(* Title: HOL/BNF/Tools/bnf_fp_def_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Sugared datatype and codatatype constructions.
*)
signature BNF_FP_DEF_SUGAR =
sig
type fp_sugar =
{T: typ,
fp: BNF_FP_Util.fp_kind,
index: int,
Xs: typ list,
ctr_TsssXs : typ list list list,
pre_bnfs: BNF_Def.bnf list,
fp_res: BNF_FP_Util.fp_result,
ctr_defss: thm list list,
ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
un_folds: term list,
co_recs: term list,
co_induct: thm,
strong_co_induct: thm,
un_fold_thmss: thm list list,
co_rec_thmss: thm list list};
val of_fp_sugar: (fp_sugar -> 'a list) -> fp_sugar -> 'a
val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
val fp_sugar_of: Proof.context -> string -> fp_sugar option
val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
val exists_subtype_in: typ list -> typ -> bool
val flat_rec: ('a -> 'b list) -> 'a list -> 'b list
val mk_co_iter: theory -> BNF_FP_Util.fp_kind -> typ -> typ list -> term -> term
val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
val indexify_fst: ''a list -> (int -> ''a * 'b -> 'c) -> ''a * 'b -> 'c
val mk_un_fold_co_rec_prelims: BNF_FP_Util.fp_kind -> typ list -> typ list -> int list ->
int list list -> term list -> term list -> Proof.context ->
(term list * term list * ((term list list * typ list list * term list list list list)
* (term list list * typ list list * term list list list list)) option
* (term list * term list list
* ((term list list * term list list list list * term list list list list)
* (typ list * typ list list list * typ list list))
* ((term list list * term list list list list * term list list list list)
* (typ list * typ list list list * typ list list))) option)
* Proof.context
val mk_map: int -> typ list -> typ list -> term -> term
val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
val mk_iter_fun_arg_typessss: typ list -> int list -> int list list -> term ->
typ list list list list
val define_fold_rec: (term list list * typ list list * term list list list list)
* (term list list * typ list list * term list list list list) -> (string -> binding) ->
typ list -> typ list -> term -> term -> Proof.context ->
(term * term * thm * thm) * Proof.context
val define_unfold_corec: term list * term list list
* ((term list list * term list list list list * term list list list list)
* (typ list * typ list list list * typ list list))
* ((term list list * term list list list list * term list list list list)
* (typ list * typ list list list * typ list list)) ->
(string -> binding) -> typ list -> typ list -> term -> term -> Proof.context ->
(term * term * thm * thm) * Proof.context
val derive_induct_fold_rec_thms_for_types: BNF_Def.bnf list -> term list -> term list -> thm ->
thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
term list list -> thm list list -> term list -> term list -> thm list -> thm list ->
local_theory ->
(thm * thm list * Args.src list) * (thm list list * Args.src list)
* (thm list list * Args.src list)
val derive_coinduct_unfold_corec_thms_for_types: BNF_Def.bnf list -> term list -> term list ->
thm -> thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list ->
typ list -> typ list -> typ list -> int list list -> int list list -> int list ->
thm list list -> BNF_Ctr_Sugar.ctr_sugar list -> term list -> term list -> thm list ->
thm list -> local_theory ->
(thm * thm list * thm * thm list * Args.src list)
* (thm list list * thm list list * Args.src list)
* (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
* (thm list list * thm list list * Args.src list)
* (thm list list * thm list list * Args.src list)
val co_datatypes: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
(bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
((((binding * binding) * (binding * typ) list) * (binding * term) list) *
mixfix) list) list ->
local_theory -> local_theory
val parse_co_datatype_cmd: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
(local_theory -> local_theory) parser
end;
structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
struct
open BNF_Util
open BNF_Ctr_Sugar
open BNF_Def
open BNF_FP_Util
open BNF_FP_Def_Sugar_Tactics
val EqN = "Eq_";
type fp_sugar =
{T: typ,
fp: fp_kind,
index: int,
Xs: typ list,
ctr_TsssXs : typ list list list,
pre_bnfs: bnf list,
fp_res: fp_result,
ctr_defss: thm list list,
ctr_sugars: ctr_sugar list,
un_folds: term list,
co_recs: term list,
co_induct: thm,
strong_co_induct: thm,
un_fold_thmss: thm list list,
co_rec_thmss: thm list list};
fun of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index;
fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
{T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
(* There is no point in morphing the low-level fields "Xs" and "ctr_TsssXs". *)
fun morph_fp_sugar phi {T, fp, index, Xs, ctr_TsssXs, pre_bnfs, fp_res, ctr_defss, ctr_sugars,
un_folds, co_recs, co_induct, strong_co_induct, un_fold_thmss, co_rec_thmss} =
{T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
Xs = Xs, ctr_TsssXs = ctr_TsssXs, fp_res = morph_fp_result phi fp_res,
ctr_defss = map (map (Morphism.thm phi)) ctr_defss,
ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars, un_folds = map (Morphism.term phi) un_folds,
co_recs = map (Morphism.term phi) co_recs, co_induct = Morphism.thm phi co_induct,
strong_co_induct = Morphism.thm phi strong_co_induct,
un_fold_thmss = map (map (Morphism.thm phi)) un_fold_thmss,
co_rec_thmss = map (map (Morphism.thm phi)) co_rec_thmss};
structure Data = Generic_Data
(
type T = fp_sugar Symtab.table;
val empty = Symtab.empty;
val extend = I;
val merge = Symtab.merge eq_fp_sugar;
);
val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof;
fun register_fp_sugar key fp_sugar =
Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (Symtab.update_new (key, morph_fp_sugar phi fp_sugar)));
fun register_fp_sugars fp Xs ctr_TsssXs pre_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars un_folds
co_recs co_induct strong_co_induct un_fold_thmss co_rec_thmss lthy =
(0, lthy)
|> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
register_fp_sugar s {T = T, fp = fp, index = kk, Xs = Xs, ctr_TsssXs = ctr_TsssXs,
pre_bnfs = pre_bnfs, fp_res = fp_res, ctr_defss = ctr_defss, ctr_sugars = ctr_sugars,
un_folds = un_folds, co_recs = co_recs, co_induct = co_induct,
strong_co_induct = strong_co_induct, un_fold_thmss = un_fold_thmss,
co_rec_thmss = co_rec_thmss} lthy)) Ts
|> snd;
(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
fun quasi_unambiguous_case_names names =
let
val ps = map (`Long_Name.base_name) names;
val dups = Library.duplicates (op =) (map fst ps);
fun underscore s =
let val ss = space_explode Long_Name.separator s in
space_implode "_" (drop (length ss - 2) ss)
end;
in
map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
end;
val mp_conj = @{thm mp_conj};
val simp_attrs = @{attributes [simp]};
val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
fun tvar_subst thy Ts Us =
Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) [];
val exists_subtype_in = Term.exists_subtype o member (op =);
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
fun typ_subst_nonatomic inst (T as Type (s, Ts)) =
(case AList.lookup (op =) inst T of
NONE => Type (s, map (typ_subst_nonatomic inst) Ts)
| SOME T' => T')
| typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T);
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
fun flat_rec unzipf xs =
let val ps = map unzipf xs in
(* The first line below gives the preferred order. The second line is for compatibility with the
old datatype package: *)
(*
flat ps
*)
map hd ps @ maps tl ps
end;
fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
| flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
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_rec I xss);
fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
fun flip_rels lthy n thm =
let
val Rs = Term.add_vars (prop_of thm) [];
val Rs' = rev (drop (length Rs - n) Rs);
val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
in
Drule.cterm_instantiate cRs thm
end;
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;
fun mk_co_iter thy fp fpT Cs t =
let
val (bindings, body) = strip_type (fastype_of t);
val (f_Cs, prebody) = split_last bindings;
val fpT0 = if fp = Least_FP then prebody else body;
val Cs0 = distinct (op =) (map (if fp = Least_FP then body_type else domain_type) f_Cs);
val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs);
in
Term.subst_TVars rho t
end;
fun mk_co_iters thy fp fpTs Cs ts0 =
let
val nn = length fpTs;
val (fpTs0, Cs0) =
map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
|> split_list;
val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
in
map (Term.subst_TVars rho) ts0
end;
val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
fun meta_unzip_rec getT left right nested fpTs y =
let val T = getT y in
if member (op =) fpTs T then [left y, right y]
else if exists_subtype_in fpTs T then [nested y]
else [y]
end;
fun project_co_recT special_Tname Cs proj =
let
fun project (Type (s, Ts as [T, U])) =
if s = special_Tname andalso member (op =) Cs U then proj (T, U)
else Type (s, map project Ts)
| project (Type (s, Ts)) = Type (s, map project Ts)
| project T = T;
in project end;
val project_recT = project_co_recT @{type_name prod};
val project_corecT = project_co_recT @{type_name sum};
fun unzip_recT Cs (T as Type (@{type_name prod}, Ts as [_, U])) =
if member (op =) Cs U then Ts else [T]
| unzip_recT _ T = [T];
fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
fun mk_iter_fun_arg_typessss Cs ns mss =
mk_fp_iter_fun_types
#> map3 mk_fun_arg_typess ns mss
#> map (map (map (unzip_recT Cs)));
fun mk_fold_rec_args_types Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy =
let
val Css = map2 replicate ns Cs;
val y_Tsss = map3 mk_fun_arg_typess ns mss ctor_fold_fun_Ts;
val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
val ((gss, ysss), lthy) =
lthy
|> mk_Freess "f" g_Tss
||>> mk_Freesss "x" y_Tsss;
val yssss = map (map (map single)) ysss;
val z_Tssss =
map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o
dest_sumTN_balanced n o domain_type) ns mss ctor_rec_fun_Ts;
val z_Tsss = map3 mk_fun_arg_typess ns mss ctor_rec_fun_Ts;
val z_Tsss' = map (map (flat_rec I)) z_Tssss;
val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' 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;
fun mk_unfold_corec_args_types Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy =
let
(*avoid "'a itself" arguments in coiterators and corecursors*)
fun repair_arity [0] = [1]
| repair_arity ms = ms;
fun unzip_corecT T =
if exists_subtype_in Cs T then [project_corecT Cs fst T, project_corecT Cs snd T]
else [T];
val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
fun mk_types maybe_unzipT 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_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
val f_Tssss = map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
val q_Tssss =
map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
in (q_Tssss, f_Tssss, (f_sum_prod_Ts, f_Tsss, pf_Tss)) end;
val (r_Tssss, g_Tssss, unfold_types) = mk_types single dtor_unfold_fun_Ts;
val (s_Tssss, h_Tssss, corec_types) = mk_types unzip_corecT dtor_corec_fun_Ts;
val (((cs, pss), gssss), lthy) =
lthy
|> mk_Frees "a" Cs
||>> mk_Freess "p" p_Tss
||>> mk_Freessss "g" g_Tssss;
val rssss = map (map (map (fn [] => []))) r_Tssss;
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 (map o rapp) cs pss;
fun mk_args qssss fssss =
let
val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
val cqssss = map2 (map o map o map o rapp) cs qssss;
val cfssss = map2 (map o map o map o rapp) cs fssss;
in (pfss, cqssss, cfssss) end;
val unfold_args = mk_args rssss gssss;
val corec_args = mk_args sssss hssss;
in
((cs, cpss, (unfold_args, unfold_types), (corec_args, corec_types)), lthy)
end;
fun mk_un_fold_co_rec_prelims fp fpTs Cs ns mss fp_folds0 fp_recs0 lthy =
let
val thy = Proof_Context.theory_of lthy;
val (fp_fold_fun_Ts, fp_folds) = mk_co_iters thy fp fpTs Cs fp_folds0
|> `(mk_fp_iter_fun_types o hd);
val (fp_rec_fun_Ts, fp_recs) = mk_co_iters thy fp fpTs Cs fp_recs0
|> `(mk_fp_iter_fun_types o hd);
val ((fold_rec_args_types, unfold_corec_args_types), lthy') =
if fp = Least_FP then
mk_fold_rec_args_types Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
|>> (rpair NONE o SOME)
else
mk_unfold_corec_args_types Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
|>> (pair NONE o SOME)
in
((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy')
end;
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 mk_rel live Ts Us t =
let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
end;
fun liveness_of_fp_bnf n bnf =
(case T_of_bnf bnf of
Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
| _ => replicate n false);
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 reassoc_conjs thm =
reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
handle THM _ => thm;
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
fun type_binding_of ((((_, b), _), _), _) = b;
fun map_binding_of (((_, (b, _)), _), _) = b;
fun rel_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 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 ctxt ctr_Tsss Us =
map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
fun indexify_fst xs f (x, y) = f (find_index (curry (op =) x) xs) (x, y);
fun build_map lthy build_simple =
let
fun build (TU as (T, U)) =
if T = U then
id_const T
else
(case TU of
(Type (s, Ts), Type (s', Us)) =>
if s = s' then
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)));
in Term.list_comb (mapx, map build TUs') end
else
build_simple TU
| _ => build_simple TU);
in build end;
fun mk_iter_body lthy Cs ctor_iter fss xssss =
let
fun build_proj sel sel_const (x as Free (_, T)) =
build_map lthy (sel_const o fst) (T, project_recT Cs sel T) $ x;
in
Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)
end;
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
let val n = length cqfss in
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)))
end;
fun mk_coiter_body lthy cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter =
let
fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
fun build_dtor_coiter_arg _ [] [cf] = cf
| build_dtor_coiter_arg T [cq] [cf, cf'] =
mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
(build_sum_inj Inr_const (fastype_of cf', T) $ cf')
val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
in
Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss)
end;
fun define_fold_rec (fold_only, rec_only) mk_binding fpTs Cs ctor_fold ctor_rec lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
val nn = length fpTs;
val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of ctor_fold));
fun generate_iter (suf, ctor_iter, (fss, f_Tss, xssss)) =
let
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
val binding = mk_binding suf;
val spec =
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
mk_iter_body lthy0 Cs ctor_iter fss xssss);
in (binding, spec) end;
val binding_specs =
map generate_iter [(foldN, ctor_fold, fold_only), (recN, ctor_rec, rec_only)];
val ((csts, defs), (lthy', lthy)) = lthy0
|> apfst split_list o fold_map (fn (b, spec) =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) binding_specs
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val [fold_def, rec_def] = map (Morphism.thm phi) defs;
val [foldx, recx] = map (mk_co_iter thy Least_FP fpT Cs o Morphism.term phi) csts;
in
((foldx, recx, fold_def, rec_def), lthy')
end;
(* TODO: merge with above function? *)
fun define_unfold_corec (cs, cpss, unfold_only, corec_only) mk_binding fpTs Cs dtor_unfold
dtor_corec lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
val nn = length fpTs;
val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of dtor_unfold));
fun generate_coiter (suf, dtor_coiter, ((pfss, cqssss, cfssss),
(f_sum_prod_Ts, f_Tsss, pf_Tss))) =
let
val res_T = fold_rev (curry (op --->)) pf_Tss C_to_fpT;
val binding = mk_binding suf;
val spec =
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
mk_coiter_body lthy0 cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter);
in (binding, spec) end;
val binding_specs =
map generate_coiter [(unfoldN, dtor_unfold, unfold_only), (corecN, dtor_corec, corec_only)];
val ((csts, defs), (lthy', lthy)) = lthy0
|> apfst split_list o fold_map (fn (b, spec) =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) binding_specs
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
val [unfold, corec] = map (mk_co_iter thy Greatest_FP fpT Cs o Morphism.term phi) csts;
in
((unfold, corec, unfold_def, corec_def), lthy')
end ;
fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_folds ctor_recs ctor_induct ctor_fold_thms
ctor_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctrss ctr_defss folds recs fold_defs rec_defs
lthy =
let
val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
val nn = length pre_bnfs;
val ns = map length ctr_Tsss;
val mss = map (map length) ctr_Tsss;
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val pre_set_defss = map set_defs_of_bnf pre_bnfs;
val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
val fp_b_names = map base_name_of_typ fpTs;
val ctor_fold_fun_Ts = mk_fp_iter_fun_types (hd ctor_folds);
val ctor_rec_fun_Ts = mk_fp_iter_fun_types (hd ctor_recs);
val (((gss, _, _), (hss, _, _)), names_lthy0) =
mk_fold_rec_args_types Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy;
val ((((ps, ps'), xsss), us'), names_lthy) =
names_lthy0
|> mk_Frees' "P" (map mk_pred1T fpTs)
||>> mk_Freesss "x" ctr_Tsss
||>> 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_subtype_in fpTs 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)
| kk => [([], (kk + 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 @ ps'))))) 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 ps (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) ps 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 $)) ps us)));
val kksss = map (map (map (fst o snd) o #2)) raw_premss;
val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
val thm =
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
pre_set_defss)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation;
in
`(conj_dests nn) thm
end;
val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
val (fold_thmss, rec_thmss) =
let
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
val gfolds = map (lists_bmoc gss) folds;
val hrecs = map (lists_bmoc hss) recs;
fun mk_goal fss fiter xctr f xs fxs =
fold_rev (fold_rev Logic.all) (xs :: fss)
(mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
val mk_U = typ_subst_nonatomic (map2 pair fpTs Cs);
fun mk_nested_U maybe_mk_prodT =
typ_subst_nonatomic (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
fun unzip_iters fiters maybe_tick maybe_mk_prodT =
meta_unzip_rec (snd o dest_Free) I
(fn x as Free (_, T) => build_map lthy (indexify_fst fpTs (K o nth fiters))
(T, mk_U T) $ x)
(fn x as Free (_, T) => build_map lthy (indexify_fst fpTs (fn kk => fn _ =>
maybe_tick (nth us kk) (nth fiters kk))) (T, mk_nested_U maybe_mk_prodT T) $ x)
fpTs;
fun tick u f = Term.lambda u (HOLogic.mk_prod (u, f $ u));
val gxsss = map (map (flat_rec (single o List.last o unzip_iters gfolds (K I) (K I)))) xsss;
val hxsss = map (map (flat_rec (unzip_iters hrecs tick (curry HOLogic.mk_prodT)))) xsss;
val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
val fold_tacss =
map2 (map o mk_iter_tac pre_map_defs nesting_map_ids'' fold_defs)
ctor_fold_thms ctr_defss;
val rec_tacss =
map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') rec_defs)
ctor_rec_thms ctr_defss;
fun prove goal tac =
Goal.prove_sorry lthy [] [] goal (tac o #context)
|> Thm.close_derivation;
in
(map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
end;
val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
in
((induct_thm, induct_thms, [induct_case_names_attr]),
(fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
end;
fun derive_coinduct_unfold_corec_thms_for_types pre_bnfs dtor_unfolds dtor_corecs dtor_coinduct
dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
As kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy =
let
val nn = length pre_bnfs;
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
val fp_b_names = map base_name_of_typ fpTs;
val dtor_unfold_fun_Ts = mk_fp_iter_fun_types (hd dtor_unfolds);
val dtor_corec_fun_Ts = mk_fp_iter_fun_types (hd dtor_corecs);
val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
val exhausts = map #exhaust ctr_sugars;
val disc_thmsss = map #disc_thmss ctr_sugars;
val discIss = map #discIs ctr_sugars;
val sel_thmsss = map #sel_thmss ctr_sugars;
val ((cs, cpss, ((pgss, crssss, cgssss), _), ((phss, csssss, chssss), _)), names_lthy0) =
mk_unfold_corec_args_types Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy;
val (((rs, us'), vs'), names_lthy) =
names_lthy0
|> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
||>> Variable.variant_fixes fp_b_names
||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
val us = map2 (curry Free) us' fpTs;
val udiscss = map2 (map o rapp) us discss;
val uselsss = map2 (map o map o rapp) us selsss;
val vs = map2 (curry Free) vs' fpTs;
val vdiscss = map2 (map o rapp) vs discss;
val vselsss = map2 (map o map o rapp) vs selsss;
val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
let
val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
val strong_rs =
map4 (fn u => fn v => fn uvr => fn uv_eq =>
fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
fun build_rel rs' T =
(case find_index (curry (op =) T) fpTs of
~1 =>
if exists_subtype_in fpTs T then
let
val Type (s, Ts) = T
val bnf = the (bnf_of lthy s);
val live = live_of_bnf bnf;
val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
in Term.list_comb (rel, map (build_rel rs') Ts') end
else
HOLogic.eq_const T
| kk => nth rs' kk);
fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
(if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
(if null usels then
[]
else
[Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
Library.foldr1 HOLogic.mk_conj
(flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
handle List.Empty => @{term True};
fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
val concl =
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
(map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
uvrs us vs));
fun mk_goal rs' =
Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
concl);
val goal = mk_goal rs;
val strong_goal = mk_goal strong_rs;
fun prove dtor_coinduct' goal =
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
exhausts ctr_defss disc_thmsss sel_thmsss)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation;
fun postproc nn thm =
Thm.permute_prems 0 nn
(if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
|> Drule.zero_var_indexes
|> `(conj_dests nn);
in
(postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
end;
fun mk_coinduct_concls ms discs ctrs =
let
fun mk_disc_concl disc = [name_of_disc disc];
fun mk_ctr_concl 0 _ = []
| mk_ctr_concl _ ctor = [name_of_ctr ctor];
val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
val ctr_concls = map2 mk_ctr_concl ms ctrs;
in
flat (map2 append disc_concls ctr_concls)
end;
val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
val coinduct_conclss =
map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
val gunfolds = map (lists_bmoc pgss) unfolds;
val hcorecs = map (lists_bmoc phss) corecs;
val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
let
fun mk_goal pfss c cps fcoiter 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 $ c, Term.list_comb (ctr, take m cfs'))));
val mk_U = typ_subst_nonatomic (map2 pair Cs fpTs);
fun intr_coiters fcoiters [] [cf] =
let val T = fastype_of cf in
if exists_subtype_in Cs T then
build_map lthy (indexify_fst Cs (K o nth fcoiters)) (T, mk_U T) $ cf
else
cf
end
| intr_coiters fcoiters [cq] [cf, cf'] =
mk_If cq (intr_coiters fcoiters [] [cf]) (intr_coiters fcoiters [] [cf']);
val crgsss = map2 (map2 (map2 (intr_coiters gunfolds))) crssss cgssss;
val cshsss = map2 (map2 (map2 (intr_coiters hcorecs))) csssss chssss;
val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
fun mk_map_if_distrib bnf =
let
val mapx = map_of_bnf bnf;
val live = live_of_bnf bnf;
val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
in
Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
@{thm if_distrib}
end;
val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
val unfold_tacss =
map3 (map oo mk_coiter_tac unfold_defs [] [] nesting_map_ids'' [])
dtor_unfold_thms pre_map_defs ctr_defss;
val corec_tacss =
map3 (map oo mk_coiter_tac corec_defs nested_map_comps'' nested_map_comp's
(nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
dtor_corec_thms pre_map_defs ctr_defss;
fun prove goal tac =
Goal.prove_sorry lthy [] [] goal (tac o #context)
|> Thm.close_derivation;
val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
val filter_safesss =
map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
val safe_unfold_thmss = filter_safesss unfold_thmss;
val safe_corec_thmss = filter_safesss corec_thmss;
in
(unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
end;
val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
let
fun mk_goal c cps fcoiter n k disc =
mk_Trueprop_eq (disc $ (fcoiter $ c),
if n = 1 then @{const True}
else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds 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 unfold_tacss =
map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
val corec_tacss =
map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
fun prove goal tac =
Goal.prove_sorry lthy [] [] goal (tac o #context)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation;
fun proves [_] [_] = []
| proves goals tacs = map2 prove goals tacs;
in
(map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
end;
val is_triv_discI = is_triv_implies orf is_concl_refl;
fun mk_disc_coiter_thms coiters discIs =
map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
fun mk_sel_coiter_thm coiter_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_thm RS arg_cong' RS sel_thm'
end;
fun mk_sel_coiter_thms coiterss =
map3 (map3 (map2 o mk_sel_coiter_thm)) coiterss selsss sel_thmsss |> map flat;
val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
val coinduct_case_concl_attrs =
map2 (fn casex => fn concls =>
Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
coinduct_cases coinduct_conclss;
val coinduct_case_attrs =
coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
in
((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
(unfold_thmss, corec_thmss, []),
(safe_unfold_thmss, safe_corec_thmss),
(disc_unfold_thmss, disc_corec_thmss, simp_attrs),
(disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
(sel_unfold_thmss, sel_corec_thmss, simp_attrs))
end;
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
(wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
let
(* TODO: sanity checks on arguments *)
val _ = if fp = Greatest_FP andalso no_dests then
error "Cannot define destructor-less codatatypes"
else
();
fun qualify mandatory fp_b_name =
Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
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;
val map_bs = map map_binding_of specs;
val rel_bs = map rel_binding_of specs;
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_named_constrained_of) specs;
val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
val set_bss = map (map fst o type_args_named_constrained_of) specs;
val (((Bs0, Cs), Xs), no_defs_lthy) =
no_defs_lthy0
|> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
|> mk_TFrees (length unsorted_As)
||>> mk_TFrees nn
||>> variant_tfrees fp_b_names;
(* TODO: Cleaner handling of fake contexts, without "background_theory". The case where the new
type is defined in a locale and shadows an existing global type is currently not handled. *)
fun add_fake_type spec =
Sign.add_type no_defs_lthy (type_binding_of spec,
length (type_args_named_constrained_of spec), mixfix_of spec);
val fake_thy = Theory.copy #> fold add_fake_type 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 (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_check (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_check _ _ = false;
fun freeze_fp (T as Type (s, Us)) =
(case find_index (eq_fpT_check T) fake_Ts of
~1 => Type (s, map freeze_fp Us)
| kk => nth Xs kk)
| 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 fp_eqs =
map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
un_folds = fp_folds0, co_recs = fp_recs0, co_induct = fp_induct,
strong_co_induct = fp_strong_induct, dtor_ctors, ctor_dtors, ctor_injects,
map_thms = fp_map_thms, set_thmss = fp_set_thmss, rel_thms = fp_rel_thms,
un_fold_thms = fp_fold_thms, co_rec_thms = fp_rec_thms, ...}, lthy)) =
fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
no_defs_lthy0;
val timer = time (Timer.startRealTimer ());
val nesting_bnfs = nesty_bnfs lthy ctr_TsssXs As;
val nested_bnfs = nesty_bnfs lthy ctr_TsssXs Xs;
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val pre_set_defss = map set_defs_of_bnf pre_bnfs;
val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
val live = live_of_bnf any_fp_bnf;
val Bs =
map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
(liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
val B_ify = Term.typ_subst_atomic (As ~~ Bs);
val ctors = map (mk_ctor As) ctors0;
val dtors = map (mk_dtor As) dtors0;
val fpTs = map (domain_type o fastype_of) dtors;
fun massage_simple_notes base =
filter_out (null o #2)
#> map (fn (thmN, thms, attrs) =>
((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
val massage_multi_notes =
maps (fn (thmN, thmss, attrs) =>
if forall null thmss then
[]
else
map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
((qualify true fp_b_name (Binding.name thmN), attrs T_name),
[(thms, [])])) fp_b_names fpTs thmss);
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 ((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy) =
mk_un_fold_co_rec_prelims fp fpTs Cs ns mss fp_folds0 fp_recs0 lthy;
fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), 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), yss), u'), names_lthy) =
no_defs_lthy
|> yield_singleton (mk_Frees "w") dtorT
||>> mk_Frees "f" case_Ts
||>> mk_Freess "x" ctr_Tss
||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
||>> yield_singleton Variable.variant_fixes fp_b_name;
val u = Free (u', fpT);
val tuple_xs = map HOLogic.mk_tuple xss;
val tuple_ys = map HOLogic.mk_tuple yss;
val ctr_rhss =
map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
val case_binding = qualify false fp_b_name (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 ctr_defs' =
map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms 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 wrap_ctrs lthy =
let
fun exhaust_tac {context = ctxt, prems = _} =
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
Goal.prove_sorry 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_thms 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 (`I 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];
val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
in
wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
(sel_bindingss, sel_defaultss))) lthy
end;
fun derive_maps_sets_rels (ctr_sugar, lthy) =
if live = 0 then
((([], [], [], []), ctr_sugar), lthy)
else
let
val rel_flip = rel_flip_of_bnf fp_bnf;
val nones = replicate live NONE;
val ctor_cong =
if fp = Least_FP then
Drule.dummy_thm
else
let val ctor' = mk_ctor Bs ctor in
cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
end;
fun mk_cIn ify =
certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
mk_InN_balanced (ify ctr_sum_prod_T) n;
val cxIns = map2 (mk_cIn I) tuple_xs ks;
val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
fun mk_map_thm ctr_def' cxIn =
fold_thms lthy [ctr_def']
(unfold_thms lthy (pre_map_def ::
(if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
(cterm_instantiate_pos (nones @ [SOME cxIn])
(if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
|> singleton (Proof_Context.export names_lthy no_defs_lthy);
fun mk_set_thm fp_set_thm ctr_def' cxIn =
fold_thms lthy [ctr_def']
(unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
(if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
(cterm_instantiate_pos [SOME cxIn] fp_set_thm))
|> singleton (Proof_Context.export names_lthy no_defs_lthy);
fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
val map_thms = map2 mk_map_thm ctr_defs' cxIns;
val set_thmss = map mk_set_thms fp_set_thms;
val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
fold_thms lthy ctr_defs'
(unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
(if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
(cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
|> postproc
|> singleton (Proof_Context.export names_lthy no_defs_lthy);
fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
cxIn cyIn;
fun mk_other_half_rel_distinct_thm thm =
flip_rels lthy live thm
RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
val half_rel_distinct_thmss =
map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
val other_half_rel_distinct_thmss =
map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
val (rel_distinct_thms, _) =
join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
val notes =
[(mapN, map_thms, code_simp_attrs),
(rel_distinctN, rel_distinct_thms, code_simp_attrs),
(rel_injectN, rel_inject_thms, code_simp_attrs),
(setsN, flat set_thmss, code_simp_attrs)]
|> massage_simple_notes fp_b_name;
in
(((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
lthy |> Local_Theory.notes notes |> snd)
end;
fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
(((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
in
(wrap_ctrs
#> derive_maps_sets_rels
##>> (if fp = Least_FP then define_fold_rec (the fold_rec_args_types)
else define_unfold_corec (the unfold_corec_args_types)) mk_binding fpTs Cs fp_fold fp_rec
#> massage_res, lthy')
end;
fun wrap_types_etc (wrap_types_etcs, lthy) =
fold_map I wrap_types_etcs lthy
|>> apsnd split_list4 o apfst (apsnd split_list4 o apfst split_list4 o split_list)
o split_list;
val mk_simp_thmss =
map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
@ rel_distincts @ flat setss);
fun derive_and_note_induct_fold_rec_thms_for_types
((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
(folds, recs, fold_defs, rec_defs)), lthy) =
let
val ((induct_thm, induct_thms, induct_attrs), (fold_thmss, fold_attrs),
(rec_thmss, rec_attrs)) =
derive_induct_fold_rec_thms_for_types pre_bnfs fp_folds fp_recs fp_induct fp_fold_thms
fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctrss ctr_defss folds recs fold_defs
rec_defs lthy;
val induct_type_attr = Attrib.internal o K o Induct.induct_type;
val simp_thmss =
mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
val common_notes =
(if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
|> massage_simple_notes fp_common_name;
val notes =
[(foldN, fold_thmss, K fold_attrs),
(inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
(recN, rec_thmss, K rec_attrs),
(simpsN, simp_thmss, K [])]
|> massage_multi_notes;
in
lthy
|> Local_Theory.notes (common_notes @ notes) |> snd
|> register_fp_sugars Least_FP Xs ctr_TsssXs pre_bnfs fp_res ctr_defss ctr_sugars folds recs
induct_thm induct_thm fold_thmss rec_thmss
end;
fun derive_and_note_coinduct_unfold_corec_thms_for_types
((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
(unfolds, corecs, unfold_defs, corec_defs)), lthy) =
let
val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
coinduct_attrs),
(unfold_thmss, corec_thmss, coiter_attrs),
(safe_unfold_thmss, safe_corec_thmss),
(disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
(disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
(sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
derive_coinduct_unfold_corec_thms_for_types pre_bnfs fp_folds fp_recs fp_induct
fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As
kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy;
val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
fun flat_coiter_thms coiters disc_coiters sel_coiters =
coiters @ disc_coiters @ sel_coiters;
val simp_thmss =
mk_simp_thmss ctr_sugars
(map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
(map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
mapsx rel_injects rel_distincts setss;
val anonymous_notes =
[(flat safe_unfold_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], coinduct_attrs),
(strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
else
[])
|> massage_simple_notes fp_common_name;
val notes =
[(coinductN, map single coinduct_thms,
fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
(corecN, corec_thmss, K coiter_attrs),
(disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
(disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
(disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
(disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
(sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
(sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
(simpsN, simp_thmss, K []),
(strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
(unfoldN, unfold_thmss, K coiter_attrs)]
|> massage_multi_notes;
in
lthy
|> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
|> register_fp_sugars Greatest_FP Xs ctr_TsssXs pre_bnfs fp_res ctr_defss ctr_sugars unfolds
corecs coinduct_thm strong_coinduct_thm unfold_thmss corec_thmss
end;
val lthy' = lthy
|> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
raw_sel_defaultsss)
|> wrap_types_etc
|> (if fp = Least_FP then derive_and_note_induct_fold_rec_thms_for_types
else derive_and_note_coinduct_unfold_corec_thms_for_types);
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
datatype_word fp));
in
timer; lthy'
end;
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
val co_datatype_cmd =
define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_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_type_arg_constrained =
Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
val parse_type_args_named_constrained =
parse_type_arg_constrained >> (single o pair Binding.empty) ||
@{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
Scan.succeed [];
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
val no_map_rel = (Binding.empty, Binding.empty);
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
that we don't want them to be highlighted everywhere. *)
fun extract_map_rel ("map", b) = apfst (K b)
| extract_map_rel ("rel", b) = apsnd (K b)
| extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
val parse_map_rel_bindings =
@{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
>> (fn ps => fold extract_map_rel ps no_map_rel) ||
Scan.succeed no_map_rel;
val parse_ctr_spec =
parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
Scan.optional parse_defaults [] -- Parse.opt_mixfix;
val parse_spec =
parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
val parse_co_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
end;