src/HOL/Tools/datatype_realizer.ML
 author berghofe Mon Oct 21 16:57:39 2002 +0200 (2002-10-21) changeset 13656 58bb243dbafb parent 13641 63d1790a43ed child 13708 a3a410782c95 permissions -rw-r--r--
Changed type of Logic.strip_horn.
```     1 (*  Title:      HOL/Tools/datatype_realizer.ML
```
```     2     ID:         \$Id\$
```
```     3     Author:     Stefan Berghofer, TU Muenchen
```
```     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
```
```     5
```
```     6 Porgram extraction from proofs involving datatypes:
```
```     7 Realizers for induction and case analysis
```
```     8 *)
```
```     9
```
```    10 signature DATATYPE_REALIZER =
```
```    11 sig
```
```    12   val add_dt_realizers: (string * sort) list ->
```
```    13     DatatypeAux.datatype_info list -> theory -> theory
```
```    14 end;
```
```    15
```
```    16 structure DatatypeRealizer : DATATYPE_REALIZER =
```
```    17 struct
```
```    18
```
```    19 open DatatypeAux;
```
```    20
```
```    21 fun subsets i j = if i <= j then
```
```    22        let val is = subsets (i+1) j
```
```    23        in map (fn ks => i::ks) is @ is end
```
```    24      else [[]];
```
```    25
```
```    26 fun forall_intr_prf (t, prf) =
```
```    27   let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
```
```    28   in Abst (a, Some T, Proofterm.prf_abstract_over t prf) end;
```
```    29
```
```    30 fun prove_goal' sg p f =
```
```    31   let
```
```    32     val (As, B) = Logic.strip_horn p;
```
```    33     val cAs = map (cterm_of sg) As;
```
```    34     val asms = map (norm_hhf_rule o assume) cAs;
```
```    35     fun check thm = if nprems_of thm > 0 then
```
```    36       error "prove_goal': unsolved goals" else thm
```
```    37   in
```
```    38     standard (implies_intr_list cAs
```
```    39       (check (Seq.hd (EVERY (f asms) (trivial (cterm_of sg B))))))
```
```    40   end;
```
```    41
```
```    42 fun prf_of thm =
```
```    43   let val {sign, prop, der = (_, prf), ...} = rep_thm thm
```
```    44   in Reconstruct.reconstruct_proof sign prop prf end;
```
```    45
```
```    46 fun prf_subst_vars inst =
```
```    47   Proofterm.map_proof_terms (subst_vars ([], inst)) I;
```
```    48
```
```    49 fun is_unit t = snd (strip_type (fastype_of t)) = HOLogic.unitT;
```
```    50
```
```    51 fun mk_realizes T = Const ("realizes", T --> HOLogic.boolT --> HOLogic.boolT);
```
```    52
```
```    53 fun make_ind sorts ({descr, rec_names, rec_rewrites, induction, ...} : datatype_info) (is, thy) =
```
```    54   let
```
```    55     val sg = sign_of thy;
```
```    56     val recTs = get_rec_types descr sorts;
```
```    57     val pnames = if length descr = 1 then ["P"]
```
```    58       else map (fn i => "P" ^ string_of_int i) (1 upto length descr);
```
```    59
```
```    60     val rec_result_Ts = map (fn ((i, _), P) =>
```
```    61       if i mem is then TFree ("'" ^ P, HOLogic.typeS) else HOLogic.unitT)
```
```    62         (descr ~~ pnames);
```
```    63
```
```    64     fun make_pred i T U r x =
```
```    65       if i mem is then
```
```    66         Free (nth_elem (i, pnames), T --> U --> HOLogic.boolT) \$ r \$ x
```
```    67       else Free (nth_elem (i, pnames), U --> HOLogic.boolT) \$ x;
```
```    68
```
```    69     fun mk_all i s T t =
```
```    70       if i mem is then list_all_free ([(s, T)], t) else t;
```
```    71
```
```    72     val (prems, rec_fns) = split_list (flat (snd (foldl_map
```
```    73       (fn (j, ((i, (_, _, constrs)), T)) => foldl_map (fn (j, (cname, cargs)) =>
```
```    74         let
```
```    75           val Ts = map (typ_of_dtyp descr sorts) cargs;
```
```    76           val tnames = variantlist (DatatypeProp.make_tnames Ts, pnames);
```
```    77           val recs = filter (is_rec_type o fst o fst) (cargs ~~ tnames ~~ Ts);
```
```    78           val frees = tnames ~~ Ts;
```
```    79
```
```    80           fun mk_prems vs [] =
```
```    81                 let
```
```    82                   val rT = nth_elem (i, rec_result_Ts);
```
```    83                   val vs' = filter_out is_unit vs;
```
```    84                   val f = mk_Free "f" (map fastype_of vs' ---> rT) j;
```
```    85                   val f' = Pattern.eta_contract (list_abs_free
```
```    86                     (map dest_Free vs, if i mem is then list_comb (f, vs')
```
```    87                       else HOLogic.unit));
```
```    88                 in (HOLogic.mk_Trueprop (make_pred i rT T (list_comb (f, vs'))
```
```    89                   (list_comb (Const (cname, Ts ---> T), map Free frees))), f')
```
```    90                 end
```
```    91             | mk_prems vs (((dt, s), T) :: ds) =
```
```    92                 let
```
```    93                   val k = body_index dt;
```
```    94                   val (Us, U) = strip_type T;
```
```    95                   val i = length Us;
```
```    96                   val rT = nth_elem (k, rec_result_Ts);
```
```    97                   val r = Free ("r" ^ s, Us ---> rT);
```
```    98                   val (p, f) = mk_prems (vs @ [r]) ds
```
```    99                 in (mk_all k ("r" ^ s) (Us ---> rT) (Logic.mk_implies
```
```   100                   (list_all (map (pair "x") Us, HOLogic.mk_Trueprop
```
```   101                     (make_pred k rT U (app_bnds r i)
```
```   102                       (app_bnds (Free (s, T)) i))), p)), f)
```
```   103                 end
```
```   104
```
```   105         in (j + 1,
```
```   106           apfst (curry list_all_free frees) (mk_prems (map Free frees) recs))
```
```   107         end) (j, constrs)) (1, descr ~~ recTs))));
```
```   108
```
```   109     fun mk_proj j [] t = t
```
```   110       | mk_proj j (i :: is) t = if null is then t else
```
```   111           if j = i then HOLogic.mk_fst t
```
```   112           else mk_proj j is (HOLogic.mk_snd t);
```
```   113
```
```   114     val tnames = DatatypeProp.make_tnames recTs;
```
```   115     val fTs = map fastype_of rec_fns;
```
```   116     val ps = map (fn ((((i, _), T), U), s) => Abs ("x", T, make_pred i U T
```
```   117       (list_comb (Const (s, fTs ---> T --> U), rec_fns) \$ Bound 0) (Bound 0)))
```
```   118         (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names);
```
```   119     val r = if null is then Extraction.nullt else
```
```   120       foldr1 HOLogic.mk_prod (mapfilter (fn (((((i, _), T), U), s), tname) =>
```
```   121         if i mem is then Some
```
```   122           (list_comb (Const (s, fTs ---> T --> U), rec_fns) \$ Free (tname, T))
```
```   123         else None) (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names ~~ tnames));
```
```   124     val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
```
```   125       (map (fn ((((i, _), T), U), tname) =>
```
```   126         make_pred i U T (mk_proj i is r) (Free (tname, T)))
```
```   127           (descr ~~ recTs ~~ rec_result_Ts ~~ tnames)));
```
```   128     val cert = cterm_of sg;
```
```   129     val inst = map (pairself cert) (map head_of (HOLogic.dest_conj
```
```   130       (HOLogic.dest_Trueprop (concl_of induction))) ~~ ps);
```
```   131
```
```   132     val thm = prove_goal' sg (Logic.list_implies (prems, concl))
```
```   133       (fn prems =>
```
```   134          [rewrite_goals_tac (map mk_meta_eq [fst_conv, snd_conv]),
```
```   135           rtac (cterm_instantiate inst induction) 1,
```
```   136           ALLGOALS ObjectLogic.atomize_tac,
```
```   137           rewrite_goals_tac (o_def :: map mk_meta_eq rec_rewrites),
```
```   138           REPEAT ((resolve_tac prems THEN_ALL_NEW (fn i =>
```
```   139             REPEAT (etac allE i) THEN atac i)) 1)]);
```
```   140
```
```   141     val {path, ...} = Sign.rep_sg sg;
```
```   142     val ind_name = Thm.name_of_thm induction;
```
```   143     val vs = map (fn i => nth_elem (i, pnames)) is;
```
```   144     val (thy', thm') = thy
```
```   145       |> Theory.absolute_path
```
```   146       |> PureThy.store_thm
```
```   147         ((space_implode "_" (ind_name :: vs @ ["correctness"]), thm), [])
```
```   148       |>> Theory.add_path (NameSpace.pack (if_none path []));
```
```   149
```
```   150     val inst = map (fn ((((i, _), s), T), U) => ((s, 0), if i mem is then
```
```   151         Abs ("r", U, Abs ("x", T, mk_realizes U \$ Bound 1 \$
```
```   152           (Var ((s, 0), T --> HOLogic.boolT) \$ Bound 0)))
```
```   153       else Abs ("x", T, mk_realizes Extraction.nullT \$ Extraction.nullt \$
```
```   154         (Var ((s, 0), T --> HOLogic.boolT) \$
```
```   155           Bound 0)))) (descr ~~ pnames ~~ map Type.varifyT recTs ~~
```
```   156             map Type.varifyT rec_result_Ts);
```
```   157
```
```   158     val ivs = map Var (Drule.vars_of_terms
```
```   159       [Logic.varify (DatatypeProp.make_ind [descr] sorts)]);
```
```   160
```
```   161     val prf = foldr forall_intr_prf (ivs,
```
```   162       prf_subst_vars inst (foldr (fn ((f, p), prf) =>
```
```   163         (case head_of (strip_abs_body f) of
```
```   164            Free (s, T) =>
```
```   165              let val T' = Type.varifyT T
```
```   166              in Abst (s, Some T', Proofterm.prf_abstract_over
```
```   167                (Var ((s, 0), T')) (AbsP ("H", Some p, prf)))
```
```   168              end
```
```   169          | _ => AbsP ("H", Some p, prf)))
```
```   170            (rec_fns ~~ prems_of thm, Proofterm.proof_combP
```
```   171              (prf_of thm', map PBound (length prems - 1 downto 0)))));
```
```   172
```
```   173     val r' = if null is then r else Logic.varify (foldr (uncurry lambda)
```
```   174       (map Logic.unvarify ivs @ filter_out is_unit
```
```   175         (map (head_of o strip_abs_body) rec_fns), r));
```
```   176
```
```   177   in Extraction.add_realizers_i [(ind_name, (vs, r', prf))] thy' end;
```
```   178
```
```   179
```
```   180 fun make_casedists sorts ({index, descr, case_name, case_rewrites, exhaustion, ...} : datatype_info, thy) =
```
```   181   let
```
```   182     val sg = sign_of thy;
```
```   183     val sorts = map (rpair HOLogic.typeS) (distinct (flat (map
```
```   184       (fn (_, (_, ds, _)) => mapfilter (try dest_DtTFree) ds) descr)));
```
```   185     val cert = cterm_of sg;
```
```   186     val rT = TFree ("'P", HOLogic.typeS);
```
```   187     val rT' = TVar (("'P", 0), HOLogic.typeS);
```
```   188
```
```   189     fun make_casedist_prem T (cname, cargs) =
```
```   190       let
```
```   191         val Ts = map (typ_of_dtyp descr sorts) cargs;
```
```   192         val frees = variantlist
```
```   193           (DatatypeProp.make_tnames Ts, ["P", "y"]) ~~ Ts;
```
```   194         val free_ts = map Free frees;
```
```   195         val r = Free ("r" ^ NameSpace.base cname, Ts ---> rT)
```
```   196       in (r, list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop
```
```   197         (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))),
```
```   198           HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) \$
```
```   199             list_comb (r, free_ts)))))
```
```   200       end;
```
```   201
```
```   202     val Some (_, _, constrs) = assoc (descr, index);
```
```   203     val T = nth_elem (index, get_rec_types descr sorts);
```
```   204     val (rs, prems) = split_list (map (make_casedist_prem T) constrs);
```
```   205     val r = Const (case_name, map fastype_of rs ---> T --> rT);
```
```   206
```
```   207     val y = Var (("y", 0), Type.varifyT T);
```
```   208     val y' = Free ("y", T);
```
```   209
```
```   210     val thm = prove_goalw_cterm [] (cert (Logic.list_implies (prems,
```
```   211       HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) \$
```
```   212         list_comb (r, rs @ [y'])))))
```
```   213       (fn prems =>
```
```   214          [rtac (cterm_instantiate [(cert y, cert y')] exhaustion) 1,
```
```   215           ALLGOALS (EVERY'
```
```   216             [asm_simp_tac (HOL_basic_ss addsimps case_rewrites),
```
```   217              resolve_tac prems, asm_simp_tac HOL_basic_ss])]);
```
```   218
```
```   219     val {path, ...} = Sign.rep_sg sg;
```
```   220     val exh_name = Thm.name_of_thm exhaustion;
```
```   221     val (thy', thm') = thy
```
```   222       |> Theory.absolute_path
```
```   223       |> PureThy.store_thm ((exh_name ^ "_P_correctness", thm), [])
```
```   224       |>> Theory.add_path (NameSpace.pack (if_none path []));
```
```   225
```
```   226     val P = Var (("P", 0), HOLogic.boolT);
```
```   227     val prf = forall_intr_prf (y, forall_intr_prf (P,
```
```   228       prf_subst_vars [(("P", 0), Abs ("r", rT',
```
```   229         mk_realizes rT' \$ Bound 0 \$ P))] (foldr (fn ((p, r), prf) =>
```
```   230           forall_intr_prf (Logic.varify r, AbsP ("H", Some (Logic.varify p),
```
```   231             prf))) (prems ~~ rs, Proofterm.proof_combP (prf_of thm',
```
```   232               map PBound (length prems - 1 downto 0))))));
```
```   233     val r' = Logic.varify (Abs ("y", Type.varifyT T,
```
```   234       Abs ("P", HOLogic.boolT, list_abs (map dest_Free rs, list_comb (r,
```
```   235         map Bound ((length rs - 1 downto 0) @ [length rs + 1]))))));
```
```   236
```
```   237     val prf' = forall_intr_prf (y, forall_intr_prf (P, prf_subst_vars
```
```   238       [(("P", 0), mk_realizes Extraction.nullT \$ Extraction.nullt \$ P)]
```
```   239         (prf_of exhaustion)));
```
```   240
```
```   241   in Extraction.add_realizers_i
```
```   242     [(exh_name, (["P"], r', prf)),
```
```   243      (exh_name, ([], Extraction.nullt, prf'))] thy'
```
```   244   end;
```
```   245
```
```   246
```
```   247 fun add_dt_realizers sorts infos thy = if !proofs < 2 then thy else
```
```   248   (message "Adding realizers for induction and case analysis ..."; thy
```
```   249    |> curry (foldr (make_ind sorts (hd infos)))
```
```   250      (subsets 0 (length (#descr (hd infos)) - 1))
```
```   251    |> curry (foldr (make_casedists sorts)) infos);
```
```   252
```
```   253 end;
```