allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Sugar for constructing LFPs and GFPs.
*)
signature BNF_FP_SUGAR =
sig
(* TODO: programmatic interface *)
end;
structure BNF_FP_Sugar : BNF_FP_SUGAR =
struct
open BNF_Util
open BNF_Wrap
open BNF_Def
open BNF_FP_Util
open BNF_LFP
open BNF_GFP
open BNF_FP_Sugar_Tactics
val caseN = "case";
val coitersN = "coiters";
val corecsN = "corecs";
val disc_coitersN = "disc_coiters";
val disc_corecsN = "disc_corecs";
val itersN = "iters";
val recsN = "recs";
val sel_coitersN = "sel_coiters";
val sel_corecsN = "sel_corecs";
fun split_list11 xs =
(map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
map #9 xs, map #10 xs, map #11 xs);
fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
| strip_map_type T = ([], T);
fun typ_subst inst (T as Type (s, Ts)) =
(case AList.lookup (op =) inst T of
NONE => Type (s, map (typ_subst inst) Ts)
| SOME T' => T')
| typ_subst inst T = the_default T (AList.lookup (op =) inst T);
fun retype_free (Free (s, _)) T = Free (s, T);
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs))
fun mk_predT T = T --> HOLogic.boolT;
fun mk_id T = Const (@{const_name id}, T --> T);
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
fun mk_uncurried2_fun f xss =
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
fun tack z_name (c, v) f =
let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
end;
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
fun merge_type_arg_constrained ctxt (T, c) (T', c') =
if T = T' then
(case (c, c') of
(_, NONE) => (T, c)
| (NONE, _) => (T, c')
| _ =>
if c = c' then
(T, c)
else
error ("Inconsistent sort constraints for type variable " ^
quote (Syntax.string_of_typ ctxt T)))
else
cannot_merge_types ();
fun merge_type_args_constrained ctxt (cAs, cAs') =
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
else cannot_merge_types ();
fun type_args_constrained_of (((cAs, _), _), _) = cAs;
val type_args_of = map fst o type_args_constrained_of;
fun type_binder_of (((_, b), _), _) = b;
fun mixfix_of ((_, mx), _) = mx;
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
fun disc_of ((((disc, _), _), _), _) = disc;
fun ctr_of ((((_, ctr), _), _), _) = ctr;
fun args_of (((_, args), _), _) = args;
fun defaults_of ((_, ds), _) = ds;
fun ctr_mixfix_of (_, mx) = mx;
fun prepare_datatype prepare_typ prepare_term lfp (no_dests, specs) fake_lthy no_defs_lthy =
let
val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
else ();
val constrained_As =
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
|> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
val As = map fst constrained_As;
val As' = map dest_TFree As;
val _ = (case duplicates (op =) As of [] => ()
| A :: _ => error ("Duplicate type parameter " ^
quote (Syntax.string_of_typ no_defs_lthy A)));
(* TODO: use sort constraints on type args *)
val N = length specs;
fun mk_fake_T b =
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
As);
val bs = map type_binder_of specs;
val fakeTs = map mk_fake_T bs;
val mixfixes = map mixfix_of specs;
val _ = (case duplicates Binding.eq_name bs of [] => ()
| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
val ctr_specss = map ctr_specs_of specs;
val disc_binderss = map (map disc_of) ctr_specss;
val ctr_binderss = map (map ctr_of) ctr_specss;
val ctr_argsss = map (map args_of) ctr_specss;
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
val sel_bindersss = map (map (map fst)) ctr_argsss;
val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
val _ = (case subtract (op =) As' rhs_As' of
[] => ()
| A' :: _ => error ("Extra type variables on rhs: " ^
quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
val ((Cs, Xs), _) =
no_defs_lthy
|> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
|> mk_TFrees N
||>> mk_TFrees N;
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
quote (Syntax.string_of_typ fake_lthy T)))
| eq_fpT _ _ = false;
fun freeze_fp (T as Type (s, Us)) =
(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
| freeze_fp T = T;
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs;
val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
fp_iter_thms, fp_rec_thms), lthy)) =
fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
val add_nested_bnf_names =
let
fun add (Type (s, Ts)) ss =
let val (needs, ss') = fold_map add Ts ss in
if exists I needs then (true, insert (op =) s ss') else (false, ss')
end
| add T ss = (member (op =) As T, ss);
in snd oo add end;
val nested_bnfs =
map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
val timer = time (Timer.startRealTimer ());
fun mk_unf_or_fld get_T Ts t =
let val Type (_, Ts0) = get_T (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
val mk_unf = mk_unf_or_fld domain_type;
val mk_fld = mk_unf_or_fld range_type;
val unfs = map (mk_unf As) unfs0;
val flds = map (mk_fld As) flds0;
val fpTs = map (domain_type o fastype_of) unfs;
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
val ns = map length ctr_Tsss;
val kss = map (fn n => 1 upto n) ns;
val mss = map (map length) ctr_Tsss;
val Css = map2 replicate ns Cs;
fun mk_iter_like Ts Us t =
let
val (binders, body) = strip_type (fastype_of t);
val (f_Us, prebody) = split_last binders;
val Type (_, Ts0) = if lfp then prebody else body;
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
in
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
end;
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
(zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
if lfp then
let
val y_Tsss =
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
ns mss fp_iter_fun_Ts;
val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
val ((gss, ysss), _) =
lthy
|> mk_Freess "f" g_Tss
||>> mk_Freesss "x" y_Tsss;
val yssss = map (map (map single)) ysss;
fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
if member (op =) Cs U then Us else [T]
| dest_rec_prodT T = [T];
val z_Tssss =
map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
val hss = map2 (map2 retype_free) gss h_Tss;
val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss;
val (zssss_tl, _) =
lthy
|> mk_Freessss "y" (map (map (map tl)) z_Tssss);
val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
in
(((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
([], [], [], (([], []), ([], [])), (([], []), ([], []))))
end
else
let
(*avoid "'a itself" arguments in coiterators and corecursors*)
val mss' = map (fn [0] => [1] | ms => ms) mss;
val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
| zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
fun mk_types maybe_dest_sumT fun_Ts =
let
val f_sum_prod_Ts = map range_type fun_Ts;
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
val f_Tssss =
map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
Cs mss' f_prod_Tss;
val q_Tssss =
map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
val ((((Free (z, _), cs), pss), gssss), _) =
lthy
|> yield_singleton (mk_Frees "z") dummyT
||>> mk_Frees "a" Cs
||>> mk_Freess "p" p_Tss
||>> mk_Freessss "g" g_Tssss;
val rssss = map (map (map (fn [] => []))) r_Tssss;
fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
if member (op =) Cs U then Us else [T]
| dest_corec_sumT T = [T];
val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
val hssss_hd = map2 (map2 (map2 (fn [g] => fn T :: _ => retype_free g T))) gssss h_Tssss;
val ((sssss, hssss_tl), _) =
lthy
|> mk_Freessss "q" s_Tssss
||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
fun mk_preds_getters_join [] [cf] = cf
| mk_preds_getters_join [cq] [cf, cf'] =
mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
fun mk_terms qssss fssss =
let
val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
in (pfss, cqfsss) end;
in
((([], [], []), ([], [], [])),
([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
(mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
end;
fun define_ctrs_case_for_type ((((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
disc_binders), sel_binderss), raw_sel_defaultss) no_defs_lthy =
let
val unfT = domain_type (fastype_of fld);
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
val ((((u, v), fs), xss), _) =
no_defs_lthy
|> yield_singleton (mk_Frees "u") unfT
||>> yield_singleton (mk_Frees "v") fpT
||>> mk_Frees "f" case_Ts
||>> mk_Freess "x" ctr_Tss;
val ctr_rhss =
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
val case_binder = Binding.suffix_name ("_" ^ caseN) b;
val case_rhs =
fold_rev Term.lambda (fs @ [v])
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
||> `Local_Theory.restore;
(*transforms defined frees into consts (and more)*)
val phi = Proof_Context.export_morphism lthy lthy';
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
val case_def = Morphism.thm phi raw_case_def;
val ctrs0 = map (Morphism.term phi) raw_ctrs;
val casex0 = Morphism.term phi raw_case;
val ctrs = map (mk_ctr As) ctrs0;
fun exhaust_tac {context = ctxt, ...} =
let
val fld_iff_unf_thm =
let
val goal =
fold_rev Logic.all [u, v]
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
in
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
(certify lthy fld) (certify lthy unf) fld_unf unf_fld)
|> Thm.close_derivation
|> Morphism.thm phi
end;
val sumEN_thm' =
Local_Defs.unfold lthy @{thms all_unit_eq}
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
(mk_sumEN_balanced n))
|> Morphism.thm phi;
in
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
end;
val inject_tacss =
map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
val half_distinct_tacss =
map (map (fn (def, def') => fn {context = ctxt, ...} =>
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
val case_tacs =
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
let
val fpT_to_C = fpT --> C;
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
let
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
val binder = Binding.suffix_name ("_" ^ suf) b;
val spec =
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
Term.list_comb (fp_iter_like,
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
in (binder, spec) end;
val iter_like_bundles =
[(iterN, fp_iter, iter_only),
(recN, fp_rec, rec_only)];
val (binders, specs) = map generate_iter_like iter_like_bundles |> split_list;
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map2 (fn b => fn spec =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) binders specs
||> `Local_Theory.restore;
(*transforms defined frees into consts (and more)*)
val phi = Proof_Context.export_morphism lthy lthy';
val [iter_def, rec_def] = map (Morphism.thm phi) defs;
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
in
((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
lthy)
end;
fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
let
val B_to_fpT = C --> fpT;
fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
Term.lambda c (mk_IfN sum_prod_T cps
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
pf_Tss))) =
let
val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
val binder = Binding.suffix_name ("_" ^ suf) b;
val spec =
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
Term.list_comb (fp_iter_like,
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
in (binder, spec) end;
val coiter_like_bundles =
[(coiterN, fp_iter, coiter_only),
(corecN, fp_rec, corec_only)];
val (binders, specs) = map generate_coiter_like coiter_like_bundles |> split_list;
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map2 (fn b => fn spec =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) binders specs
||> `Local_Theory.restore;
(*transforms defined frees into consts (and more)*)
val phi = Proof_Context.export_morphism lthy lthy';
val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
in
((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
corec_def), lthy)
end;
fun wrap lthy =
let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss,
sel_defaultss))) lthy
end;
val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
in
((wrap, define_iter_likes), lthy')
end;
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val map_ids = map map_id_of_bnf nested_bnfs;
fun mk_map Ts Us t =
let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
end;
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
let
val map0 = map_of_bnf (the (bnf_of lthy s));
val mapx = mk_map Ts Us map0;
val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
val args = map build_arg TUs;
in Term.list_comb (mapx, args) end;
fun derive_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
rec_defs), lthy) =
let
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
val giters = map (lists_bmoc gss) iters;
val hrecs = map (lists_bmoc hss) recs;
val (iter_thmss, rec_thmss) =
let
fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
fold_rev (fold_rev Logic.all) (xs :: fss)
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
fun build_call fiter_likes maybe_tick (T, U) =
if T = U then
mk_id T
else
(case find_index (curry (op =) T) fpTs of
~1 => build_map (build_call fiter_likes maybe_tick) T U
| j => maybe_tick (nth vs j) (nth fiter_likes j));
fun mk_U maybe_mk_prodT =
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
if member (op =) fpTs T then
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
else if exists_subtype (member (op =) fpTs) T then
[build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
else
[x];
val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
val hxsss =
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
val iter_tacss =
map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
val rec_tacss =
map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
in
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
goal_iterss iter_tacss,
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
goal_recss rec_tacss)
end;
val notes =
[(itersN, iter_thmss),
(recsN, rec_thmss)]
|> maps (fn (thmN, thmss) =>
map2 (fn b => fn thms =>
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
bs thmss);
in
lthy |> Local_Theory.notes notes |> snd
end;
fun derive_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss,
discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
let
val z = the_single zs;
val gcoiters = map (lists_bmoc pgss) coiters;
val hcorecs = map (lists_bmoc phss) corecs;
val (coiter_thmss, corec_thmss) =
let
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
fold_rev (fold_rev Logic.all) ([c] :: pfss)
(Logic.list_implies (seq_conds mk_goal_cond n k cps,
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
fun build_call fiter_likes maybe_tack (T, U) =
if T = U then
mk_id T
else
(case find_index (curry (op =) U) fpTs of
~1 => build_map (build_call fiter_likes maybe_tack) T U
| j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
fun mk_U maybe_mk_sumT =
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
let val T = fastype_of cqf in
if exists_subtype (member (op =) Cs) T then
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
else
cqf
end;
val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
val goal_coiterss =
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
val goal_corecss =
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
val coiter_tacss =
map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
ctr_defss;
val corec_tacss =
map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
ctr_defss;
in
(map2 (map2 (fn goal => fn tac =>
Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
goal_coiterss coiter_tacss,
map2 (map2 (fn goal => fn tac =>
Skip_Proof.prove lthy [] [] goal (tac o #context)
|> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
goal_corecss corec_tacss)
end;
fun mk_disc_coiter_like_thms [_] = K []
| mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
let
val (domT, ranT) = dest_funT (fastype_of sel0);
val arg_cong' =
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
[NONE, NONE, SOME (certify lthy sel0)] arg_cong
|> Thm.varifyT_global;
val sel_thm' = sel_thm RSN (2, trans);
in
coiter_like_thm RS arg_cong' RS sel_thm'
end;
val sel_coiter_thmsss =
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
val sel_corec_thmsss =
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
val notes =
[(coitersN, coiter_thmss),
(disc_coitersN, disc_coiter_thmss),
(sel_coitersN, map flat sel_coiter_thmsss),
(corecsN, corec_thmss),
(disc_corecsN, disc_corec_thmss),
(sel_corecsN, map flat sel_corec_thmsss)]
|> maps (fn (thmN, thmss) =>
map_filter (fn (_, []) => NONE | (b, thms) =>
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
[(thms, [])])) (bs ~~ thmss));
in
lthy |> Local_Theory.notes notes |> snd
end;
fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
val lthy' = lthy
|> fold_map define_ctrs_case_for_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss ~~ raw_sel_defaultsss)
|>> split_list |> wrap_types_and_define_iter_likes
|> (if lfp then derive_iter_rec_thms_for_types else derive_coiter_corec_thms_for_types);
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
(if lfp then "" else "co") ^ "datatype"));
in
(timer; lthy')
end;
fun datatype_cmd lfp (bundle as (_, specs)) lthy =
let
(* TODO: cleaner handling of fake contexts, without "background_theory" *)
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
locale and shadows an existing global type*)
val fake_thy = Theory.copy
#> fold (fn spec => perhaps (try (Sign.add_type lthy
(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
val fake_lthy = Proof_Context.background_theory fake_thy lthy;
in
prepare_datatype Syntax.read_typ Syntax.read_term lfp bundle fake_lthy lthy
end;
val parse_opt_binding_colon = Scan.optional (Parse.binding --| @{keyword ":"}) no_binder
val parse_ctr_arg =
@{keyword "("} |-- parse_opt_binding_colon -- Parse.typ --| @{keyword ")"} ||
(Parse.typ >> pair no_binder);
val parse_defaults =
@{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
val parse_single_spec =
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
val _ =
Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
(parse_datatype >> datatype_cmd true);
val _ =
Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
(parse_datatype >> datatype_cmd false);
end;