end;
    66 
    67 structure DatatypeAux : DATATYPE_AUX =
    68 struct
    69 
    70 val quiet_mode = ref false;
    71 fun message s = if !quiet_mode then () else writeln s;
    72 
    73 (* FIXME: move to library ? *)
    74 fun foldl1 f (x::xs) = Library.foldl f (x, xs);
    75 
    76 fun add_path flat_names s = if flat_names then I else Theory.add_path s;
    77 fun parent_path flat_names = if flat_names then I else Theory.parent_path;
    78 
    79 
    80 (* store theorems in theory *)
    81 
    82 fun store_thmss label tnames thmss thy =
    83   (thy, tnames ~~ thmss) |>
    84   foldl_map (fn (thy', (tname, thms)) => thy' |>
    85     Theory.add_path tname |>
    86     (apsnd hd o PureThy.add_thmss [((label, thms), [])]) |>>
    87     Theory.parent_path);
    88 
    89 fun store_thms_atts label tnames attss thms thy =
    90   (thy, tnames ~~ attss ~~ thms) |>
    91   foldl_map (fn (thy', ((tname, atts), thm)) => thy' |>
    92     Theory.add_path tname |>
    93     (apsnd hd o PureThy.add_thms [((label, thm), atts)]) |>>
    94     Theory.parent_path);
    95 
    96 fun store_thms label tnames = store_thms_atts label tnames (replicate (length tnames) []);
    97 
    98 
    99 (* split theorem thm_1 & ... & thm_n into n theorems *)
   100 
   101 fun split_conj_thm th =
   102   ((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th];
   103 
   104 val mk_conj = foldr1 (HOLogic.mk_binop "op &");
   105 val mk_disj = foldr1 (HOLogic.mk_binop "op |");
   106 
   107 fun app_bnds t i = list_comb (t, map Bound (i - 1 downto 0));
   108 
   109 
   110 fun cong_tac i st = (case Logic.strip_assums_concl
   111   (List.nth (prems_of st, i - 1)) of
   112     _ $ (_ $ (f $ x) $ (g $ y)) =>
   113       let
   114         val cong' = lift_rule (st, i) cong;
   115         val _ $ (_ $ (f' $ x') $ (g' $ y')) =
   116           Logic.strip_assums_concl (prop_of cong');
   117         val insts = map (pairself (cterm_of (#sign (rep_thm st))) o
   118           apsnd (curry list_abs (Logic.strip_params (concl_of cong'))) o
   119             apfst head_of) [(f', f), (g', g), (x', x), (y', y)]
   120       in compose_tac (false, cterm_instantiate insts cong', 2) i st
   121         handle THM _ => no_tac st
   122       end
   123   | _ => no_tac st);
   124 
   125 (* instantiate induction rule *)
   126 
   127 fun indtac indrule i st =
   128   let
   129     val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
   130     val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
   131       (Logic.strip_imp_concl (List.nth (prems_of st, i - 1))));
   132     val getP = if can HOLogic.dest_imp (hd ts) then
   133       (apfst SOME) o HOLogic.dest_imp else pair NONE;
   134     fun abstr (t1, t2) = (case t1 of
   135         NONE => let val [Free (s, T)] = add_term_frees (t2, [])
   136           in absfree (s, T, t2) end
   137       | SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
   138     val cert = cterm_of (Thm.sign_of_thm st);
   139     val Ps = map (cert o head_of o snd o getP) ts;
   140     val indrule' = cterm_instantiate (Ps ~~
   141       (map (cert o abstr o getP) ts')) indrule
   142   in
   143     rtac indrule' i st
   144   end;
   145 
   146 (* perform exhaustive case analysis on last parameter of subgoal i *)
   147 
   148 fun exh_tac exh_thm_of i state =
   149   let
   150     val sg = Thm.sign_of_thm state;
   151     val prem = List.nth (prems_of state, i - 1);
   152     val params = Logic.strip_params prem;
   153     val (_, Type (tname, _)) = hd (rev params);
   154     val exhaustion = lift_rule (state, i) (exh_thm_of tname);
   155     val prem' = hd (prems_of exhaustion);
   156     val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem'));
   157     val exhaustion' = cterm_instantiate [(cterm_of sg (head_of lhs),
   158       cterm_of sg (foldr (fn ((_, T), t) => Abs ("z", T, t))
   159         (Bound 0) params))] exhaustion
   160   in compose_tac (false, exhaustion', nprems_of exhaustion) i state
   161   end;
   162 
   163 (* handling of distinctness theorems *)
   164 
   165 datatype simproc_dist = QuickAndDirty
   166                       | FewConstrs of thm list
   167                       | ManyConstrs of thm * simpset;
   168 
   169 (********************** Internal description of datatypes *********************)
   170 
   171 datatype dtyp =
   172     DtTFree of string
   173   | DtType of string * (dtyp list)
   174   | DtRec of int;
   175 
   176 (* information about datatypes *)
   177 
   178 (* index, datatype name, type arguments, constructor name, types of constructor's arguments *)
   179 type descr = (int * (string * dtyp list * (string * dtyp list) list)) list;
   180 
   181 type datatype_info =
   182   {index : int,
   183    descr : descr,
   184    rec_names : string list,
   185    rec_rewrites : thm list,
   186    case_name : string,
   187    case_rewrites : thm list,
   188    induction : thm,
   189    exhaustion : thm,
   190    distinct : simproc_dist,
   191    inject : thm list,
   192    nchotomy : thm,
   193    case_cong : thm,
   194    weak_case_cong : thm};
   195 
   196 fun mk_Free s T i = Free (s ^ (string_of_int i), T);
   197 
   198 fun subst_DtTFree _ substs (T as (DtTFree name)) =
   199       (case assoc (substs, name) of
   200          NONE => T
   201        | SOME U => U)
   202   | subst_DtTFree i substs (DtType (name, ts)) =
   203       DtType (name, map (subst_DtTFree i substs) ts)
   204   | subst_DtTFree i _ (DtRec j) = DtRec (i + j);
   205 
   206 exception Datatype;
   207 exception Datatype_Empty of string;
   208 
   209 fun dest_DtTFree (DtTFree a) = a
   210   | dest_DtTFree _ = raise Datatype;
   211 
   212 fun dest_DtRec (DtRec i) = i
   213   | dest_DtRec _ = raise Datatype;
   214 
   215 fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts
   216   | is_rec_type (DtRec _) = true
   217   | is_rec_type _ = false;
   218 
   219 fun strip_dtyp (DtType ("fun", [T, U])) = apfst (cons T) (strip_dtyp U)
   220   | strip_dtyp T = ([], T);
   221 
   222 val body_index = dest_DtRec o snd o strip_dtyp;
   223 
   224 fun mk_fun_dtyp [] U = U
   225   | mk_fun_dtyp (T :: Ts) U = DtType ("fun", [T, mk_fun_dtyp Ts U]);
   226 
   227 fun dest_TFree (TFree (n, _)) = n;
   228 
   229 fun name_of_typ (Type (s, Ts)) =
   230       let val s' = Sign.base_name s
   231       in space_implode "_" (List.filter (not o equal "") (map name_of_typ Ts) @
   232         [if Syntax.is_identifier s' then s' else "x"])
   233       end
   234   | name_of_typ _ = "";
   235 
   236 fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n
   237   | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)"
   238   | dtyp_of_typ new_dts (Type (tname, Ts)) =
   239       (case assoc (new_dts, tname) of
   240          NONE => DtType (tname, map (dtyp_of_typ new_dts) Ts)
   241        | SOME vs => if map (try dest_TFree) Ts = map SOME vs then
   242              DtRec (find_index (curry op = tname o fst) new_dts)
   243            else error ("Illegal occurence of recursive type " ^ tname));
   244 
   245 fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, valOf (assoc (sorts, a)))
   246   | typ_of_dtyp descr sorts (DtRec i) =
   247       let val (s, ds, _) = valOf (assoc (descr, i))
   248       in Type (s, map (typ_of_dtyp descr sorts) ds) end
   249   | typ_of_dtyp descr sorts (DtType (s, ds)) =
   250       Type (s, map (typ_of_dtyp descr sorts) ds);
   251 
   252 (* find all non-recursive types in datatype description *)
   253 
   254 fun get_nonrec_types descr sorts =
   255   map (typ_of_dtyp descr sorts) (Library.foldl (fn (Ts, (_, (_, _, constrs))) =>
   256     Library.foldl (fn (Ts', (_, cargs)) =>
   257       filter_out is_rec_type cargs union Ts') (Ts, constrs)) ([], descr));
   258 
   259 (* get all recursive types in datatype description *)
   260 
   261 fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) =>
   262   Type (s, map (typ_of_dtyp descr sorts) ds)) descr;
   263 
   264 (* get all branching types *)
   265 
   266 fun get_branching_types descr sorts =
   267   map (typ_of_dtyp descr sorts) (Library.foldl (fn (Ts, (_, (_, _, constrs))) =>
   268     Library.foldl (fn (Ts', (_, cargs)) => foldr op union Ts' (map (fst o strip_dtyp)
   269       cargs)) (Ts, constrs)) ([], descr));
   270 
   271 fun get_arities descr = Library.foldl (fn (is, (_, (_, _, constrs))) =>
   272   Library.foldl (fn (is', (_, cargs)) => map (length o fst o strip_dtyp)
   273     (List.filter is_rec_type cargs) union is') (is, constrs)) ([], descr);
   274 
   275 (* nonemptiness check for datatypes *)
   276 
   277 fun check_nonempty descr =
   278   let
   279     val descr' = List.concat descr;
   280     fun is_nonempty_dt is i =
   281       let
   282         val (_, _, constrs) = valOf (assoc (descr', i));
   283         fun arg_nonempty (_, DtRec i) = if i mem is then false
   284               else is_nonempty_dt (i::is) i
   285           | arg_nonempty _ = true;
   286       in exists ((forall (arg_nonempty o strip_dtyp)) o snd) constrs
   287       end
   288   in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr)
   289     (fn (_, (s, _, _)) => raise Datatype_Empty s)
   290   end;
   291 
   292 (* unfold a list of mutually recursive datatype specifications *)
   293 (* all types of the form DtType (dt_name, [..., DtRec _, ...]) *)
   294 (* need to be unfolded                                         *)
   295 
   296 fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i =
   297   let
   298     fun typ_error T msg = error ("Non-admissible type expression\n" ^
   299       Sign.string_of_typ sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg);
   300 
   301     fun get_dt_descr T i tname dts =
   302       (case Symtab.curried_lookup dt_info tname of
   303          NONE => typ_error T (tname ^ " is not a datatype - can't use it in\
   304            \ nested recursion")
   305        | (SOME {index, descr, ...}) =>
   306            let val (_, vars, _) = valOf (assoc (descr, index));
   307                val subst = ((map dest_DtTFree vars) ~~ dts) handle UnequalLengths =>
   308                  typ_error T ("Type constructor " ^ tname ^ " used with wrong\
   309                   \ number of arguments")
   310            in (i + index, map (fn (j, (tn, args, cs)) => (i + j,
   311              (tn, map (subst_DtTFree i subst) args,
   312               map (apsnd (map (subst_DtTFree i subst))) cs))) descr)
   313            end);
   314 
   315     (* unfold a single constructor argument *)
   316 
   317     fun unfold_arg ((i, Ts, descrs), T) =
   318       if is_rec_type T then
   319         let val (Us, U) = strip_dtyp T
   320         in if exists is_rec_type Us then
   321             typ_error T "Non-strictly positive recursive occurrence of type"
   322           else (case U of
   323               DtType (tname, dts) =>  
   324                 let
   325                   val (index, descr) = get_dt_descr T i tname dts;
   326                   val (descr', i') = unfold_datatypes sign orig_descr sorts
   327                     dt_info descr (i + length descr)
   328                 in (i', Ts @ [mk_fun_dtyp Us (DtRec index)], descrs @ descr') end
   329             | _ => (i, Ts @ [T], descrs))
   330         end
   331       else (i, Ts @ [T], descrs);
   332 
   333     (* unfold a constructor *)
   334 
   335     fun unfold_constr ((i, constrs, descrs), (cname, cargs)) =
   336       let val (i', cargs', descrs') = Library.foldl unfold_arg ((i, [], descrs), cargs)
   337       in (i', constrs @ [(cname, cargs')], descrs') end;
   338 
   339     (* unfold a single datatype *)
   340 
   341     fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) =
   342       let val (i', constrs', descrs') =
   343         Library.foldl unfold_constr ((i, [], descrs), constrs)
   344       in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs')
   345       end;
   346 
   347     val (i', descr', descrs) = Library.foldl unfold_datatype ((i, [],[]), descr);
   348 
   349   in (descr' :: descrs, i') end;
   350 
   351 end;