src/HOL/Tools/datatype_aux.ML
author berghofe
Fri Jul 24 12:50:06 1998 +0200 (1998-07-24)
changeset 5177 0d3a168e4d44
child 5661 6ecb6ea25f19
permissions -rw-r--r--
New datatype definition package
     1 (*  Title:      HOL/Tools/datatype_aux.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer
     4     Copyright   1998  TU Muenchen
     5 
     6 Auxiliary functions for defining datatypes
     7 *)
     8 
     9 signature DATATYPE_AUX =
    10 sig
    11   val foldl1 : ('a * 'a -> 'a) -> 'a list -> 'a
    12 
    13   val get_thy : string -> theory -> theory option
    14 
    15   val store_thmss : string -> string list -> thm list list -> theory -> theory
    16   val store_thms : string -> string list -> thm list -> theory -> theory
    17 
    18   val split_conj_thm : thm -> thm list
    19   val mk_conj : term list -> term
    20   val mk_disj : term list -> term
    21 
    22   val indtac : thm -> int -> tactic
    23   val exh_tac : (string -> thm) -> int -> tactic
    24 
    25   datatype dtyp =
    26       DtTFree of string
    27     | DtType of string * (dtyp list)
    28     | DtRec of int;
    29 
    30   type datatype_info
    31 
    32   val dtyp_of_typ : (string * string list) list -> typ -> dtyp
    33   val mk_Free : string -> typ -> int -> term
    34   val is_rec_type : dtyp -> bool
    35   val typ_of_dtyp : (int * (string * dtyp list *
    36     (string * dtyp list) list)) list -> (string * sort) list -> dtyp -> typ
    37   val dest_DtTFree : dtyp -> string
    38   val dest_DtRec : dtyp -> int
    39   val dest_TFree : typ -> string
    40   val dest_conj : term -> term list
    41   val get_nonrec_types : (int * (string * dtyp list *
    42     (string * dtyp list) list)) list -> (string * sort) list -> typ list
    43   val get_rec_types : (int * (string * dtyp list *
    44     (string * dtyp list) list)) list -> (string * sort) list -> typ list
    45   val check_nonempty : (int * (string * dtyp list *
    46     (string * dtyp list) list)) list list -> unit
    47   val unfold_datatypes : 
    48     datatype_info Symtab.table ->
    49       (int * (string * dtyp list *
    50         (string * dtyp list) list)) list -> int ->
    51           (int * (string * dtyp list *
    52             (string * dtyp list) list)) list list * int
    53 end;
    54 
    55 structure DatatypeAux : DATATYPE_AUX =
    56 struct
    57 
    58 (* FIXME: move to library ? *)
    59 fun foldl1 f (x::xs) = foldl f (x, xs);
    60 
    61 fun get_thy name thy = find_first
    62   (equal name o Sign.name_of o sign_of) (ancestors_of thy);
    63 
    64 (* store theorems in theory *)
    65 
    66 fun store_thmss label tnames thmss thy =
    67   foldr (fn ((tname, thms), thy') => thy' |>
    68     (if length tnames = 1 then I else Theory.add_path tname) |>
    69     PureThy.add_tthmss [((label, map Attribute.tthm_of thms), [])] |>
    70     (if length tnames = 1 then I else Theory.parent_path))
    71     (tnames ~~ thmss, thy);
    72 
    73 fun store_thms label tnames thms thy =
    74   foldr (fn ((tname, thm), thy') => thy' |>
    75     (if length tnames = 1 then I else Theory.add_path tname) |>
    76     PureThy.add_tthms [((label, Attribute.tthm_of thm), [])] |>
    77     (if length tnames = 1 then I else Theory.parent_path))
    78     (tnames ~~ thms, thy);
    79 
    80 (* split theorem thm_1 & ... & thm_n into n theorems *)
    81 
    82 fun split_conj_thm th =
    83   ((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle _ => [th];
    84 
    85 val mk_conj = foldr1 (HOLogic.mk_binop "op &");
    86 val mk_disj = foldr1 (HOLogic.mk_binop "op |");
    87 
    88 fun dest_conj (Const ("op &", _) $ t $ t') = t::(dest_conj t')
    89   | dest_conj t = [t];
    90 
    91 (* instantiate induction rule *)
    92 
    93 fun indtac indrule i st =
    94   let
    95     val ts = dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
    96     val ts' = dest_conj (HOLogic.dest_Trueprop
    97       (Logic.strip_imp_concl (nth_elem (i - 1, prems_of st))));
    98     val getP = if can HOLogic.dest_imp (hd ts) then
    99       (apfst Some) o HOLogic.dest_imp else pair None;
   100     fun abstr (t1, t2) = (case t1 of
   101         None => let val [Free (s, T)] = add_term_frees (t2, [])
   102           in absfree (s, T, t2) end
   103       | Some (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
   104     val cert = cterm_of (sign_of_thm st);
   105     val Ps = map (cert o head_of o snd o getP) ts;
   106     val indrule' = cterm_instantiate (Ps ~~
   107       (map (cert o abstr o getP) ts')) indrule
   108   in
   109     rtac indrule' i st
   110   end;
   111 
   112 (* perform exhaustive case analysis on last parameter of subgoal i *)
   113 
   114 fun exh_tac exh_thm_of i state =
   115   let
   116     val sg = sign_of_thm state;
   117     val prem = nth_elem (i - 1, prems_of state);
   118     val params = Logic.strip_params prem;
   119     val (_, Type (tname, _)) = hd (rev params);
   120     val exhaustion = lift_rule (state, i) (exh_thm_of tname);
   121     val prem' = hd (prems_of exhaustion);
   122     val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem'));
   123     val exhaustion' = cterm_instantiate [(cterm_of sg (head_of lhs),
   124       cterm_of sg (foldr (fn ((_, T), t) => Abs ("z", T, t))
   125         (params, Bound 0)))] exhaustion
   126   in compose_tac (false, exhaustion', nprems_of exhaustion) i state
   127   end;
   128 
   129 (********************** Internal description of datatypes *********************)
   130 
   131 datatype dtyp =
   132     DtTFree of string
   133   | DtType of string * (dtyp list)
   134   | DtRec of int;
   135 
   136 (* information about datatypes *)
   137 
   138 type datatype_info =
   139   {index : int,
   140    descr : (int * (string * dtyp list *
   141      (string * dtyp list) list)) list,
   142    rec_names : string list,
   143    rec_rewrites : thm list,
   144    case_name : string,
   145    case_rewrites : thm list,
   146    induction : thm,
   147    exhaustion : thm,
   148    distinct : thm list,
   149    inject : thm list,
   150    nchotomy : thm,
   151    case_cong : thm};
   152 
   153 fun mk_Free s T i = Free (s ^ (string_of_int i), T);
   154 
   155 fun subst_DtTFree _ substs (T as (DtTFree name)) =
   156       (case assoc (substs, name) of
   157          None => T
   158        | Some U => U)
   159   | subst_DtTFree i substs (DtType (name, ts)) =
   160       DtType (name, map (subst_DtTFree i substs) ts)
   161   | subst_DtTFree i _ (DtRec j) = DtRec (i + j);
   162 
   163 fun dest_DtTFree (DtTFree a) = a;
   164 fun dest_DtRec (DtRec i) = i;
   165 
   166 fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts
   167   | is_rec_type (DtRec _) = true
   168   | is_rec_type _ = false;
   169 
   170 fun dest_TFree (TFree (n, _)) = n;
   171 
   172 fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n
   173   | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)"
   174   | dtyp_of_typ new_dts (Type (tname, Ts)) =
   175       (case assoc (new_dts, tname) of
   176          None => DtType (tname, map (dtyp_of_typ new_dts) Ts)
   177        | Some vs => if map (try dest_TFree) Ts = map Some vs then
   178              DtRec (find_index (curry op = tname o fst) new_dts)
   179            else error ("Illegal occurence of recursive type " ^ tname));
   180 
   181 fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, the (assoc (sorts, a)))
   182   | typ_of_dtyp descr sorts (DtRec i) =
   183       let val (s, ds, _) = the (assoc (descr, i))
   184       in Type (s, map (typ_of_dtyp descr sorts) ds) end
   185   | typ_of_dtyp descr sorts (DtType (s, ds)) =
   186       Type (s, map (typ_of_dtyp descr sorts) ds);
   187 
   188 (* find all non-recursive types in datatype description *)
   189 
   190 fun get_nonrec_types descr sorts =
   191   let fun add (Ts, T as DtTFree _) = T ins Ts
   192         | add (Ts, T as DtType _) = T ins Ts
   193         | add (Ts, _) = Ts
   194   in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) =>
   195     foldl (fn (Ts', (_, cargs)) =>
   196       foldl add (Ts', cargs)) (Ts, constrs)) ([], descr))
   197   end;
   198 
   199 (* get all recursive types in datatype description *)
   200 
   201 fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) =>
   202   Type (s, map (typ_of_dtyp descr sorts) ds)) descr;
   203 
   204 (* nonemptiness check for datatypes *)
   205 
   206 fun check_nonempty descr =
   207   let
   208     val descr' = flat descr;
   209     fun is_nonempty_dt is i =
   210       let
   211         val (_, _, constrs) = the (assoc (descr', i));
   212         fun arg_nonempty (DtRec i) = if i mem is then false
   213               else is_nonempty_dt (i::is) i
   214           | arg_nonempty _ = true;
   215       in exists ((forall arg_nonempty) o snd) constrs
   216       end
   217   in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr)
   218     (fn (_, (s, _, _)) => "Nonemptiness check failed for datatype " ^ s)
   219   end;
   220 
   221 (* unfold a list of mutually recursive datatype specifications *)
   222 (* all types of the form DtType (dt_name, [..., DtRec _, ...]) *)
   223 (* need to be unfolded                                         *)
   224 
   225 fun unfold_datatypes (dt_info : datatype_info Symtab.table) descr i =
   226   let
   227     fun get_dt_descr i tname dts =
   228       (case Symtab.lookup (dt_info, tname) of
   229          None => error (tname ^ " is not a datatype - can't use it in\
   230            \ indirect recursion")
   231        | (Some {index, descr, ...}) =>
   232            let val (_, vars, _) = the (assoc (descr, index));
   233                val subst = ((map dest_DtTFree vars) ~~ dts) handle _ =>
   234                  error ("Type constructor " ^ tname ^ " used with wrong\
   235                   \ number of arguments")
   236            in (i + index, map (fn (j, (tn, args, cs)) => (i + j,
   237              (tn, map (subst_DtTFree i subst) args,
   238               map (apsnd (map (subst_DtTFree i subst))) cs))) descr)
   239            end);
   240 
   241     (* unfold a single constructor argument *)
   242 
   243     fun unfold_arg ((i, Ts, descrs), T as (DtType (tname, dts))) =
   244           if is_rec_type T then
   245             let val (index, descr) = get_dt_descr i tname dts;
   246                 val (descr', i') = unfold_datatypes dt_info descr (i + length descr)
   247             in (i', Ts @ [DtRec index], descrs @ descr') end
   248           else (i, Ts @ [T], descrs)
   249       | unfold_arg ((i, Ts, descrs), T) = (i, Ts @ [T], descrs);
   250 
   251     (* unfold a constructor *)
   252 
   253     fun unfold_constr ((i, constrs, descrs), (cname, cargs)) =
   254       let val (i', cargs', descrs') = foldl unfold_arg ((i, [], descrs), cargs)
   255       in (i', constrs @ [(cname, cargs')], descrs') end;
   256 
   257     (* unfold a single datatype *)
   258 
   259     fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) =
   260       let val (i', constrs', descrs') =
   261         foldl unfold_constr ((i, [], descrs), constrs)
   262       in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs')
   263       end;
   264 
   265     val (i', descr', descrs) = foldl unfold_datatype ((i, [],[]), descr);
   266 
   267   in (descr' :: descrs, i') end;
   268 
   269 end;