(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Sugared datatype and codatatype constructions.
*)
signature BNF_FP_SUGAR =
sig
val datatyp: bool ->
(mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
BNF_Def.BNF list -> local_theory ->
(term list * term list * term list * term list * thm * thm list * thm list * thm list *
thm list * thm list) * local_theory) ->
bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
(binding * typ) list) * (binding * term) list) * mixfix) list) list ->
local_theory -> local_theory
val parse_datatype_cmd: bool ->
(mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
BNF_Def.BNF list -> local_theory ->
(term list * term list * term list * term list * thm * thm list * thm list * thm list *
thm list * thm list) * local_theory) ->
(local_theory -> local_theory) parser
end;
structure BNF_FP_Sugar : BNF_FP_SUGAR =
struct
open BNF_Util
open BNF_Wrap
open BNF_Def
open BNF_FP
open BNF_FP_Sugar_Tactics
val simp_attrs = @{attributes [simp]};
fun split_list8 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);
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
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);
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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 u f = Term.lambda u (HOLogic.mk_prod (u, f $ u));
fun tack z_name (c, u) f =
let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
Term.lambda z (mk_sum_case (Term.lambda u u, 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 T T' = if T = T' then T else cannot_merge_types ();
fun merge_type_args (As, As') =
if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
fun is_triv_implies thm =
op aconv (Logic.dest_implies (Thm.prop_of thm))
handle TERM _ => false;
fun type_args_constrained_of (((cAs, _), _), _) = cAs;
fun type_binding_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 define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
no_defs_lthy0 =
let
(* TODO: sanity checks on arguments *)
(* TODO: integration with function package ("size") *)
val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
else ();
val nn = length specs;
val fp_bs = map type_binding_of specs;
val fp_b_names = map Binding.name_of fp_bs;
val fp_common_name = mk_common_name fp_b_names;
fun prepare_type_arg (ty, c) =
let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
TFree (s, prepare_constraint no_defs_lthy0 c)
end;
val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
val ((Bs, Cs), no_defs_lthy) =
no_defs_lthy0
|> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
|> mk_TFrees nn
||>> mk_TFrees nn;
(* 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 no_defs_lthy
(type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
fun mk_fake_T b =
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
unsorted_As);
val fake_Ts = map mk_fake_T fp_bs;
val mixfixes = map mixfix_of specs;
val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
val ctr_specss = map ctr_specs_of specs;
val disc_bindingss = map (map disc_of) ctr_specss;
val ctr_bindingss =
map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
val ctr_argsss = map (map args_of) ctr_specss;
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
val sel_bindingsss = map (map (map fst)) ctr_argsss;
val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
val (As :: _) :: fake_ctr_Tsss =
burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
val _ = (case duplicates (op =) unsorted_As of [] => ()
| A :: _ => error ("Duplicate type parameter " ^
quote (Syntax.string_of_typ no_defs_lthy A)));
val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
[] => ()
| A' :: _ => error ("Extra type variable on right-hand side: " ^
quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
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) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
| freeze_fp T = T;
val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
val fp_eqs =
map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
val (pre_bnfs, ((dtors0, ctors0, fp_iters0, fp_recs0, fp_induct, dtor_ctors, ctor_dtors,
ctor_injects, fp_iter_thms, fp_rec_thms), lthy)) =
fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
fun add_nesty_bnf_names Us =
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 =) Us T, ss);
in snd oo add end;
fun nesty_bnfs Us =
map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
val nesting_bnfs = nesty_bnfs As;
val nested_bnfs = nesty_bnfs Bs;
val timer = time (Timer.startRealTimer ());
fun mk_ctor_or_dtor get_T Ts t =
let val Type (_, Ts0) = get_T (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
val mk_ctor = mk_ctor_or_dtor range_type;
val mk_dtor = mk_ctor_or_dtor domain_type;
val ctors = map (mk_ctor As) ctors0;
val dtors = map (mk_dtor As) dtors0;
val fpTs = map (domain_type o fastype_of) dtors;
val exists_fp_subtype = exists_subtype (member (op =) fpTs);
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
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 (bindings, body) = strip_type (fastype_of t);
val (f_Us, prebody) = split_last bindings;
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), _))),
names_lthy) =
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) =
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) h_Tss gss;
val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
val (zssss_tl, lthy) =
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)),
([], [], [], (([], []), ([], [])), (([], []), ([], [])))), lthy)
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_pred1T) 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_pred1T (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) =
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 T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
val ((sssss, hssss_tl), lthy) =
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)))), lthy)
end;
fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), ctor), dtor), fp_iter), fp_rec),
ctor_dtor), dtor_ctor), ctor_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
let
val fp_b_name = Binding.name_of fp_b;
val dtorT = domain_type (fastype_of ctor);
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 ((((w, fs), xss), u'), _) =
no_defs_lthy
|> yield_singleton (mk_Frees "w") dtorT
||>> mk_Frees "f" case_Ts
||>> mk_Freess "x" ctr_Tss
||>> yield_singleton Variable.variant_fixes fp_b_name;
val u = Free (u', fpT);
val ctr_rhss =
map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
val case_rhs =
fold_rev Term.lambda (fs @ [u])
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
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_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
||> `Local_Theory.restore;
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 ctor_iff_dtor_thm =
let
val goal =
fold_rev Logic.all [w, u]
(mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
in
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
(certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
|> Thm.close_derivation
|> Morphism.thm phi
end;
val sumEN_thm' =
unfold_defs 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 ctor_iff_dtor_thm sumEN_thm'
end;
val inject_tacss =
map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
val half_distinct_tacss =
map (map (fn (def, def') => fn {context = ctxt, ...} =>
mk_half_distinct_tac ctxt ctor_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 dtor_ctor) ks ms ctr_defs;
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
fun define_iter_rec (wrap_res, 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 binding = Binding.suffix_name ("_" ^ suf) fp_b;
val spec =
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
Term.list_comb (fp_iter_like,
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
in (binding, spec) end;
val iter_like_infos =
[(iterN, fp_iter, iter_only),
(recN, fp_rec, rec_only)];
val (bindings, specs) = map generate_iter_like iter_like_infos |> 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) bindings specs
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val [iter_def, rec_def] = map (Morphism.thm phi) defs;
val [iterx, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
in
((wrap_res, ctrs, iterx, recx, xss, ctr_defs, iter_def, rec_def), lthy)
end;
fun define_coiter_corec (wrap_res, 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 binding = Binding.suffix_name ("_" ^ suf) fp_b;
val spec =
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
Term.list_comb (fp_iter_like,
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
in (binding, spec) end;
val coiter_like_infos =
[(coiterN, fp_iter, coiter_only),
(corecN, fp_rec, corec_only)];
val (bindings, specs) = map generate_coiter_like coiter_like_infos |> 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) bindings specs
||> `Local_Theory.restore;
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
((wrap_res, ctrs, coiter, corec, xss, ctr_defs, 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_bindings, (sel_bindingss,
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 pre_set_defss = map set_defs_of_bnf pre_bnfs;
val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
fun mk_map live Ts Us t =
let
val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (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 bnf = the (bnf_of lthy s);
val live = live_of_bnf bnf;
val mapx = mk_map live Ts Us (map_of_bnf bnf);
val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
val args = map build_arg TUs;
in Term.list_comb (mapx, args) end;
val mk_simp_thmss =
map3 (fn (_, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn iter_likes =>
injects @ distincts @ cases @ rec_likes @ iter_likes);
fun derive_induct_iter_rec_thms_for_types ((wrap_ress, ctrss, iters, recs, xsss, ctr_defss,
iter_defs, rec_defs), lthy) =
let
val (((phis, phis'), us'), names_lthy) =
lthy
|> mk_Frees' "P" (map mk_pred1T fpTs)
||>> Variable.variant_fixes fp_b_names;
val us = map2 (curry Free) us' fpTs;
fun mk_sets_nested bnf =
let
val Type (T_name, Us) = T_of_bnf bnf;
val lives = lives_of_bnf bnf;
val sets = sets_of_bnf bnf;
fun mk_set U =
(case find_index (curry (op =) U) lives of
~1 => Term.dummy
| i => nth sets i);
in
(T_name, map mk_set Us)
end;
val setss_nested = map mk_sets_nested nested_bnfs;
val (induct_thms, induct_thm) =
let
fun mk_set Ts t =
let val Type (_, Ts0) = domain_type (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
(case find_index (curry (op =) T) fpTs of
~1 =>
(case AList.lookup (op =) setss_nested T_name of
NONE => []
| SOME raw_sets0 =>
let
val (Ts, raw_sets) =
split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
val sets = map (mk_set Ts0) raw_sets;
val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
val xysets = map (pair x) (ys ~~ sets);
val ppremss = map (mk_raw_prem_prems names_lthy') ys;
in
flat (map2 (map o apfst o cons) xysets ppremss)
end)
| i => [([], (i + 1, x))])
| mk_raw_prem_prems _ _ = [];
fun close_prem_prem xs t =
fold_rev Logic.all (map Free (drop (nn + length xs)
(rev (Term.add_frees t (map dest_Free xs @ phis'))))) t;
fun mk_prem_prem xs (xysets, (j, x)) =
close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
HOLogic.mk_Trueprop (nth phis (j - 1) $ x)));
fun mk_raw_prem phi ctr ctr_Ts =
let
val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
val pprems = maps (mk_raw_prem_prems names_lthy') xs;
in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
fun mk_prem (xs, raw_pprems, concl) =
fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
val goal =
Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) phis us)));
val kksss = map (map (map (fst o snd) o #2)) raw_premss;
val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
val induct_thm =
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
mk_induct_tac ctxt ns mss kksss (flat ctr_defss) ctor_induct'
nested_set_natural's pre_set_defss)
|> singleton (Proof_Context.export names_lthy lthy)
in
`(conj_dests nn) induct_thm
end;
(* TODO: Generate nicer names in case of clashes *)
val induct_cases = Datatype_Prop.indexify_names (maps (map base_name_of_ctr) ctrss);
val (iter_thmss, rec_thmss) =
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;
fun mk_goal 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
id_const 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 us 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 intr_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_fp_subtype T then
[build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
else
[x];
val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
val iter_goalss = map5 (map4 o mk_goal gss) giters xctrss gss xsss gxsss;
val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
val iter_tacss =
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
ctr_defss;
val rec_tacss =
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
ctr_defss;
fun prove goal tac = Skip_Proof.prove lthy [] [] goal (tac o #context);
in
(map2 (map2 prove) iter_goalss iter_tacss,
map2 (map2 prove) rec_goalss rec_tacss)
end;
val simp_thmss = mk_simp_thmss wrap_ress rec_thmss iter_thmss;
val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
(* TODO: Also note "recs", "simps", and "splits" if "nn > 1" (for compatibility with the
old package)? And for codatatypes as well? *)
val common_notes =
(if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
val notes =
[(inductN, map single induct_thms,
fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
(itersN, iter_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
(recsN, rec_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
(simpsN, simp_thmss, K [])]
|> maps (fn (thmN, thmss, attrs) =>
map3 (fn b => fn Type (T_name, _) => fn thms =>
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs T_name),
[(thms, [])])) fp_bs fpTs thmss);
in
lthy |> Local_Theory.notes (common_notes @ notes) |> snd
end;
fun derive_coinduct_coiter_corec_thms_for_types ((wrap_ress, ctrss, coiters, corecs, _,
ctr_defss, coiter_defs, corec_defs), lthy) =
let
val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
val selsss = map #2 wrap_ress;
val disc_thmsss = map #6 wrap_ress;
val discIss = map #7 wrap_ress;
val sel_thmsss = map #8 wrap_ress;
val (us', _) =
lthy
|> Variable.variant_fixes fp_b_names;
val us = map2 (curry Free) us' fpTs;
val (coinduct_thms, coinduct_thm) =
let
val coinduct_thm = fp_induct;
in
`(conj_dests nn) coinduct_thm
end;
fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
val z = the_single zs;
val gcoiters = map (lists_bmoc pgss) coiters;
val hcorecs = map (lists_bmoc phss) corecs;
val (coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss) =
let
fun mk_goal pfss c cps fcoiter_like n k ctr m cfs' =
fold_rev (fold_rev Logic.all) ([c] :: pfss)
(Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) 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
id_const 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 us 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 intr_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 (intr_calls gcoiters (K I) (K I)))) crgsss;
val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
val coiter_goalss =
map8 (map4 oooo mk_goal pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
val corec_goalss =
map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
val coiter_tacss =
map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
ctr_defss;
val corec_tacss =
map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
ctr_defss;
fun prove goal tac =
Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation;
val coiter_thmss = map2 (map2 prove) coiter_goalss coiter_tacss;
val corec_thmss =
map2 (map2 prove) corec_goalss corec_tacss
|> map (map (unfold_defs lthy @{thms sum_case_if}));
val coiter_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
val filter_safesss =
map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
curry (op ~~));
val safe_coiter_thmss = filter_safesss coiter_safesss coiter_thmss;
val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
in
(coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss)
end;
val (disc_coiter_iff_thmss, disc_corec_iff_thmss) =
let
fun mk_goal c cps fcoiter_like n k disc =
mk_Trueprop_eq (disc $ (fcoiter_like $ c),
if n = 1 then @{const True}
else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
val coiter_goalss = map6 (map2 oooo mk_goal) cs cpss gcoiters ns kss discss;
val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
fun mk_case_split' cp =
Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
val case_splitss' = map (map mk_case_split') cpss;
val coiter_tacss =
map3 (map oo mk_disc_coiter_like_iff_tac) case_splitss' coiter_thmss disc_thmsss;
val corec_tacss =
map3 (map oo mk_disc_coiter_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
fun prove goal tac =
Skip_Proof.prove lthy [] [] goal (tac o #context)
|> Thm.close_derivation
|> singleton (Proof_Context.export names_lthy no_defs_lthy);
fun proves [_] [_] = []
| proves goals tacs = map2 prove goals tacs;
in
(map2 proves coiter_goalss coiter_tacss,
map2 proves corec_goalss corec_tacss)
end;
fun mk_disc_coiter_like_thms coiter_likes discIs =
map (op RS) (filter_out (is_triv_implies o snd) (coiter_likes ~~ discIs));
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 sel sel_thm =
let
val (domT, ranT) = dest_funT (fastype_of sel);
val arg_cong' =
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
[NONE, NONE, SOME (certify lthy sel)] arg_cong
|> Thm.varifyT_global;
val sel_thm' = sel_thm RSN (2, trans);
in
coiter_like_thm RS arg_cong' RS sel_thm'
end;
fun mk_sel_coiter_like_thms coiter_likess =
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_likess selsss sel_thmsss |> map flat;
val sel_coiter_thmss = mk_sel_coiter_like_thms coiter_thmss;
val sel_corec_thmss = mk_sel_coiter_like_thms corec_thmss;
fun zip_coiter_like_thms coiter_likes disc_coiter_likes sel_coiter_likes =
coiter_likes @ disc_coiter_likes @ sel_coiter_likes;
val simp_thmss =
mk_simp_thmss wrap_ress
(map3 zip_coiter_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
(map3 zip_coiter_like_thms safe_coiter_thmss disc_coiter_thmss sel_coiter_thmss);
val anonymous_notes =
[(flat safe_coiter_thmss @ flat safe_corec_thmss, simp_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
val common_notes =
(if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
val notes =
[(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
(coitersN, coiter_thmss, []),
(corecsN, corec_thmss, []),
(disc_coiter_iffN, disc_coiter_iff_thmss, simp_attrs),
(disc_coitersN, disc_coiter_thmss, simp_attrs),
(disc_corec_iffN, disc_corec_iff_thmss, simp_attrs),
(disc_corecsN, disc_corec_thmss, simp_attrs),
(sel_coitersN, sel_coiter_thmss, simp_attrs),
(sel_corecsN, sel_corec_thmss, simp_attrs),
(simpsN, simp_thmss, [])]
|> maps (fn (thmN, thmss, attrs) =>
map_filter (fn (_, []) => NONE | (b, thms) =>
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
[(thms, [])])) (fp_bs ~~ thmss));
in
lthy |> Local_Theory.notes (anonymous_notes @ common_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_list8
val lthy' = lthy
|> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~ fp_iters ~~
fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
|>> split_list |> wrap_types_and_define_iter_likes
|> (if lfp then derive_induct_iter_rec_thms_for_types
else derive_coinduct_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;
val datatyp = define_datatype (K I) (K I) (K I);
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
val parse_ctr_arg =
@{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
(Parse.typ >> pair Binding.empty);
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;
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;
end;