src/HOL/Tools/inductive_realizer.ML
author wenzelm
Wed Nov 30 23:30:08 2011 +0100 (2011-11-30)
changeset 45701 615da8b8d758
parent 44241 7943b69f0188
child 45839 43a5b86bc102
permissions -rw-r--r--
discontinued obsolete datatype "alt_names";
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(*  Title:      HOL/Tools/inductive_realizer.ML
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    Author:     Stefan Berghofer, TU Muenchen
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Program extraction from proofs involving inductive predicates:
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Realizers for induction and elimination rules.
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*)
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signature INDUCTIVE_REALIZER =
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sig
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  val add_ind_realizers: string -> string list -> theory -> theory
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  val setup: theory -> theory
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end;
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structure InductiveRealizer : INDUCTIVE_REALIZER =
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struct
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(* FIXME: Local_Theory.note should return theorems with proper names! *)  (* FIXME ?? *)
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fun name_of_thm thm =
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  (case Proofterm.fold_proof_atoms false (fn PThm (_, ((name, _, _), _)) => cons name | _ => I)
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      [Thm.proof_of thm] [] of
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    [name] => name
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  | _ => error ("name_of_thm: bad proof of theorem\n" ^ Display.string_of_thm_without_context thm));
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fun prf_of thm =
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  Reconstruct.proof_of thm
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  |> Reconstruct.expand_proof (Thm.theory_of_thm thm) [("", NONE)];  (* FIXME *)
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fun subsets [] = [[]]
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  | subsets (x::xs) =
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      let val ys = subsets xs
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      in ys @ map (cons x) ys end;
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val pred_of = fst o dest_Const o head_of;
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fun strip_all' used names (Const ("all", _) $ Abs (s, T, t)) =
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      let val (s', names') = (case names of
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          [] => (singleton (Name.variant_list used) s, [])
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        | name :: names' => (name, names'))
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      in strip_all' (s'::used) names' (subst_bound (Free (s', T), t)) end
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  | strip_all' used names ((t as Const ("==>", _) $ P) $ Q) =
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      t $ strip_all' used names Q
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  | strip_all' _ _ t = t;
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fun strip_all t = strip_all' (Term.add_free_names t []) [] t;
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fun strip_one name (Const ("all", _) $ Abs (s, T, Const ("==>", _) $ P $ Q)) =
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      (subst_bound (Free (name, T), P), subst_bound (Free (name, T), Q))
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  | strip_one _ (Const ("==>", _) $ P $ Q) = (P, Q);
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fun relevant_vars prop = fold (fn ((a, i), T) => fn vs =>
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     (case strip_type T of
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        (_, Type (s, _)) => if s = @{type_name bool} then (a, T) :: vs else vs
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      | _ => vs)) (Term.add_vars prop []) [];
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val attach_typeS = map_types (map_atyps
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  (fn TFree (s, []) => TFree (s, HOLogic.typeS)
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    | TVar (ixn, []) => TVar (ixn, HOLogic.typeS)
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    | T => T));
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fun dt_of_intrs thy vs nparms intrs =
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  let
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    val iTs = rev (Term.add_tvars (prop_of (hd intrs)) []);
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    val (Const (s, _), ts) = strip_comb (HOLogic.dest_Trueprop
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      (Logic.strip_imp_concl (prop_of (hd intrs))));
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    val params = map dest_Var (take nparms ts);
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    val tname = Binding.name (space_implode "_" (Long_Name.base_name s ^ "T" :: vs));
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    fun constr_of_intr intr = (Binding.name (Long_Name.base_name (name_of_thm intr)),
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      map (Logic.unvarifyT_global o snd) (subtract (op =) params (rev (Term.add_vars (prop_of intr) []))) @
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        filter_out (equal Extraction.nullT) (map
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          (Logic.unvarifyT_global o Extraction.etype_of thy vs []) (prems_of intr)),
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            NoSyn);
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  in (map (fn a => "'" ^ a) vs @ map (fst o fst) iTs, tname, NoSyn,
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    map constr_of_intr intrs)
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  end;
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fun mk_rlz T = Const ("realizes", [T, HOLogic.boolT] ---> HOLogic.boolT);
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(** turn "P" into "%r x. realizes r (P x)" **)
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fun gen_rvar vs (t as Var ((a, 0), T)) =
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      if body_type T <> HOLogic.boolT then t else
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        let
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          val U = TVar (("'" ^ a, 0), [])
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          val Ts = binder_types T;
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          val i = length Ts;
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          val xs = map (pair "x") Ts;
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          val u = list_comb (t, map Bound (i - 1 downto 0))
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        in 
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          if member (op =) vs a then
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            list_abs (("r", U) :: xs, mk_rlz U $ Bound i $ u)
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          else list_abs (xs, mk_rlz Extraction.nullT $ Extraction.nullt $ u)
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        end
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  | gen_rvar _ t = t;
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fun mk_realizes_eqn n vs nparms intrs =
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  let
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    val intr = map_types Type.strip_sorts (prop_of (hd intrs));
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    val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl intr);
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    val iTs = rev (Term.add_tvars intr []);
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    val Tvs = map TVar iTs;
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    val (h as Const (s, T), us) = strip_comb concl;
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    val params = List.take (us, nparms);
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    val elTs = List.drop (binder_types T, nparms);
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    val predT = elTs ---> HOLogic.boolT;
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    val used = map (fst o fst o dest_Var) params;
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    val xs = map (Var o apfst (rpair 0))
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      (Name.variant_list used (replicate (length elTs) "x") ~~ elTs);
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    val rT = if n then Extraction.nullT
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      else Type (space_implode "_" (s ^ "T" :: vs),
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        map (fn a => TVar (("'" ^ a, 0), [])) vs @ Tvs);
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    val r = if n then Extraction.nullt else Var ((Long_Name.base_name s, 0), rT);
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    val S = list_comb (h, params @ xs);
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    val rvs = relevant_vars S;
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    val vs' = subtract (op =) vs (map fst rvs);
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    val rname = space_implode "_" (s ^ "R" :: vs);
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    fun mk_Tprem n v =
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      let val T = (the o AList.lookup (op =) rvs) v
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      in (Const ("typeof", T --> Type ("Type", [])) $ Var ((v, 0), T),
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        Extraction.mk_typ (if n then Extraction.nullT
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          else TVar (("'" ^ v, 0), [])))
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      end;
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    val prems = map (mk_Tprem true) vs' @ map (mk_Tprem false) vs;
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    val ts = map (gen_rvar vs) params;
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    val argTs = map fastype_of ts;
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  in ((prems, (Const ("typeof", HOLogic.boolT --> Type ("Type", [])) $ S,
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       Extraction.mk_typ rT)),
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    (prems, (mk_rlz rT $ r $ S,
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       if n then list_comb (Const (rname, argTs ---> predT), ts @ xs)
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       else list_comb (Const (rname, argTs @ [rT] ---> predT), ts @ [r] @ xs))))
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  end;
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fun fun_of_prem thy rsets vs params rule ivs intr =
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  let
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    val ctxt = Proof_Context.init_global thy
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    val args = map (Free o apfst fst o dest_Var) ivs;
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    val args' = map (Free o apfst fst)
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      (subtract (op =) params (Term.add_vars (prop_of intr) []));
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    val rule' = strip_all rule;
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    val conclT = Extraction.etype_of thy vs [] (Logic.strip_imp_concl rule');
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    val used = map (fst o dest_Free) args;
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    val is_rec = exists_Const (fn (c, _) => member (op =) rsets c);
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    fun is_meta (Const ("all", _) $ Abs (s, _, P)) = is_meta P
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      | is_meta (Const ("==>", _) $ _ $ Q) = is_meta Q
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      | is_meta (Const (@{const_name Trueprop}, _) $ t) =
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          (case head_of t of
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            Const (s, _) => can (Inductive.the_inductive ctxt) s
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          | _ => true)
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      | is_meta _ = false;
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    fun fun_of ts rts args used (prem :: prems) =
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          let
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            val T = Extraction.etype_of thy vs [] prem;
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            val [x, r] = Name.variant_list used ["x", "r"]
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          in if T = Extraction.nullT
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            then fun_of ts rts args used prems
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            else if is_rec prem then
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              if is_meta prem then
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                let
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                  val prem' :: prems' = prems;
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                  val U = Extraction.etype_of thy vs [] prem';
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                in if U = Extraction.nullT
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                  then fun_of (Free (x, T) :: ts)
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                    (Free (r, binder_types T ---> HOLogic.unitT) :: rts)
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                    (Free (x, T) :: args) (x :: r :: used) prems'
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                  else fun_of (Free (x, T) :: ts) (Free (r, U) :: rts)
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                    (Free (r, U) :: Free (x, T) :: args) (x :: r :: used) prems'
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                end
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              else (case strip_type T of
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                  (Ts, Type (@{type_name Product_Type.prod}, [T1, T2])) =>
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                    let
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                      val fx = Free (x, Ts ---> T1);
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                      val fr = Free (r, Ts ---> T2);
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                      val bs = map Bound (length Ts - 1 downto 0);
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                      val t = list_abs (map (pair "z") Ts,
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                        HOLogic.mk_prod (list_comb (fx, bs), list_comb (fr, bs)))
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                    in fun_of (fx :: ts) (fr :: rts) (t::args)
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                      (x :: r :: used) prems
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                    end
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                | (Ts, U) => fun_of (Free (x, T) :: ts)
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                    (Free (r, binder_types T ---> HOLogic.unitT) :: rts)
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                    (Free (x, T) :: args) (x :: r :: used) prems)
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            else fun_of (Free (x, T) :: ts) rts (Free (x, T) :: args)
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              (x :: used) prems
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          end
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      | fun_of ts rts args used [] =
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          let val xs = rev (rts @ ts)
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          in if conclT = Extraction.nullT
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            then fold_rev (absfree o dest_Free) xs HOLogic.unit
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            else fold_rev (absfree o dest_Free) xs
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              (list_comb
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                (Free ("r" ^ Long_Name.base_name (name_of_thm intr),
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                  map fastype_of (rev args) ---> conclT), rev args))
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          end
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  in fun_of args' [] (rev args) used (Logic.strip_imp_prems rule') end;
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fun indrule_realizer thy induct raw_induct rsets params vs rec_names rss intrs dummies =
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  let
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    val concls = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of raw_induct));
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    val premss = map_filter (fn (s, rs) => if member (op =) rsets s then
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      SOME (rs, map (fn (_, r) => nth (prems_of raw_induct)
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        (find_index (fn prp => prp = prop_of r) (map prop_of intrs))) rs) else NONE) rss;
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    val fs = maps (fn ((intrs, prems), dummy) =>
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      let
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        val fs = map (fn (rule, (ivs, intr)) =>
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          fun_of_prem thy rsets vs params rule ivs intr) (prems ~~ intrs)
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      in
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        if dummy then Const (@{const_name default},
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            HOLogic.unitT --> body_type (fastype_of (hd fs))) :: fs
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        else fs
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      end) (premss ~~ dummies);
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    val frees = fold Term.add_frees fs [];
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    val Ts = map fastype_of fs;
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    fun name_of_fn intr = "r" ^ Long_Name.base_name (name_of_thm intr)
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  in
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    fst (fold_map (fn concl => fn names =>
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      let val T = Extraction.etype_of thy vs [] concl
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      in if T = Extraction.nullT then (Extraction.nullt, names) else
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        let
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          val Type ("fun", [U, _]) = T;
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          val a :: names' = names
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        in
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          (fold_rev absfree (("x", U) :: map_filter (fn intr =>
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            Option.map (pair (name_of_fn intr))
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              (AList.lookup (op =) frees (name_of_fn intr))) intrs)
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            (list_comb (Const (a, Ts ---> T), fs) $ Free ("x", U)), names')
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        end
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      end) concls rec_names)
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  end;
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fun add_dummy name dname (x as (_, (vs, s, mfx, cs))) =
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  if Binding.eq_name (name, s) then (true, (vs, s, mfx, (dname, [HOLogic.unitT], NoSyn) :: cs))
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  else x;
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fun add_dummies f [] _ thy =
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      (([], NONE), thy)
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  | add_dummies f dts used thy =
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      thy
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      |> f (map snd dts)
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      |-> (fn dtinfo => pair (map fst dts, SOME dtinfo))
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    handle Datatype_Aux.Datatype_Empty name' =>
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      let
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        val name = Long_Name.base_name name';
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        val dname = singleton (Name.variant_list used) "Dummy";
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      in
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        thy
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        |> add_dummies f (map (add_dummy (Binding.name name) (Binding.name dname)) dts) (dname :: used)
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      end;
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fun mk_realizer thy vs (name, rule, rrule, rlz, rt) =
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  let
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    val rvs = map fst (relevant_vars (prop_of rule));
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    val xs = rev (Term.add_vars (prop_of rule) []);
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    val vs1 = map Var (filter_out (fn ((a, _), _) => member (op =) rvs a) xs);
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    val rlzvs = rev (Term.add_vars (prop_of rrule) []);
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    val vs2 = map (fn (ixn, _) => Var (ixn, (the o AList.lookup (op =) rlzvs) ixn)) xs;
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    val rs = map Var (subtract (op = o pairself fst) xs rlzvs);
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    val rlz' = fold_rev Logic.all rs (prop_of rrule)
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  in (name, (vs,
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    if rt = Extraction.nullt then rt else fold_rev lambda vs1 rt,
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    Extraction.abs_corr_shyps thy rule vs vs2
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      (ProofRewriteRules.un_hhf_proof rlz' (attach_typeS rlz)
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         (fold_rev Proofterm.forall_intr_proof' rs (prf_of rrule)))))
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  end;
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fun rename tab = map (fn x => the_default x (AList.lookup op = tab x));
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fun add_ind_realizer rsets intrs induct raw_induct elims vs thy =
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  let
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    val qualifier = Long_Name.qualifier (name_of_thm induct);
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    val inducts = Global_Theory.get_thms thy (Long_Name.qualify qualifier "inducts");
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    val iTs = rev (Term.add_tvars (prop_of (hd intrs)) []);
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    val ar = length vs + length iTs;
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    val params = Inductive.params_of raw_induct;
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    val arities = Inductive.arities_of raw_induct;
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    val nparms = length params;
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    val params' = map dest_Var params;
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    val rss = Inductive.partition_rules raw_induct intrs;
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    val rss' = map (fn (((s, rs), (_, arity)), elim) =>
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      (s, (Inductive.infer_intro_vars elim arity rs ~~ rs)))
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        (rss ~~ arities ~~ elims);
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    val (prfx, _) = split_last (Long_Name.explode (fst (hd rss)));
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    val tnames = map (fn s => space_implode "_" (s ^ "T" :: vs)) rsets;
wenzelm@16123
   289
berghofe@13710
   290
    val thy1 = thy |>
wenzelm@24712
   291
      Sign.root_path |>
wenzelm@30364
   292
      Sign.add_path (Long_Name.implode prfx);
berghofe@13710
   293
    val (ty_eqs, rlz_eqs) = split_list
haftmann@36692
   294
      (map (fn (s, rs) => mk_realizes_eqn (not (member (op =) rsets s)) vs nparms rs) rss);
berghofe@13710
   295
berghofe@13710
   296
    val thy1' = thy1 |>
berghofe@13710
   297
      Theory.copy |>
wenzelm@42375
   298
      Sign.add_types_global
wenzelm@42375
   299
        (map (fn s => (Binding.name (Long_Name.base_name s), ar, NoSyn)) tnames) |>
wenzelm@42375
   300
      Extraction.add_typeof_eqns_i ty_eqs;
haftmann@36692
   301
    val dts = map_filter (fn (s, rs) => if member (op =) rsets s then
berghofe@22271
   302
      SOME (dt_of_intrs thy1' vs nparms rs) else NONE) rss;
berghofe@13710
   303
berghofe@13710
   304
    (** datatype representing computational content of inductive set **)
berghofe@13710
   305
haftmann@31783
   306
    val ((dummies, some_dt_names), thy2) =
haftmann@18008
   307
      thy1
wenzelm@45701
   308
      |> add_dummies (Datatype.add_datatype {strict = false, quiet = false})
wenzelm@45701
   309
        (map (pair false) dts) []
haftmann@18314
   310
      ||> Extraction.add_typeof_eqns_i ty_eqs
haftmann@18314
   311
      ||> Extraction.add_realizes_eqns_i rlz_eqs;
haftmann@31783
   312
    val dt_names = these some_dt_names;
haftmann@31784
   313
    val case_thms = map (#case_rewrites o Datatype.the_info thy2) dt_names;
wenzelm@45701
   314
    val rec_thms =
wenzelm@45701
   315
      if null dt_names then []
wenzelm@45701
   316
      else #rec_rewrites (Datatype.the_info thy2 (hd dt_names));
wenzelm@19046
   317
    val rec_names = distinct (op =) (map (fst o dest_Const o head_of o fst o
haftmann@31781
   318
      HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) rec_thms);
haftmann@31458
   319
    val (constrss, _) = fold_map (fn (s, rs) => fn (recs, dummies) =>
haftmann@31458
   320
      if member (op =) rsets s then
berghofe@13710
   321
        let
berghofe@13710
   322
          val (d :: dummies') = dummies;
wenzelm@19473
   323
          val (recs1, recs2) = chop (length rs) (if d then tl recs else recs)
haftmann@31458
   324
        in (map (head_of o hd o rev o snd o strip_comb o fst o
haftmann@31458
   325
          HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) recs1, (recs2, dummies'))
berghofe@13710
   326
        end
haftmann@31458
   327
      else (replicate (length rs) Extraction.nullt, (recs, dummies)))
haftmann@31781
   328
        rss (rec_thms, dummies);
berghofe@37233
   329
    val rintrs = map (fn (intr, c) => attach_typeS (Envir.eta_contract
berghofe@13710
   330
      (Extraction.realizes_of thy2 vs
berghofe@22271
   331
        (if c = Extraction.nullt then c else list_comb (c, map Var (rev
berghofe@37233
   332
          (subtract (op =) params' (Term.add_vars (prop_of intr) []))))) (prop_of intr))))
wenzelm@32952
   333
            (maps snd rss ~~ flat constrss);
wenzelm@30345
   334
    val (rlzpreds, rlzpreds') =
wenzelm@30345
   335
      rintrs |> map (fn rintr =>
berghofe@22271
   336
        let
wenzelm@30345
   337
          val Const (s, T) = head_of (HOLogic.dest_Trueprop (Logic.strip_assums_concl rintr));
wenzelm@30364
   338
          val s' = Long_Name.base_name s;
wenzelm@35845
   339
          val T' = Logic.unvarifyT_global T;
wenzelm@30345
   340
        in (((s', T'), NoSyn), (Const (s, T'), Free (s', T'))) end)
wenzelm@30345
   341
      |> distinct (op = o pairself (#1 o #1))
wenzelm@30345
   342
      |> map (apfst (apfst (apfst Binding.name)))
wenzelm@30345
   343
      |> split_list;
wenzelm@30345
   344
wenzelm@35845
   345
    val rlzparams = map (fn Var ((s, _), T) => (s, Logic.unvarifyT_global T))
berghofe@22271
   346
      (List.take (snd (strip_comb
berghofe@22271
   347
        (HOLogic.dest_Trueprop (Logic.strip_assums_concl (hd rintrs)))), nparms));
berghofe@13710
   348
berghofe@13710
   349
    (** realizability predicate **)
berghofe@13710
   350
berghofe@22271
   351
    val (ind_info, thy3') = thy2 |>
wenzelm@33726
   352
      Inductive.add_inductive_global
wenzelm@33669
   353
        {quiet_mode = false, verbose = false, alt_name = Binding.empty, coind = false,
wenzelm@33669
   354
          no_elim = false, no_ind = false, skip_mono = false, fork_mono = false}
berghofe@22271
   355
        rlzpreds rlzparams (map (fn (rintr, intr) =>
wenzelm@30364
   356
          ((Binding.name (Long_Name.base_name (name_of_thm intr)), []),
wenzelm@35845
   357
           subst_atomic rlzpreds' (Logic.unvarify_global rintr)))
berghofe@22271
   358
             (rintrs ~~ maps snd rss)) [] ||>
wenzelm@30435
   359
      Sign.root_path;
wenzelm@39557
   360
    val thy3 = fold (Global_Theory.hide_fact false o name_of_thm) (#intrs ind_info) thy3';
berghofe@13710
   361
berghofe@13710
   362
    (** realizer for induction rule **)
berghofe@13710
   363
haftmann@36692
   364
    val Ps = map_filter (fn _ $ M $ P => if member (op =) rsets (pred_of M) then
skalberg@15531
   365
      SOME (fst (fst (dest_Var (head_of P)))) else NONE)
berghofe@13710
   366
        (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of raw_induct)));
berghofe@13710
   367
wenzelm@33244
   368
    fun add_ind_realizer Ps thy =
berghofe@13710
   369
      let
berghofe@24157
   370
        val vs' = rename (map (pairself (fst o fst o dest_Var))
berghofe@24157
   371
          (params ~~ List.take (snd (strip_comb (HOLogic.dest_Trueprop
berghofe@24157
   372
            (hd (prems_of (hd inducts))))), nparms))) vs;
berghofe@22271
   373
        val rs = indrule_realizer thy induct raw_induct rsets params'
berghofe@24157
   374
          (vs' @ Ps) rec_names rss' intrs dummies;
berghofe@24157
   375
        val rlzs = map (fn (r, ind) => Extraction.realizes_of thy (vs' @ Ps) r
berghofe@22271
   376
          (prop_of ind)) (rs ~~ inducts);
wenzelm@29281
   377
        val used = fold Term.add_free_names rlzs [];
berghofe@22271
   378
        val rnames = Name.variant_list used (replicate (length inducts) "r");
berghofe@22271
   379
        val rnames' = Name.variant_list
berghofe@22271
   380
          (used @ rnames) (replicate (length intrs) "s");
berghofe@22271
   381
        val rlzs' as (prems, _, _) :: _ = map (fn (rlz, name) =>
berghofe@22271
   382
          let
wenzelm@35845
   383
            val (P, Q) = strip_one name (Logic.unvarify_global rlz);
berghofe@22271
   384
            val Q' = strip_all' [] rnames' Q
berghofe@22271
   385
          in
berghofe@22271
   386
            (Logic.strip_imp_prems Q', P, Logic.strip_imp_concl Q')
berghofe@22271
   387
          end) (rlzs ~~ rnames);
berghofe@22271
   388
        val concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@22271
   389
          (fn (_, _ $ P, _ $ Q) => HOLogic.mk_imp (P, Q)) rlzs'));
haftmann@37136
   390
        val rews = map mk_meta_eq (@{thm fst_conv} :: @{thm snd_conv} :: rec_thms);
berghofe@37233
   391
        val thm = Goal.prove_global thy []
berghofe@37233
   392
          (map attach_typeS prems) (attach_typeS concl)
berghofe@37233
   393
          (fn {prems, ...} => EVERY
berghofe@22271
   394
          [rtac (#raw_induct ind_info) 1,
berghofe@13710
   395
           rewrite_goals_tac rews,
berghofe@13710
   396
           REPEAT ((resolve_tac prems THEN_ALL_NEW EVERY'
wenzelm@35625
   397
             [K (rewrite_goals_tac rews), Object_Logic.atomize_prems_tac,
berghofe@13710
   398
              DEPTH_SOLVE_1 o FIRST' [atac, etac allE, etac impE]]) 1)]);
wenzelm@39557
   399
        val (thm', thy') = Global_Theory.store_thm (Binding.qualified_name (space_implode "_"
wenzelm@30364
   400
          (Long_Name.qualify qualifier "induct" :: vs' @ Ps @ ["correctness"])), thm) thy;
berghofe@22271
   401
        val thms = map (fn th => zero_var_indexes (rotate_prems ~1 (th RS mp)))
haftmann@33968
   402
          (Datatype_Aux.split_conj_thm thm');
wenzelm@39557
   403
        val ([thms'], thy'') = Global_Theory.add_thmss
wenzelm@30435
   404
          [((Binding.qualified_name (space_implode "_"
wenzelm@30364
   405
             (Long_Name.qualify qualifier "inducts" :: vs' @ Ps @
haftmann@29579
   406
               ["correctness"])), thms), [])] thy';
berghofe@22271
   407
        val realizers = inducts ~~ thms' ~~ rlzs ~~ rs;
berghofe@13710
   408
      in
berghofe@13710
   409
        Extraction.add_realizers_i
berghofe@22271
   410
          (map (fn (((ind, corr), rlz), r) =>
berghofe@37233
   411
              mk_realizer thy'' (vs' @ Ps) (Thm.derivation_name ind, ind, corr, rlz, r))
berghofe@22271
   412
            realizers @ (case realizers of
berghofe@22271
   413
             [(((ind, corr), rlz), r)] =>
berghofe@37233
   414
               [mk_realizer thy'' (vs' @ Ps) (Long_Name.qualify qualifier "induct",
berghofe@22271
   415
                  ind, corr, rlz, r)]
berghofe@22271
   416
           | _ => [])) thy''
berghofe@13710
   417
      end;
berghofe@13710
   418
berghofe@13710
   419
    (** realizer for elimination rules **)
berghofe@13710
   420
berghofe@13710
   421
    val case_names = map (fst o dest_Const o head_of o fst o HOLogic.dest_eq o
haftmann@31781
   422
      HOLogic.dest_Trueprop o prop_of o hd) case_thms;
berghofe@13710
   423
berghofe@13921
   424
    fun add_elim_realizer Ps
berghofe@13921
   425
      (((((elim, elimR), intrs), case_thms), case_name), dummy) thy =
berghofe@13710
   426
      let
berghofe@13710
   427
        val (prem :: prems) = prems_of elim;
berghofe@22271
   428
        fun reorder1 (p, (_, intr)) =
wenzelm@33244
   429
          fold (fn ((s, _), T) => Logic.all (Free (s, T)))
wenzelm@33244
   430
            (subtract (op =) params' (Term.add_vars (prop_of intr) []))
wenzelm@33244
   431
            (strip_all p);
berghofe@22271
   432
        fun reorder2 ((ivs, intr), i) =
haftmann@33040
   433
          let val fs = subtract (op =) params' (Term.add_vars (prop_of intr) [])
wenzelm@33244
   434
          in fold (lambda o Var) fs (list_comb (Bound (i + length ivs), ivs)) end;
berghofe@13921
   435
        val p = Logic.list_implies
berghofe@13921
   436
          (map reorder1 (prems ~~ intrs) @ [prem], concl_of elim);
berghofe@13710
   437
        val T' = Extraction.etype_of thy (vs @ Ps) [] p;
berghofe@13710
   438
        val T = if dummy then (HOLogic.unitT --> body_type T') --> T' else T';
berghofe@13921
   439
        val Ts = map (Extraction.etype_of thy (vs @ Ps) []) (prems_of elim);
berghofe@13710
   440
        val r = if null Ps then Extraction.nullt
berghofe@13710
   441
          else list_abs (map (pair "x") Ts, list_comb (Const (case_name, T),
berghofe@13710
   442
            (if dummy then
wenzelm@35364
   443
               [Abs ("x", HOLogic.unitT, Const (@{const_name default}, body_type T))]
berghofe@13710
   444
             else []) @
berghofe@13921
   445
            map reorder2 (intrs ~~ (length prems - 1 downto 0)) @
berghofe@13921
   446
            [Bound (length prems)]));
berghofe@22271
   447
        val rlz = Extraction.realizes_of thy (vs @ Ps) r (prop_of elim);
berghofe@37233
   448
        val rlz' = attach_typeS (strip_all (Logic.unvarify_global rlz));
berghofe@13710
   449
        val rews = map mk_meta_eq case_thms;
berghofe@22271
   450
        val thm = Goal.prove_global thy []
wenzelm@26711
   451
          (Logic.strip_imp_prems rlz') (Logic.strip_imp_concl rlz') (fn {prems, ...} => EVERY
berghofe@13710
   452
          [cut_facts_tac [hd prems] 1,
berghofe@13710
   453
           etac elimR 1,
berghofe@22271
   454
           ALLGOALS (asm_simp_tac HOL_basic_ss),
berghofe@13710
   455
           rewrite_goals_tac rews,
wenzelm@35625
   456
           REPEAT ((resolve_tac prems THEN_ALL_NEW (Object_Logic.atomize_prems_tac THEN'
berghofe@13710
   457
             DEPTH_SOLVE_1 o FIRST' [atac, etac allE, etac impE])) 1)]);
wenzelm@39557
   458
        val (thm', thy') = Global_Theory.store_thm (Binding.qualified_name (space_implode "_"
haftmann@29579
   459
          (name_of_thm elim :: vs @ Ps @ ["correctness"])), thm) thy
berghofe@13710
   460
      in
berghofe@13710
   461
        Extraction.add_realizers_i
berghofe@22271
   462
          [mk_realizer thy' (vs @ Ps) (name_of_thm elim, elim, thm', rlz, r)] thy'
berghofe@13710
   463
      end;
berghofe@13710
   464
berghofe@13710
   465
    (** add realizers to theory **)
berghofe@13710
   466
wenzelm@33244
   467
    val thy4 = fold add_ind_realizer (subsets Ps) thy3;
berghofe@13710
   468
    val thy5 = Extraction.add_realizers_i
berghofe@22271
   469
      (map (mk_realizer thy4 vs) (map (fn (((rule, rrule), rlz), c) =>
berghofe@22271
   470
         (name_of_thm rule, rule, rrule, rlz,
haftmann@33040
   471
            list_comb (c, map Var (subtract (op =) params' (rev (Term.add_vars (prop_of rule) []))))))
wenzelm@32952
   472
              (maps snd rss ~~ #intrs ind_info ~~ rintrs ~~ flat constrss))) thy4;
wenzelm@32952
   473
    val elimps = map_filter (fn ((s, intrs), p) =>
haftmann@36692
   474
      if member (op =) rsets s then SOME (p, intrs) else NONE)
berghofe@22271
   475
        (rss' ~~ (elims ~~ #elims ind_info));
wenzelm@33244
   476
    val thy6 =
wenzelm@33244
   477
      fold (fn p as (((((elim, _), _), _), _), _) =>
wenzelm@33244
   478
        add_elim_realizer [] p #>
wenzelm@33244
   479
        add_elim_realizer [fst (fst (dest_Var (HOLogic.dest_Trueprop (concl_of elim))))] p)
wenzelm@33244
   480
      (elimps ~~ case_thms ~~ case_names ~~ dummies) thy5;
berghofe@13710
   481
wenzelm@24712
   482
  in Sign.restore_naming thy thy6 end;
berghofe@13710
   483
berghofe@13710
   484
fun add_ind_realizers name rsets thy =
berghofe@13710
   485
  let
berghofe@13710
   486
    val (_, {intrs, induct, raw_induct, elims, ...}) =
wenzelm@42361
   487
      Inductive.the_inductive (Proof_Context.init_global thy) name;
berghofe@13710
   488
    val vss = sort (int_ord o pairself length)
berghofe@22271
   489
      (subsets (map fst (relevant_vars (concl_of (hd intrs)))))
berghofe@13710
   490
  in
berghofe@37233
   491
    fold_rev (add_ind_realizer rsets intrs induct raw_induct elims) vss thy
berghofe@13710
   492
  end
berghofe@13710
   493
wenzelm@20897
   494
fun rlz_attrib arg = Thm.declaration_attribute (fn thm => Context.mapping
berghofe@13710
   495
  let
berghofe@13710
   496
    fun err () = error "ind_realizer: bad rule";
berghofe@13710
   497
    val sets =
berghofe@13710
   498
      (case HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of thm)) of
berghofe@22271
   499
           [_] => [pred_of (HOLogic.dest_Trueprop (hd (prems_of thm)))]
berghofe@22271
   500
         | xs => map (pred_of o fst o HOLogic.dest_imp) xs)
skalberg@15570
   501
         handle TERM _ => err () | Empty => err ();
berghofe@13710
   502
  in 
wenzelm@18728
   503
    add_ind_realizers (hd sets)
wenzelm@18728
   504
      (case arg of
skalberg@15531
   505
        NONE => sets | SOME NONE => []
haftmann@33040
   506
      | SOME (SOME sets') => subtract (op =) sets' sets)
wenzelm@20897
   507
  end I);
berghofe@13710
   508
wenzelm@18708
   509
val setup =
wenzelm@30722
   510
  Attrib.setup @{binding ind_realizer}
wenzelm@30722
   511
    ((Scan.option (Scan.lift (Args.$$$ "irrelevant") |--
wenzelm@35402
   512
      Scan.option (Scan.lift (Args.colon) |-- Scan.repeat1 (Args.const true)))) >> rlz_attrib)
wenzelm@30722
   513
    "add realizers for inductive set";
berghofe@13710
   514
berghofe@13710
   515
end;
wenzelm@15706
   516