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(* Title: HOL/BNF/Tools/bnf_fp_rec_sugar.ML
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Author: Lorenz Panny, TU Muenchen
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Copyright 2013
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Recursor and corecursor sugar.
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*)
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signature BNF_FP_REC_SUGAR =
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sig
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val add_primrec_cmd: (binding * string option * mixfix) list ->
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(Attrib.binding * string) list -> local_theory -> local_theory;
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val add_primcorec_cmd: bool ->
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(binding * string option * mixfix) list * (Attrib.binding * string) list -> Proof.context ->
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Proof.state
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end;
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structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
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struct
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open BNF_Util
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open BNF_FP_Util
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open BNF_FP_Rec_Sugar_Util
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open BNF_FP_Rec_Sugar_Tactics
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exception Primrec_Error of string * term list;
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fun primrec_error str = raise Primrec_Error (str, []);
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fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
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fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
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fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
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val free_name = try (fn Free (v, _) => v);
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val const_name = try (fn Const (v, _) => v);
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val undef_const = Const (@{const_name undefined}, dummyT);
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fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
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|> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);
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val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
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fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
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strip_qnt_body @{const_name all} t)
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fun mk_not @{const True} = @{const False}
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| mk_not @{const False} = @{const True}
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| mk_not (@{const Not} $ t) = t
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| mk_not (@{const Trueprop} $ t) = @{const Trueprop} $ mk_not t
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| mk_not t = HOLogic.mk_not t
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val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
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val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
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fun invert_prems [t] = map mk_not (HOLogic.disjuncts t)
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| invert_prems ts = [mk_disjs (map mk_not ts)];
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fun invert_prems_disj [t] = map mk_not (HOLogic.disjuncts t)
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| invert_prems_disj ts = [mk_disjs (map (mk_conjs o map mk_not o HOLogic.disjuncts) ts)];
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fun abstract vs =
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let fun a n (t $ u) = a n t $ a n u
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| a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
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| a n t = let val idx = find_index (equal t) vs in
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if idx < 0 then t else Bound (n + idx) end
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in a 0 end;
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val simp_attrs = @{attributes [simp]};
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(* Primrec *)
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type eqn_data = {
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fun_name: string,
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rec_type: typ,
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ctr: term,
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ctr_args: term list,
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left_args: term list,
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right_args: term list,
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res_type: typ,
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rhs_term: term,
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user_eqn: term
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};
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fun dissect_eqn lthy fun_names eqn' =
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let
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val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
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handle TERM _ =>
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primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
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val (lhs, rhs) = HOLogic.dest_eq eqn
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handle TERM _ =>
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primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
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val (fun_name, args) = strip_comb lhs
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|>> (fn x => if is_Free x then fst (dest_Free x)
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else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
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val (left_args, rest) = take_prefix is_Free args;
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val (nonfrees, right_args) = take_suffix is_Free rest;
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val _ = length nonfrees = 1 orelse if length nonfrees = 0 then
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primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
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primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
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val _ = member (op =) fun_names fun_name orelse
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primrec_error_eqn "malformed function equation (does not start with function name)" eqn
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val (ctr, ctr_args) = strip_comb (the_single nonfrees);
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val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
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primrec_error_eqn "partially applied constructor in pattern" eqn;
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val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
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primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
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"\" in left-hand side") eqn end;
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val _ = forall is_Free ctr_args orelse
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primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
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val _ =
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let val b = fold_aterms (fn x as Free (v, _) =>
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if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
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not (member (op =) fun_names v) andalso
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not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
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in
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null b orelse
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primrec_error_eqn ("extra variable(s) in right-hand side: " ^
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commas (map (Syntax.string_of_term lthy) b)) eqn
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end;
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in
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{fun_name = fun_name,
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rec_type = body_type (type_of ctr),
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ctr = ctr,
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ctr_args = ctr_args,
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left_args = left_args,
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right_args = right_args,
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res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
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rhs_term = rhs,
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user_eqn = eqn'}
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end;
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fun rewrite_map_arg get_ctr_pos rec_type res_type =
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let
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val pT = HOLogic.mk_prodT (rec_type, res_type);
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val maybe_suc = Option.map (fn x => x + 1);
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fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
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| subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
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| subst d t =
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let
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val (u, vs) = strip_comb t;
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val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
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in
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if ctr_pos >= 0 then
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if d = SOME ~1 andalso length vs = ctr_pos then
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list_comb (permute_args ctr_pos (snd_const pT), vs)
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else if length vs > ctr_pos andalso is_some d
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andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
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list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
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else
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primrec_error_eqn ("recursive call not directly applied to constructor argument") t
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else if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then
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list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs)
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else
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list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
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end
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in
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subst (SOME ~1)
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end;
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fun subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls t =
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let
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fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
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| subst bound_Ts (t as g' $ y) =
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let
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val maybe_direct_y' = AList.lookup (op =) direct_calls y;
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val maybe_indirect_y' = AList.lookup (op =) indirect_calls y;
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val (g, g_args) = strip_comb g';
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val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1;
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val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse
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primrec_error_eqn "too few arguments in recursive call" t;
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in
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if not (member (op =) ctr_args y) then
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pairself (subst bound_Ts) (g', y) |> (op $)
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else if ctr_pos >= 0 then
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list_comb (the maybe_direct_y', g_args)
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else if is_some maybe_indirect_y' then
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(if has_call g' then t else y)
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|> massage_indirect_rec_call lthy has_call
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(rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y')
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|> (if has_call g' then I else curry (op $) g')
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else
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t
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end
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| subst _ t = t
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in
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subst [] t
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|> tap (fn u => has_call u andalso (* FIXME detect this case earlier *)
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primrec_error_eqn "recursive call not directly applied to constructor argument" t)
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end;
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fun build_rec_arg lthy funs_data has_call ctr_spec maybe_eqn_data =
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if is_none maybe_eqn_data then undef_const else
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let
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val eqn_data = the maybe_eqn_data;
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val t = #rhs_term eqn_data;
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val ctr_args = #ctr_args eqn_data;
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val calls = #calls ctr_spec;
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val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0;
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val no_calls' = tag_list 0 calls
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|> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n)));
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val direct_calls' = tag_list 0 calls
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|> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
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val indirect_calls' = tag_list 0 calls
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|> map_filter (try (apsnd (fn Indirect_Rec n => n)));
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fun make_direct_type T = dummyT; (* FIXME? *)
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val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
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fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
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let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
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if is_some maybe_res_type
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then HOLogic.mk_prodT (T, the maybe_res_type)
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else make_indirect_type T end))
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| make_indirect_type T = T;
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val args = replicate n_args ("", dummyT)
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|> Term.rename_wrt_term t
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|> map Free
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|> fold (fn (ctr_arg_idx, arg_idx) =>
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nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
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no_calls'
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|> fold (fn (ctr_arg_idx, arg_idx) =>
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nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
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direct_calls'
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|> fold (fn (ctr_arg_idx, arg_idx) =>
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nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type)))
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indirect_calls';
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val fun_name_ctr_pos_list =
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map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
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val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
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val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
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val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
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val abstractions = args @ #left_args eqn_data @ #right_args eqn_data;
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in
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t
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|> subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls
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|> fold_rev lambda abstractions
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end;
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fun build_defs lthy bs mxs funs_data rec_specs has_call =
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let
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val n_funs = length funs_data;
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val ctr_spec_eqn_data_list' =
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(take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
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|> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
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##> (fn x => null x orelse
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primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
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|
249 |
val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
|
blanchet@54440
|
250 |
primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
|
blanchet@54440
|
251 |
|
blanchet@54440
|
252 |
val ctr_spec_eqn_data_list =
|
blanchet@54440
|
253 |
ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
|
blanchet@54440
|
254 |
|
blanchet@54440
|
255 |
val recs = take n_funs rec_specs |> map #recx;
|
blanchet@54440
|
256 |
val rec_args = ctr_spec_eqn_data_list
|
blanchet@54440
|
257 |
|> sort ((op <) o pairself (#offset o fst) |> make_ord)
|
panny@54495
|
258 |
|> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
|
blanchet@54440
|
259 |
val ctr_poss = map (fn x =>
|
blanchet@54440
|
260 |
if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
|
blanchet@54440
|
261 |
primrec_error ("inconstant constructor pattern position for function " ^
|
blanchet@54440
|
262 |
quote (#fun_name (hd x)))
|
blanchet@54440
|
263 |
else
|
blanchet@54440
|
264 |
hd x |> #left_args |> length) funs_data;
|
blanchet@54440
|
265 |
in
|
blanchet@54440
|
266 |
(recs, ctr_poss)
|
blanchet@54440
|
267 |
|-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
|
blanchet@54440
|
268 |
|> Syntax.check_terms lthy
|
traytel@54489
|
269 |
|> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
|
blanchet@54440
|
270 |
end;
|
blanchet@54440
|
271 |
|
panny@54495
|
272 |
fun find_rec_calls has_call eqn_data =
|
blanchet@54440
|
273 |
let
|
blanchet@54440
|
274 |
fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
|
blanchet@54440
|
275 |
| find (t as _ $ _) ctr_arg =
|
blanchet@54440
|
276 |
let
|
blanchet@54440
|
277 |
val (f', args') = strip_comb t;
|
blanchet@54440
|
278 |
val n = find_index (equal ctr_arg) args';
|
blanchet@54440
|
279 |
in
|
blanchet@54440
|
280 |
if n < 0 then
|
blanchet@54440
|
281 |
find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
|
blanchet@54440
|
282 |
else
|
blanchet@54440
|
283 |
let val (f, args) = chop n args' |>> curry list_comb f' in
|
panny@54495
|
284 |
if has_call f then
|
blanchet@54440
|
285 |
f :: maps (fn x => find x ctr_arg) args
|
blanchet@54440
|
286 |
else
|
blanchet@54440
|
287 |
find f ctr_arg @ maps (fn x => find x ctr_arg) args
|
blanchet@54440
|
288 |
end
|
blanchet@54440
|
289 |
end
|
blanchet@54440
|
290 |
| find _ _ = [];
|
blanchet@54440
|
291 |
in
|
blanchet@54440
|
292 |
map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
|
blanchet@54440
|
293 |
|> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
|
blanchet@54440
|
294 |
end;
|
blanchet@54440
|
295 |
|
blanchet@54440
|
296 |
fun add_primrec fixes specs lthy =
|
blanchet@54440
|
297 |
let
|
traytel@54489
|
298 |
val (bs, mxs) = map_split (apfst fst) fixes;
|
blanchet@54440
|
299 |
val fun_names = map Binding.name_of bs;
|
blanchet@54440
|
300 |
val eqns_data = map (snd #> dissect_eqn lthy fun_names) specs;
|
blanchet@54440
|
301 |
val funs_data = eqns_data
|
blanchet@54440
|
302 |
|> partition_eq ((op =) o pairself #fun_name)
|
blanchet@54440
|
303 |
|> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
|
blanchet@54440
|
304 |
|> map (fn (x, y) => the_single y handle List.Empty =>
|
blanchet@54440
|
305 |
primrec_error ("missing equations for function " ^ quote x));
|
blanchet@54440
|
306 |
|
panny@54495
|
307 |
val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
|
blanchet@54440
|
308 |
val arg_Ts = map (#rec_type o hd) funs_data;
|
blanchet@54440
|
309 |
val res_Ts = map (#res_type o hd) funs_data;
|
blanchet@54440
|
310 |
val callssss = funs_data
|
blanchet@54440
|
311 |
|> map (partition_eq ((op =) o pairself #ctr))
|
panny@54495
|
312 |
|> map (maps (map_filter (find_rec_calls has_call)));
|
blanchet@54440
|
313 |
|
panny@54495
|
314 |
fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
|
panny@54495
|
315 |
|> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
|
panny@54495
|
316 |
|> map_filter I;
|
blanchet@54440
|
317 |
val ((nontriv, rec_specs, _, induct_thm, induct_thms), lthy') =
|
blanchet@54440
|
318 |
rec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
|
blanchet@54440
|
319 |
|
blanchet@54440
|
320 |
val actual_nn = length funs_data;
|
blanchet@54440
|
321 |
|
blanchet@54440
|
322 |
val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
|
blanchet@54440
|
323 |
map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
|
blanchet@54440
|
324 |
primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
|
blanchet@54440
|
325 |
" is not a constructor in left-hand side") user_eqn) eqns_data end;
|
blanchet@54440
|
326 |
|
panny@54495
|
327 |
val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
|
blanchet@54440
|
328 |
|
blanchet@54466
|
329 |
fun prove def_thms' {ctr_specs, nested_map_idents, nested_map_comps, ...} induct_thm fun_data
|
blanchet@54440
|
330 |
lthy =
|
blanchet@54440
|
331 |
let
|
blanchet@54440
|
332 |
val fun_name = #fun_name (hd fun_data);
|
blanchet@54440
|
333 |
val def_thms = map (snd o snd) def_thms';
|
blanchet@54440
|
334 |
val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
|
blanchet@54440
|
335 |
|> fst
|
blanchet@54440
|
336 |
|> map_filter (try (fn (x, [y]) =>
|
blanchet@54440
|
337 |
(#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
|
blanchet@54440
|
338 |
|> map (fn (user_eqn, num_extra_args, rec_thm) =>
|
blanchet@54466
|
339 |
mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
|
blanchet@54440
|
340 |
|> K |> Goal.prove lthy [] [] user_eqn)
|
blanchet@54440
|
341 |
|
blanchet@54440
|
342 |
val notes =
|
blanchet@54440
|
343 |
[(inductN, if actual_nn > 1 then [induct_thm] else [], []),
|
blanchet@54440
|
344 |
(simpsN, simp_thms, simp_attrs)]
|
blanchet@54440
|
345 |
|> filter_out (null o #2)
|
blanchet@54440
|
346 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@54440
|
347 |
((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]));
|
blanchet@54440
|
348 |
in
|
blanchet@54440
|
349 |
lthy |> Local_Theory.notes notes
|
blanchet@54440
|
350 |
end;
|
blanchet@54440
|
351 |
|
blanchet@54440
|
352 |
val common_name = mk_common_name fun_names;
|
blanchet@54440
|
353 |
|
blanchet@54440
|
354 |
val common_notes =
|
blanchet@54440
|
355 |
[(inductN, if nontriv andalso actual_nn > 1 then [induct_thm] else [], [])]
|
blanchet@54440
|
356 |
|> filter_out (null o #2)
|
blanchet@54440
|
357 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@54440
|
358 |
((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
|
blanchet@54440
|
359 |
in
|
blanchet@54440
|
360 |
lthy'
|
blanchet@54440
|
361 |
|> fold_map Local_Theory.define defs
|
panny@54791
|
362 |
|-> snd oo (fn def_thms' => fold_map3 (prove def_thms') (take actual_nn rec_specs)
|
blanchet@54440
|
363 |
(take actual_nn induct_thms) funs_data)
|
panny@54791
|
364 |
|> snd o Local_Theory.notes common_notes
|
blanchet@54440
|
365 |
end;
|
blanchet@54440
|
366 |
|
blanchet@54440
|
367 |
fun add_primrec_cmd raw_fixes raw_specs lthy =
|
blanchet@54440
|
368 |
let
|
blanchet@54440
|
369 |
val _ = let val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) in null d orelse
|
blanchet@54440
|
370 |
primrec_error ("duplicate function name(s): " ^ commas d) end;
|
blanchet@54440
|
371 |
val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
|
blanchet@54440
|
372 |
in
|
blanchet@54440
|
373 |
add_primrec fixes specs lthy
|
blanchet@54440
|
374 |
handle ERROR str => primrec_error str
|
blanchet@54440
|
375 |
end
|
blanchet@54440
|
376 |
handle Primrec_Error (str, eqns) =>
|
blanchet@54440
|
377 |
if null eqns
|
blanchet@54440
|
378 |
then error ("primrec_new error:\n " ^ str)
|
blanchet@54440
|
379 |
else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^
|
blanchet@54440
|
380 |
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))
|
blanchet@54440
|
381 |
|
blanchet@54440
|
382 |
|
blanchet@54440
|
383 |
|
blanchet@54447
|
384 |
(* Primcorec *)
|
blanchet@54440
|
385 |
|
panny@54478
|
386 |
type co_eqn_data_disc = {
|
blanchet@54440
|
387 |
fun_name: string,
|
panny@54857
|
388 |
fun_T: typ,
|
panny@54538
|
389 |
fun_args: term list,
|
panny@54857
|
390 |
ctr: term,
|
panny@54478
|
391 |
ctr_no: int, (*###*)
|
panny@54857
|
392 |
disc: term,
|
panny@54791
|
393 |
prems: term list,
|
blanchet@54440
|
394 |
user_eqn: term
|
blanchet@54440
|
395 |
};
|
panny@54478
|
396 |
type co_eqn_data_sel = {
|
blanchet@54440
|
397 |
fun_name: string,
|
panny@54857
|
398 |
fun_T: typ,
|
panny@54538
|
399 |
fun_args: term list,
|
panny@54478
|
400 |
ctr: term,
|
panny@54478
|
401 |
sel: term,
|
blanchet@54440
|
402 |
rhs_term: term,
|
blanchet@54440
|
403 |
user_eqn: term
|
blanchet@54440
|
404 |
};
|
blanchet@54440
|
405 |
datatype co_eqn_data =
|
panny@54478
|
406 |
Disc of co_eqn_data_disc |
|
panny@54478
|
407 |
Sel of co_eqn_data_sel;
|
blanchet@54440
|
408 |
|
panny@54857
|
409 |
fun co_dissect_eqn_disc sequential fun_names corec_specs prems' concl matchedsss =
|
blanchet@54440
|
410 |
let
|
blanchet@54440
|
411 |
fun find_subterm p = let (* FIXME \<exists>? *)
|
panny@54538
|
412 |
fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
|
blanchet@54440
|
413 |
| f t = if p t then SOME t else NONE
|
blanchet@54440
|
414 |
in f end;
|
blanchet@54440
|
415 |
|
panny@54791
|
416 |
val applied_fun = concl
|
panny@54791
|
417 |
|> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
|
panny@54791
|
418 |
|> the
|
panny@54791
|
419 |
handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
|
panny@54857
|
420 |
val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
|
panny@54857
|
421 |
val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
|
blanchet@54440
|
422 |
|
panny@54857
|
423 |
val discs = map #disc ctr_specs;
|
panny@54857
|
424 |
val ctrs = map #ctr ctr_specs;
|
panny@54791
|
425 |
val not_disc = head_of concl = @{term Not};
|
panny@54538
|
426 |
val _ = not_disc andalso length ctrs <> 2 andalso
|
panny@54791
|
427 |
primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
|
panny@54791
|
428 |
val disc = find_subterm (member (op =) discs o head_of) concl;
|
panny@54791
|
429 |
val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
|
blanchet@54440
|
430 |
|> (fn SOME t => let val n = find_index (equal t) ctrs in
|
blanchet@54440
|
431 |
if n >= 0 then SOME n else NONE end | _ => NONE);
|
blanchet@54440
|
432 |
val _ = is_some disc orelse is_some eq_ctr0 orelse
|
panny@54791
|
433 |
primrec_error_eqn "no discriminator in equation" concl;
|
blanchet@54440
|
434 |
val ctr_no' =
|
blanchet@54440
|
435 |
if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
|
blanchet@54440
|
436 |
val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
|
panny@54857
|
437 |
val ctr = #ctr (nth ctr_specs ctr_no);
|
blanchet@54440
|
438 |
|
panny@54791
|
439 |
val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
|
panny@54857
|
440 |
val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
|
panny@54857
|
441 |
val prems = map (abstract (List.rev fun_args)) prems';
|
panny@54857
|
442 |
val real_prems =
|
panny@54857
|
443 |
(if catch_all orelse sequential then maps invert_prems_disj matchedss else []) @
|
panny@54791
|
444 |
(if catch_all then [] else prems);
|
blanchet@54440
|
445 |
|
panny@54857
|
446 |
val matchedsss' = AList.delete (op =) fun_name matchedsss
|
panny@54857
|
447 |
|> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [real_prems]);
|
panny@54791
|
448 |
|
panny@54791
|
449 |
val user_eqn =
|
panny@54857
|
450 |
(real_prems, betapply (#disc (nth ctr_specs ctr_no), applied_fun))
|
panny@54791
|
451 |
|>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop
|
panny@54791
|
452 |
|> Logic.list_implies;
|
blanchet@54440
|
453 |
in
|
panny@54478
|
454 |
(Disc {
|
blanchet@54440
|
455 |
fun_name = fun_name,
|
panny@54857
|
456 |
fun_T = fun_T,
|
panny@54538
|
457 |
fun_args = fun_args,
|
panny@54857
|
458 |
ctr = ctr,
|
blanchet@54440
|
459 |
ctr_no = ctr_no,
|
panny@54857
|
460 |
disc = #disc (nth ctr_specs ctr_no),
|
panny@54791
|
461 |
prems = real_prems,
|
panny@54791
|
462 |
user_eqn = user_eqn
|
panny@54857
|
463 |
}, matchedsss')
|
blanchet@54440
|
464 |
end;
|
blanchet@54440
|
465 |
|
panny@54791
|
466 |
fun co_dissect_eqn_sel fun_names corec_specs eqn' eqn =
|
blanchet@54440
|
467 |
let
|
blanchet@54440
|
468 |
val (lhs, rhs) = HOLogic.dest_eq eqn
|
blanchet@54440
|
469 |
handle TERM _ =>
|
blanchet@54440
|
470 |
primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
|
blanchet@54440
|
471 |
val sel = head_of lhs;
|
panny@54857
|
472 |
val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
|
blanchet@54440
|
473 |
handle TERM _ =>
|
blanchet@54440
|
474 |
primrec_error_eqn "malformed selector argument in left-hand side" eqn;
|
panny@54791
|
475 |
val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
|
blanchet@54440
|
476 |
handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
|
panny@54478
|
477 |
val (ctr_spec, sel) = #ctr_specs corec_spec
|
blanchet@54440
|
478 |
|> the o get_index (try (the o find_first (equal sel) o #sels))
|
panny@54478
|
479 |
|>> nth (#ctr_specs corec_spec);
|
panny@54791
|
480 |
val user_eqn = drop_All eqn';
|
blanchet@54440
|
481 |
in
|
panny@54478
|
482 |
Sel {
|
blanchet@54440
|
483 |
fun_name = fun_name,
|
panny@54857
|
484 |
fun_T = fun_T,
|
panny@54538
|
485 |
fun_args = fun_args,
|
panny@54478
|
486 |
ctr = #ctr ctr_spec,
|
panny@54478
|
487 |
sel = sel,
|
blanchet@54440
|
488 |
rhs_term = rhs,
|
panny@54791
|
489 |
user_eqn = user_eqn
|
blanchet@54440
|
490 |
}
|
blanchet@54440
|
491 |
end;
|
blanchet@54440
|
492 |
|
panny@54857
|
493 |
fun co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss =
|
blanchet@54440
|
494 |
let
|
blanchet@54440
|
495 |
val (lhs, rhs) = HOLogic.dest_eq imp_rhs;
|
blanchet@54440
|
496 |
val fun_name = head_of lhs |> fst o dest_Free;
|
panny@54857
|
497 |
val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
|
blanchet@54440
|
498 |
val (ctr, ctr_args) = strip_comb rhs;
|
panny@54857
|
499 |
val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
|
blanchet@54440
|
500 |
handle Option.Option => primrec_error_eqn "not a constructor" ctr;
|
panny@54478
|
501 |
|
panny@54857
|
502 |
val disc_imp_rhs = betapply (disc, lhs);
|
panny@54857
|
503 |
val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
|
panny@54857
|
504 |
then (NONE, matchedsss)
|
panny@54478
|
505 |
else apfst SOME (co_dissect_eqn_disc
|
panny@54857
|
506 |
sequential fun_names corec_specs imp_prems disc_imp_rhs matchedsss);
|
blanchet@54440
|
507 |
|
panny@54857
|
508 |
val sel_imp_rhss = (sels ~~ ctr_args)
|
blanchet@54440
|
509 |
|> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
|
blanchet@54440
|
510 |
|
panny@54497
|
511 |
val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n \<cdot> " ^
|
panny@54478
|
512 |
(is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_imp_rhs ^ "\n \<cdot> ")) "" ^
|
blanchet@54440
|
513 |
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss));
|
blanchet@54440
|
514 |
|
blanchet@54440
|
515 |
val eqns_data_sel =
|
panny@54791
|
516 |
map (co_dissect_eqn_sel fun_names corec_specs eqn') sel_imp_rhss;
|
blanchet@54440
|
517 |
in
|
panny@54857
|
518 |
(the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
|
blanchet@54440
|
519 |
end;
|
blanchet@54440
|
520 |
|
panny@54857
|
521 |
fun co_dissect_eqn sequential fun_names corec_specs eqn' matchedsss =
|
blanchet@54440
|
522 |
let
|
panny@54791
|
523 |
val eqn = drop_All eqn'
|
panny@54791
|
524 |
handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
|
panny@54791
|
525 |
val (imp_prems, imp_rhs) = Logic.strip_horn eqn
|
panny@54478
|
526 |
|> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
|
blanchet@54440
|
527 |
|
blanchet@54440
|
528 |
val head = imp_rhs
|
blanchet@54440
|
529 |
|> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
|
blanchet@54440
|
530 |
|> head_of;
|
blanchet@54440
|
531 |
|
blanchet@54440
|
532 |
val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
|
blanchet@54440
|
533 |
|
panny@54791
|
534 |
val discs = maps #ctr_specs corec_specs |> map #disc;
|
panny@54791
|
535 |
val sels = maps #ctr_specs corec_specs |> maps #sels;
|
panny@54791
|
536 |
val ctrs = maps #ctr_specs corec_specs |> map #ctr;
|
blanchet@54440
|
537 |
in
|
blanchet@54440
|
538 |
if member (op =) discs head orelse
|
blanchet@54440
|
539 |
is_some maybe_rhs andalso
|
blanchet@54440
|
540 |
member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
|
panny@54857
|
541 |
co_dissect_eqn_disc sequential fun_names corec_specs imp_prems imp_rhs matchedsss
|
blanchet@54440
|
542 |
|>> single
|
blanchet@54440
|
543 |
else if member (op =) sels head then
|
panny@54857
|
544 |
([co_dissect_eqn_sel fun_names corec_specs eqn' imp_rhs], matchedsss)
|
blanchet@54440
|
545 |
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
|
panny@54857
|
546 |
co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss
|
blanchet@54440
|
547 |
else
|
blanchet@54440
|
548 |
primrec_error_eqn "malformed function equation" eqn
|
blanchet@54440
|
549 |
end;
|
blanchet@54440
|
550 |
|
panny@54791
|
551 |
fun build_corec_arg_disc ctr_specs {fun_args, ctr_no, prems, ...} =
|
panny@54791
|
552 |
if is_none (#pred (nth ctr_specs ctr_no)) then I else
|
panny@54791
|
553 |
mk_conjs prems
|
panny@54791
|
554 |
|> curry subst_bounds (List.rev fun_args)
|
panny@54791
|
555 |
|> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
|
panny@54791
|
556 |
|> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
|
blanchet@54440
|
557 |
|
panny@54857
|
558 |
fun build_corec_arg_no_call sel_eqns sel =
|
panny@54857
|
559 |
find_first (equal sel o #sel) sel_eqns
|
panny@54857
|
560 |
|> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
|
panny@54857
|
561 |
|> the_default undef_const
|
panny@54548
|
562 |
|> K;
|
panny@54497
|
563 |
|
panny@54497
|
564 |
fun build_corec_arg_direct_call lthy has_call sel_eqns sel =
|
panny@54497
|
565 |
let
|
panny@54548
|
566 |
val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
|
panny@54791
|
567 |
fun rewrite is_end U _ t =
|
panny@54497
|
568 |
if U = @{typ bool} then @{term True} |> has_call t ? K @{term False} (* stop? *)
|
panny@54538
|
569 |
else if is_end = has_call t then undef_const
|
panny@54538
|
570 |
else if is_end then t (* end *)
|
panny@54497
|
571 |
else HOLogic.mk_tuple (snd (strip_comb t)); (* continue *)
|
panny@54538
|
572 |
fun massage rhs_term is_end t = massage_direct_corec_call
|
panny@54538
|
573 |
lthy has_call (rewrite is_end) [] (range_type (fastype_of t)) rhs_term;
|
panny@54497
|
574 |
in
|
panny@54538
|
575 |
if is_none maybe_sel_eqn then K I else
|
panny@54538
|
576 |
abs_tuple (#fun_args (the maybe_sel_eqn)) oo massage (#rhs_term (the maybe_sel_eqn))
|
panny@54497
|
577 |
end;
|
panny@54497
|
578 |
|
panny@54548
|
579 |
fun build_corec_arg_indirect_call lthy has_call sel_eqns sel =
|
panny@54548
|
580 |
let
|
panny@54548
|
581 |
val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
|
panny@54548
|
582 |
fun rewrite _ _ =
|
panny@54548
|
583 |
let
|
panny@54548
|
584 |
fun subst (Abs (v, T, b)) = Abs (v, T, subst b)
|
panny@54548
|
585 |
| subst (t as _ $ _) =
|
panny@54548
|
586 |
let val (u, vs) = strip_comb t in
|
panny@54548
|
587 |
if is_Free u andalso has_call u then
|
panny@54857
|
588 |
Const (@{const_name Inr}, dummyT) $
|
panny@54548
|
589 |
(try (foldr1 (fn (x, y) => Const (@{const_name Pair}, dummyT) $ x $ y)) vs
|
panny@54548
|
590 |
|> the_default (hd vs))
|
panny@54548
|
591 |
else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
|
panny@54548
|
592 |
list_comb (u |> map_types (K dummyT), map subst vs)
|
panny@54548
|
593 |
else
|
panny@54548
|
594 |
list_comb (subst u, map subst vs)
|
panny@54548
|
595 |
end
|
panny@54548
|
596 |
| subst t = t;
|
panny@54548
|
597 |
in
|
panny@54548
|
598 |
subst
|
panny@54548
|
599 |
end;
|
panny@54548
|
600 |
fun massage rhs_term t = massage_indirect_corec_call
|
panny@54857
|
601 |
lthy has_call rewrite [] (range_type (fastype_of t)) rhs_term;
|
panny@54548
|
602 |
in
|
panny@54548
|
603 |
if is_none maybe_sel_eqn then I else
|
panny@54548
|
604 |
abs_tuple (#fun_args (the maybe_sel_eqn)) o massage (#rhs_term (the maybe_sel_eqn))
|
panny@54548
|
605 |
end;
|
panny@54497
|
606 |
|
panny@54497
|
607 |
fun build_corec_args_sel lthy has_call all_sel_eqns ctr_spec =
|
panny@54478
|
608 |
let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
|
panny@54478
|
609 |
if null sel_eqns then I else
|
panny@54478
|
610 |
let
|
panny@54478
|
611 |
val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
|
panny@54478
|
612 |
|
panny@54478
|
613 |
val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
|
panny@54478
|
614 |
val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
|
panny@54478
|
615 |
val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
|
panny@54478
|
616 |
in
|
panny@54497
|
617 |
I
|
panny@54497
|
618 |
#> fold (fn (sel, n) => nth_map n
|
panny@54548
|
619 |
(build_corec_arg_no_call sel_eqns sel)) no_calls'
|
panny@54497
|
620 |
#> fold (fn (sel, (q, g, h)) =>
|
panny@54497
|
621 |
let val f = build_corec_arg_direct_call lthy has_call sel_eqns sel in
|
panny@54538
|
622 |
nth_map h (f false) o nth_map g (f true) o nth_map q (f true) end) direct_calls'
|
panny@54497
|
623 |
#> fold (fn (sel, n) => nth_map n
|
panny@54548
|
624 |
(build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
|
panny@54478
|
625 |
end
|
blanchet@54440
|
626 |
end;
|
blanchet@54440
|
627 |
|
panny@54791
|
628 |
fun co_build_defs lthy bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss =
|
panny@54791
|
629 |
let
|
panny@54791
|
630 |
val corec_specs' = take (length bs) corec_specs;
|
panny@54791
|
631 |
val corecs = map #corec corec_specs';
|
panny@54791
|
632 |
val ctr_specss = map #ctr_specs corec_specs';
|
panny@54497
|
633 |
val corec_args = hd corecs
|
panny@54497
|
634 |
|> fst o split_last o binder_types o fastype_of
|
panny@54497
|
635 |
|> map (Const o pair @{const_name undefined})
|
panny@54857
|
636 |
|> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
|
panny@54497
|
637 |
|> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
|
panny@54538
|
638 |
fun currys Ts t = if length Ts <= 1 then t else
|
panny@54538
|
639 |
t $ foldr1 (fn (u, v) => HOLogic.pair_const dummyT dummyT $ u $ v)
|
panny@54538
|
640 |
(length Ts - 1 downto 0 |> map Bound)
|
panny@54857
|
641 |
|> fold_rev (Term.abs o pair Name.uu) Ts;
|
panny@54538
|
642 |
|
panny@54497
|
643 |
val _ = tracing ("corecursor arguments:\n \<cdot> " ^
|
panny@54548
|
644 |
space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
|
blanchet@54440
|
645 |
|
panny@54791
|
646 |
val exclss' =
|
panny@54857
|
647 |
disc_eqnss
|
panny@54791
|
648 |
|> map (map (fn {fun_args, ctr_no, prems, ...} => (fun_args, ctr_no, prems))
|
panny@54791
|
649 |
#> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
|
panny@54791
|
650 |
#> maps (uncurry (map o pair)
|
panny@54791
|
651 |
#> map (fn ((fun_args, c, x), (_, c', y)) => ((c, c'), (x, mk_not (mk_conjs y)))
|
panny@54791
|
652 |
||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
|
panny@54791
|
653 |
||> Logic.list_implies
|
panny@54791
|
654 |
||> curry Logic.list_all (map dest_Free fun_args))))
|
blanchet@54440
|
655 |
in
|
blanchet@54440
|
656 |
map (list_comb o rpair corec_args) corecs
|
blanchet@54440
|
657 |
|> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
|
blanchet@54440
|
658 |
|> map2 currys arg_Tss
|
blanchet@54440
|
659 |
|> Syntax.check_terms lthy
|
traytel@54489
|
660 |
|> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
|
panny@54791
|
661 |
|> rpair exclss'
|
blanchet@54440
|
662 |
end;
|
blanchet@54440
|
663 |
|
panny@54859
|
664 |
fun mk_real_disc_eqns fun_binding arg_Ts {ctr_specs, ...} sel_eqns disc_eqns =
|
panny@54857
|
665 |
if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
|
panny@54857
|
666 |
let
|
panny@54857
|
667 |
val n = 0 upto length ctr_specs
|
panny@54857
|
668 |
|> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
|
panny@54859
|
669 |
val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
|
panny@54859
|
670 |
|> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
|
panny@54857
|
671 |
val extra_disc_eqn = {
|
panny@54857
|
672 |
fun_name = Binding.name_of fun_binding,
|
panny@54857
|
673 |
fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
|
panny@54859
|
674 |
fun_args = fun_args,
|
panny@54857
|
675 |
ctr = #ctr (nth ctr_specs n),
|
panny@54857
|
676 |
ctr_no = n,
|
panny@54857
|
677 |
disc = #disc (nth ctr_specs n),
|
panny@54857
|
678 |
prems = maps (invert_prems o #prems) disc_eqns,
|
panny@54857
|
679 |
user_eqn = undef_const};
|
panny@54857
|
680 |
in
|
panny@54857
|
681 |
chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
|
panny@54857
|
682 |
end;
|
panny@54857
|
683 |
|
blanchet@54440
|
684 |
fun add_primcorec sequential fixes specs lthy =
|
blanchet@54440
|
685 |
let
|
traytel@54489
|
686 |
val (bs, mxs) = map_split (apfst fst) fixes;
|
blanchet@54440
|
687 |
val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
|
blanchet@54440
|
688 |
|
blanchet@54440
|
689 |
(* copied from primrec_new *)
|
blanchet@54440
|
690 |
fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
|
blanchet@54440
|
691 |
|> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
|
blanchet@54440
|
692 |
|> map_filter I;
|
blanchet@54440
|
693 |
|
blanchet@54440
|
694 |
val callssss = []; (* FIXME *)
|
blanchet@54440
|
695 |
|
panny@54791
|
696 |
val ((nontriv, corec_specs', _, coinduct_thm, strong_co_induct_thm, coinduct_thmss,
|
blanchet@54440
|
697 |
strong_coinduct_thmss), lthy') =
|
blanchet@54440
|
698 |
corec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
|
blanchet@54440
|
699 |
|
blanchet@54440
|
700 |
val fun_names = map Binding.name_of bs;
|
panny@54791
|
701 |
val corec_specs = take (length fun_names) corec_specs'; (*###*)
|
blanchet@54440
|
702 |
|
blanchet@54440
|
703 |
val (eqns_data, _) =
|
panny@54791
|
704 |
fold_map (co_dissect_eqn sequential fun_names corec_specs) (map snd specs) []
|
blanchet@54440
|
705 |
|>> flat;
|
blanchet@54440
|
706 |
|
panny@54857
|
707 |
val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
|
panny@54791
|
708 |
|> partition_eq ((op =) o pairself #fun_name)
|
panny@54857
|
709 |
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|
panny@54791
|
710 |
|> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
|
panny@54857
|
711 |
val _ = disc_eqnss' |> map (fn x =>
|
panny@54857
|
712 |
let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
|
panny@54857
|
713 |
primrec_error_eqns "excess discriminator equations in definition"
|
panny@54857
|
714 |
(maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
|
panny@54791
|
715 |
|
panny@54791
|
716 |
val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
|
panny@54791
|
717 |
|> partition_eq ((op =) o pairself #fun_name)
|
panny@54857
|
718 |
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|
panny@54791
|
719 |
|> map (flat o snd);
|
panny@54791
|
720 |
|
panny@54497
|
721 |
val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
|
panny@54497
|
722 |
val arg_Tss = map (binder_types o snd o fst) fixes;
|
panny@54859
|
723 |
val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
|
panny@54791
|
724 |
val (defs, exclss') =
|
panny@54791
|
725 |
co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
|
panny@54791
|
726 |
|
panny@54791
|
727 |
(* try to prove (automatically generated) tautologies by ourselves *)
|
panny@54791
|
728 |
val exclss'' = exclss'
|
panny@54791
|
729 |
|> map (map (apsnd
|
blanchet@54836
|
730 |
(`(try (fn t => Goal.prove lthy [] [] t (mk_primcorec_assumption_tac lthy |> K))))));
|
panny@54791
|
731 |
val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
|
panny@54791
|
732 |
val (obligation_idxss, obligationss) = exclss''
|
panny@54791
|
733 |
|> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
|
panny@54791
|
734 |
|> split_list o map split_list;
|
panny@54791
|
735 |
|
panny@54791
|
736 |
fun prove thmss' def_thms' lthy =
|
panny@54791
|
737 |
let
|
panny@54791
|
738 |
val def_thms = map (snd o snd) def_thms';
|
panny@54791
|
739 |
|
panny@54791
|
740 |
val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
|
panny@54791
|
741 |
fun mk_exclsss excls n =
|
panny@54791
|
742 |
(excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
|
panny@54791
|
743 |
|-> fold (fn ((c, c'), thm) => nth_map c (nth_map c' (K [thm])));
|
panny@54791
|
744 |
val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
|
panny@54791
|
745 |
|-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
|
panny@54791
|
746 |
|
panny@54791
|
747 |
fun prove_disc {ctr_specs, ...} exclsss
|
panny@54857
|
748 |
{fun_name, fun_T, fun_args, ctr_no, prems, user_eqn, ...} =
|
panny@54859
|
749 |
if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
|
panny@54857
|
750 |
let
|
panny@54859
|
751 |
val {disc_corec, ...} = nth ctr_specs ctr_no;
|
panny@54857
|
752 |
val k = 1 + ctr_no;
|
panny@54857
|
753 |
val m = length prems;
|
panny@54857
|
754 |
val t =
|
panny@54857
|
755 |
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|
panny@54857
|
756 |
|> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
|
panny@54857
|
757 |
|> HOLogic.mk_Trueprop
|
panny@54857
|
758 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
759 |
|> curry Logic.list_all (map dest_Free fun_args);
|
panny@54857
|
760 |
in
|
panny@54857
|
761 |
mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
|
panny@54857
|
762 |
|> K |> Goal.prove lthy [] [] t
|
panny@54857
|
763 |
|> pair (#disc (nth ctr_specs ctr_no))
|
panny@54857
|
764 |
|> single
|
panny@54857
|
765 |
end;
|
panny@54857
|
766 |
|
panny@54857
|
767 |
fun prove_sel {ctr_specs, nested_maps, nested_map_idents, nested_map_comps, ...}
|
panny@54857
|
768 |
disc_eqns exclsss {fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} =
|
panny@54791
|
769 |
let
|
panny@54857
|
770 |
val (SOME ctr_spec) = find_first (equal ctr o #ctr) ctr_specs;
|
panny@54857
|
771 |
val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
|
panny@54857
|
772 |
val prems = the_default (maps (invert_prems o #prems) disc_eqns)
|
panny@54857
|
773 |
(find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
|
panny@54857
|
774 |
val sel_corec = find_index (equal sel) (#sels ctr_spec)
|
panny@54857
|
775 |
|> nth (#sel_corecs ctr_spec);
|
panny@54791
|
776 |
val k = 1 + ctr_no;
|
panny@54791
|
777 |
val m = length prems;
|
panny@54791
|
778 |
val t =
|
panny@54857
|
779 |
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|
panny@54857
|
780 |
|> curry betapply sel
|
panny@54857
|
781 |
|> rpair (abstract (List.rev fun_args) rhs_term)
|
panny@54857
|
782 |
|> HOLogic.mk_Trueprop o HOLogic.mk_eq
|
panny@54791
|
783 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
784 |
|> curry Logic.list_all (map dest_Free fun_args);
|
panny@54791
|
785 |
in
|
blanchet@54829
|
786 |
mk_primcorec_ctr_or_sel_tac lthy def_thms sel_corec k m exclsss
|
panny@54791
|
787 |
nested_maps nested_map_idents nested_map_comps
|
panny@54791
|
788 |
|> K |> Goal.prove lthy [] [] t
|
panny@54857
|
789 |
|> pair sel
|
panny@54791
|
790 |
end;
|
panny@54791
|
791 |
|
panny@54857
|
792 |
fun prove_ctr (_, disc_thms) (_, sel_thms') disc_eqns sel_eqns
|
panny@54857
|
793 |
{ctr, disc, sels, collapse, ...} =
|
panny@54859
|
794 |
let val _ = tracing ("disc = " ^ @{make_string} disc); in
|
panny@54857
|
795 |
if not (exists (equal ctr o #ctr) disc_eqns)
|
panny@54859
|
796 |
andalso not (exists (equal ctr o #ctr) sel_eqns)
|
panny@54859
|
797 |
andalso (warning ("no eqns for ctr " ^ Syntax.string_of_term lthy ctr); true)
|
panny@54859
|
798 |
orelse (* don't try to prove theorems when some sel_eqns are missing *)
|
panny@54857
|
799 |
filter (equal ctr o #ctr) sel_eqns
|
panny@54857
|
800 |
|> fst o finds ((op =) o apsnd #sel) sels
|
panny@54857
|
801 |
|> exists (null o snd)
|
panny@54857
|
802 |
andalso (warning ("sel_eqn(s) missing for ctr " ^ Syntax.string_of_term lthy ctr); true)
|
panny@54857
|
803 |
then [] else
|
panny@54857
|
804 |
let
|
panny@54857
|
805 |
val _ = tracing ("ctr = " ^ Syntax.string_of_term lthy ctr);
|
panny@54859
|
806 |
val _ = tracing (the_default "NO disc_eqn" (Option.map (curry (op ^) "disc = " o Syntax.string_of_term lthy o #disc) (find_first (equal ctr o #ctr) disc_eqns)));
|
panny@54859
|
807 |
val (fun_name, fun_T, fun_args, prems) =
|
panny@54859
|
808 |
(find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
|
panny@54859
|
809 |
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x))
|
panny@54859
|
810 |
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, []))
|
panny@54859
|
811 |
|> the o merge_options;
|
panny@54857
|
812 |
val m = length prems;
|
panny@54857
|
813 |
val t = sel_eqns
|
panny@54857
|
814 |
|> fst o finds ((op =) o apsnd #sel) sels
|
panny@54857
|
815 |
|> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
|
panny@54857
|
816 |
|> curry list_comb ctr
|
panny@54857
|
817 |
|> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
|
panny@54857
|
818 |
map Bound (length fun_args - 1 downto 0)))
|
panny@54857
|
819 |
|> HOLogic.mk_Trueprop
|
panny@54857
|
820 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
821 |
|> curry Logic.list_all (map dest_Free fun_args);
|
panny@54859
|
822 |
val maybe_disc_thm = AList.lookup (op =) disc_thms disc;
|
panny@54857
|
823 |
val sel_thms = map snd (filter (member (op =) sels o fst) sel_thms');
|
panny@54857
|
824 |
val _ = tracing ("t = " ^ Syntax.string_of_term lthy t);
|
panny@54857
|
825 |
val _ = tracing ("m = " ^ @{make_string} m);
|
panny@54857
|
826 |
val _ = tracing ("collapse = " ^ @{make_string} collapse);
|
panny@54859
|
827 |
val _ = tracing ("maybe_disc_thm = " ^ @{make_string} maybe_disc_thm);
|
panny@54857
|
828 |
val _ = tracing ("sel_thms = " ^ @{make_string} sel_thms);
|
panny@54857
|
829 |
in
|
panny@54859
|
830 |
mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
|
panny@54857
|
831 |
|> K |> Goal.prove lthy [] [] t
|
panny@54857
|
832 |
|> single
|
panny@54859
|
833 |
(*handle ERROR x => (warning x; []))*)
|
panny@54859
|
834 |
end
|
panny@54857
|
835 |
end;
|
panny@54857
|
836 |
|
panny@54857
|
837 |
val (disc_notes, disc_thmss) =
|
panny@54857
|
838 |
fun_names ~~ map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss
|
panny@54857
|
839 |
|> `(map (fn (fun_name, thms) =>
|
panny@54857
|
840 |
((Binding.qualify true fun_name (@{binding disc}), simp_attrs), [(map snd thms, [])])));
|
panny@54857
|
841 |
val (sel_notes, sel_thmss) =
|
panny@54857
|
842 |
fun_names ~~ map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss
|
panny@54857
|
843 |
|> `(map (fn (fun_name, thms) =>
|
panny@54857
|
844 |
((Binding.qualify true fun_name (@{binding sel}), simp_attrs), [(map snd thms, [])])));
|
panny@54857
|
845 |
val ctr_notes =
|
panny@54857
|
846 |
fun_names ~~ map5 (maps oooo prove_ctr) disc_thmss sel_thmss
|
panny@54857
|
847 |
disc_eqnss sel_eqnss (map #ctr_specs corec_specs)
|
panny@54791
|
848 |
|> map (fn (fun_name, thms) =>
|
panny@54857
|
849 |
((Binding.qualify true fun_name (@{binding ctr}), simp_attrs), [(thms, [])]));
|
panny@54791
|
850 |
in
|
panny@54857
|
851 |
lthy |> snd o Local_Theory.notes
|
panny@54857
|
852 |
(filter (not o null o fst o the_single o snd) (disc_notes @ sel_notes @ ctr_notes))
|
panny@54791
|
853 |
end;
|
blanchet@54440
|
854 |
in
|
blanchet@54440
|
855 |
lthy'
|
panny@54791
|
856 |
|> Proof.theorem NONE (curry (op #->) (fold_map Local_Theory.define defs) o prove) obligationss
|
blanchet@54440
|
857 |
|> Proof.refine (Method.primitive_text I)
|
blanchet@54440
|
858 |
|> Seq.hd
|
blanchet@54440
|
859 |
end
|
blanchet@54440
|
860 |
|
blanchet@54440
|
861 |
fun add_primcorec_cmd seq (raw_fixes, raw_specs) lthy =
|
blanchet@54440
|
862 |
let
|
blanchet@54440
|
863 |
val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
|
blanchet@54440
|
864 |
in
|
blanchet@54440
|
865 |
add_primcorec seq fixes specs lthy
|
blanchet@54440
|
866 |
handle ERROR str => primrec_error str
|
blanchet@54440
|
867 |
end
|
blanchet@54440
|
868 |
handle Primrec_Error (str, eqns) =>
|
blanchet@54440
|
869 |
if null eqns
|
blanchet@54440
|
870 |
then error ("primcorec error:\n " ^ str)
|
blanchet@54440
|
871 |
else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
|
blanchet@54440
|
872 |
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))
|
blanchet@54440
|
873 |
|
blanchet@54440
|
874 |
end;
|