(* Title: HOL/BNF/Tools/bnf_fp_def_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012, 2013
Sugared datatype and codatatype constructions.
*)
signature BNF_FP_DEF_SUGAR =
sig
type fp_sugar =
{T: typ,
fp: BNF_FP_Util.fp_kind,
index: int,
pre_bnfs: BNF_Def.bnf list,
nested_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,
co_iterss: term list list,
co_inducts: thm list,
co_iter_thmsss: thm list 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 co_induct_of: 'a list -> 'a
val strong_co_induct_of: 'a list -> 'a
val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
val exists_subtype_in: typ list -> typ -> bool
val flat_rec_arg_args: 'a list list -> 'a list
val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
'a 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 mk_map: int -> typ list -> typ list -> term -> term
val mk_rel: int -> typ list -> typ list -> term -> term
val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
val build_rel: local_theory -> (typ * typ -> term) -> typ * typ -> term
val dest_map: Proof.context -> string -> term -> term * term list
val dest_ctr: Proof.context -> string -> term -> term * term list
val mk_co_iters_prelims: BNF_FP_Util.fp_kind -> typ list -> typ list -> int list ->
int list list -> term list list -> Proof.context ->
(term list list
* (typ list list * typ list list list list * term list list
* term list list list list) list option
* (string * term list * term list list
* ((term list list * term list list list) * (typ list * typ list list)) list) option)
* Proof.context
val mk_iter_fun_arg_types: typ list -> int list -> int list list -> term ->
typ list list list list
val mk_coiter_fun_arg_types: typ list -> int list -> int list list -> term ->
typ list list
* (typ list list list list * typ list list list * typ list list list list * typ list)
val define_iters: string list ->
(typ list list * typ list list list list * term list list * term list list list list) list ->
(string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
(term list * thm list) * Proof.context
val define_coiters: string list -> string * term list * term list list
* ((term list list * term list list list) * (typ list * typ list list)) list ->
(string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
(term list * thm list) * Proof.context
val derive_induct_iters_thms_for_types: BNF_Def.bnf list ->
(typ list list * typ list list list list * term list list * term list list list list) list ->
thm -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
typ list -> typ list list list -> term list list -> thm list list -> term list list ->
thm list list -> local_theory ->
(thm list * thm * Args.src list) * (thm list list * Args.src list)
* (thm list list * Args.src list)
val derive_coinduct_coiters_thms_for_types: BNF_Def.bnf list ->
string * term list * term list list * ((term list list * term list list list)
* (typ list * typ list list)) list ->
thm -> thm list -> thm list -> thm list list -> BNF_Def.bnf list -> typ list -> typ list ->
int list list -> int list list -> int list -> thm list list -> BNF_Ctr_Sugar.ctr_sugar list ->
term list list -> thm list list -> (thm list -> thm list) -> local_theory ->
((thm list * 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_Comp
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,
pre_bnfs: bnf list,
nested_bnfs: bnf list,
fp_res: fp_result,
ctr_defss: thm list list,
ctr_sugars: ctr_sugar list,
co_iterss: term list list,
co_inducts: thm list,
co_iter_thmsss: thm list 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);
fun morph_fp_sugar phi {T, fp, index, pre_bnfs, nested_bnfs, fp_res, ctr_defss, ctr_sugars,
co_iterss, co_inducts, co_iter_thmsss} =
{T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
nested_bnfs = map (morph_bnf phi) nested_bnfs, 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,
co_iterss = map (map (Morphism.term phi)) co_iterss,
co_inducts = map (Morphism.thm phi) co_inducts,
co_iter_thmsss = map (map (map (Morphism.thm phi))) co_iter_thmsss};
structure Data = Generic_Data
(
type T = fp_sugar Symtab.table;
val empty = Symtab.empty;
val extend = I;
val merge = Symtab.merge eq_fp_sugar;
);
fun fp_sugar_of ctxt =
Symtab.lookup (Data.get (Context.Proof ctxt))
#> Option.map (morph_fp_sugar
(Morphism.thm_morphism (Thm.transfer (Proof_Context.theory_of ctxt))));
fun co_induct_of (i :: _) = i;
fun strong_co_induct_of [_, s] = s;
(* TODO: register "sum" and "prod" as datatypes to enable N2M reduction for them *)
fun register_fp_sugar key fp_sugar =
Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (Symtab.default (key, morph_fp_sugar phi fp_sugar)));
fun register_fp_sugars fp pre_bnfs nested_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars co_iterss
co_inducts co_iter_thmsss lthy =
(0, lthy)
|> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
register_fp_sugar s {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs,
nested_bnfs = nested_bnfs, fp_res = fp_res, ctr_defss = ctr_defss, ctr_sugars = ctr_sugars,
co_iterss = co_iterss, co_inducts = co_inducts, co_iter_thmsss = co_iter_thmsss}
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 id_def = @{thm id_def};
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 =);
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
fun flat_rec_arg_args xss =
(* FIXME (once the old datatype package is phased out): The first line below gives the preferred
order. The second line is for compatibility with the old datatype package. *)
(*
flat xss
*)
map hd xss @ maps tl xss;
fun flat_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
| flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
p :: flat_corec_predss_getterss qss fss @ flat_corec_preds_predsss_gettersss ps qsss fsss;
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
fun mk_uncurried2_fun f xss =
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec_arg_args 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 (f_Cs, Type (_, [prebody, body])) = strip_fun_type (fastype_of t);
val fpT0 = fp_case fp prebody body;
val Cs0 = distinct (op =) (map (fp_case fp body_type 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 = binder_fun_types o fastype_of;
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 unzip_corecT Cs (T as Type (@{type_name sum}, Ts as [_, U])) =
if member (op =) Cs U then Ts else [T]
| unzip_corecT _ T = [T];
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;
local
fun build_map_or_rel mk const of_bnf dest lthy build_simple =
let
fun build (TU as (T, U)) =
if T = U then
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 live Ts Us (of_bnf bnf);
val TUs' = map dest (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;
in
val build_map = build_map_or_rel mk_map HOLogic.id_const map_of_bnf dest_funT;
val build_rel = build_map_or_rel mk_rel HOLogic.eq_const rel_of_bnf dest_pred2T;
end;
fun fo_match ctxt t pat =
let val thy = Proof_Context.theory_of ctxt in
Pattern.first_order_match thy (pat, t) (Vartab.empty, Vartab.empty)
end;
val dummy_var_name = "?f"
fun mk_map_pattern ctxt s =
let
val bnf = the (bnf_of ctxt s);
val mapx = map_of_bnf bnf;
val live = live_of_bnf bnf;
val (f_Ts, _) = strip_typeN live (fastype_of mapx);
val fs = map_index (fn (i, T) => Var ((dummy_var_name, i), T)) f_Ts;
in
(mapx, betapplys (mapx, fs))
end;
fun dest_map ctxt s call =
let
val (map0, pat) = mk_map_pattern ctxt s;
val (_, tenv) = fo_match ctxt call pat;
in
(map0, Vartab.fold_rev (fn (_, (_, f)) => cons f) tenv [])
end;
fun dest_ctr ctxt s t =
let
val (f, args) = Term.strip_comb t;
in
(case fp_sugar_of ctxt s of
SOME fp_sugar =>
(case find_first (can (fo_match ctxt f)) (#ctrs (of_fp_sugar #ctr_sugars fp_sugar)) of
SOME f' => (f', args)
| NONE => raise Fail "dest_ctr")
| NONE => raise Fail "dest_ctr")
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 proj xs f p = f (find_index (curry op = (proj p)) xs) p;
fun mk_iter_fun_arg_types0 n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
fun mk_iter_fun_arg_types Cs ns mss =
mk_fp_iter_fun_types
#> map3 mk_iter_fun_arg_types0 ns mss
#> map (map (map (unzip_recT Cs)));
fun mk_iters_args_types Cs ns mss ctor_iter_fun_Tss lthy =
let
val Css = map2 replicate ns Cs;
val y_Tsss = map3 mk_iter_fun_arg_types0 ns mss (map un_fold_of ctor_iter_fun_Tss);
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 y_Tssss = map (map (map single)) 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 o co_rec_of) ns mss ctor_iter_fun_Tss;
val z_Tsss' = map (map flat_rec_arg_args) 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
([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
end;
fun mk_coiter_fun_arg_types0 Cs ns mss fun_Ts =
let
(*avoid "'a itself" arguments in coiterators and corecursors*)
fun repair_arity [0] = [1]
| repair_arity ms = ms;
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 unzip_corecT Cs))) Cs f_Tsss;
val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
in
(q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts)
end;
fun mk_coiter_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
fun mk_coiter_fun_arg_types Cs ns mss dtor_coiter =
(mk_coiter_p_pred_types Cs ns,
mk_fp_iter_fun_types dtor_coiter |> mk_coiter_fun_arg_types0 Cs ns mss);
fun mk_coiters_args_types Cs ns mss dtor_coiter_fun_Tss lthy =
let
val p_Tss = mk_coiter_p_pred_types Cs ns;
fun mk_types get_Ts =
let
val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
val (q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts) = mk_coiter_fun_arg_types0 Cs ns mss fun_Ts;
val pf_Tss = map3 flat_corec_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
in
(q_Tssss, f_Tsss, f_Tssss, (f_sum_prod_Ts, pf_Tss))
end;
val (r_Tssss, g_Tsss, g_Tssss, unfold_types) = mk_types un_fold_of;
val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types co_rec_of;
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;
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 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');
fun mk_args qssss fssss f_Tsss =
let
val pfss = map3 flat_corec_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;
val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
in (pfss, cqfsss) end;
val unfold_args = mk_args rssss gssss g_Tsss;
val corec_args = mk_args sssss hssss h_Tsss;
in
((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
end;
fun mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy =
let
val thy = Proof_Context.theory_of lthy;
val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
map (mk_co_iters thy fp fpTs Cs #> `(mk_fp_iter_fun_types o hd)) (transpose xtor_co_iterss0)
|> apsnd transpose o apfst transpose o split_list;
val ((iters_args_types, coiters_args_types), lthy') =
if fp = Least_FP then
mk_iters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (rpair NONE o SOME)
else
mk_coiters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (pair NONE o SOME)
in
((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
end;
fun mk_iter_body ctor_iter fss xssss =
Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
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 cs cpss f_sum_prod_Ts cqfsss dtor_coiter =
Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss);
fun define_co_iters fp fpT Cs binding_specs lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
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 csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
val defs' = map (Morphism.thm phi) defs;
in
((csts', defs'), lthy')
end;
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs ctor_iters lthy =
let
val nn = length fpTs;
val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of (hd ctor_iters)));
fun generate_iter suf (f_Tss, _, fss, xssss) ctor_iter =
let
val res_T = fold_rev (curry op --->) f_Tss fpT_to_C;
val b = mk_binding suf;
val spec =
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
mk_iter_body ctor_iter fss xssss);
in (b, spec) end;
in
define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
end;
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs dtor_coiters
lthy =
let
val nn = length fpTs;
val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
fun generate_coiter suf ((pfss, cqfsss), (f_sum_prod_Ts, pf_Tss)) dtor_coiter =
let
val res_T = fold_rev (curry op --->) pf_Tss C_to_fpT;
val b = mk_binding suf;
val spec =
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter);
in (b, spec) end;
in
define_co_iters Greatest_FP fpT Cs
(map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
end;
fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] ctor_induct
ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss iter_defss
lthy =
let
val iterss' = transpose iterss;
val iter_defss' = transpose iter_defss;
val [folds, recs] = iterss';
val [fold_defs, rec_defs] = iter_defss';
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 [id_def] o map_id_of_bnf) nesting_bnfs;
val nested_map_ids'' = map (unfold_thms lthy [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 ((((ps, ps'), xsss), us'), names_lthy) =
lthy
|> 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 _ (x as Free (_, Type _)) (X as TFree _) =
[([], (find_index (curry op = X) Xs + 1, x))]
| mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
(case AList.lookup (op =) setss_nested T_name of
NONE => []
| SOME raw_sets0 =>
let
val (Xs_Ts, (Ts, raw_sets)) =
filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
|> split_list ||> split_list;
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 = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
in
flat (map2 (map o apfst o cons) xysets ppremss)
end)
| 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 ctrXs_Ts =
let
val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
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 = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_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 induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
let
val fiters = map (lists_bmoc fss) iters;
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)));
fun maybe_tick (T, U) u f =
if try (fst o HOLogic.dest_prodT) U = SOME T then
Term.lambda u (HOLogic.mk_prod (u, f $ u))
else
f;
fun build_iter (x as Free (_, T)) U =
if T = U then
x
else
build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
(fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
val tacss =
map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') iter_defs)
ctor_iter_thms ctr_defss;
fun prove goal tac =
Goal.prove_sorry lthy [] [] goal (tac o #context)
|> Thm.close_derivation;
in
map2 (map2 prove) goalss tacss
end;
val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
in
((induct_thms, induct_thm, [induct_case_names_attr]),
(fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
end;
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
coiters_args_types as [((pgss, crgsss), _), ((phss, cshsss), _)])
dtor_coinduct dtor_injects dtor_ctors dtor_coiter_thmss nesting_bnfs fpTs Cs kss mss ns
ctr_defss ctr_sugars coiterss coiter_defss export_args lthy =
let
fun mk_ctor_dtor_coiter_thm dtor_inject dtor_ctor coiter =
iffD1 OF [dtor_inject, trans OF [coiter, dtor_ctor RS sym]];
val ctor_dtor_coiter_thmss =
map3 (map oo mk_ctor_dtor_coiter_thm) dtor_injects dtor_ctors dtor_coiter_thmss;
val coiterss' = transpose coiterss;
val coiter_defss' = transpose coiter_defss;
val [unfold_defs, corec_defs] = coiter_defss';
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 [id_def] o map_id_of_bnf) nesting_bnfs;
val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
val fp_b_names = map base_name_of_typ fpTs;
val ctrss = map #ctrs ctr_sugars;
val discss = map #discs ctr_sugars;
val selsss = map #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 (((rs, us'), vs'), names_lthy) =
lthy
|> 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_pairs =
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;
(* TODO: generalize (cf. "build_map") *)
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 goals = map mk_goal [rs, 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);
val rel_eqs = map rel_eq_of_bnf pre_bnfs;
val rel_monos = map rel_mono_of_bnf pre_bnfs;
val dtor_coinducts =
[dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos lthy];
in
map2 (postproc nn oo prove) dtor_coinducts goals
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 fcoiterss' as [gunfolds, hcorecs] =
map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
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'))));
fun mk_U maybe_mk_sumT =
typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
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 build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
let val T = fastype_of cqf in
if exists_subtype_in Cs T then
let val U = mk_U maybe_mk_sumT T in
build_map lthy (indexify snd fpTs (fn kk => fn _ =>
maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
end
else
cqf
end;
val crgsss' = map (map (map (build_coiter (un_fold_of fcoiterss') (K I) (K I)))) crgsss;
val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
cshsss;
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';
val unfold_tacss =
map3 (map oo mk_coiter_tac unfold_defs nesting_map_ids'')
(map un_fold_of ctor_dtor_coiter_thmss) pre_map_defs ctr_defss;
val corec_tacss =
map3 (map oo mk_coiter_tac corec_defs nesting_map_ids'')
(map co_rec_of ctor_dtor_coiter_thmss) 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
|> map (map (unfold_thms lthy @{thms sum_case_if}));
val unfold_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_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
val safe_corec_thmss = filter_safesss corec_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 export_args
|> 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 coiter_thmss =
map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss 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_thms_pairs, 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_discs_sels, rep_compat), specs) no_defs_lthy0 =
let
(* TODO: sanity checks on arguments *)
val _ = if fp = Greatest_FP andalso no_discs_sels then
error "Cannot define codatatypes without discriminators and selectors"
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 = map2 (fn fp_b_name => qualify false fp_b_name o map_binding_of) fp_b_names specs;
val rel_bs = map2 (fn fp_b_name => qualify false fp_b_name o rel_binding_of) fp_b_names 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 _ = has_duplicates (op =) unsorted_As andalso
error ("Duplicate parameters in " ^ co_prefix fp ^ "datatype specification");
val bad_args =
map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
|> filter_out Term.is_TVar;
val _ = null bad_args orelse
error ("Locally fixed type argument " ^
quote (Syntax.string_of_typ no_defs_lthy0 (hd bad_args)) ^ " in " ^ co_prefix fp ^
"datatype specification");
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". *)
fun add_fake_type spec =
(*The "qualify" hack below is for the case where the new type shadows an existing global type
defined in the same theory.*)
Sign.add_type no_defs_lthy (qualify false "" (type_binding_of spec),
length (type_args_named_constrained_of spec), mixfix_of spec);
val fake_thy = 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, Ts)) =
(case find_index (eq_fpT_check T) fake_Ts of
~1 => Type (s, map freeze_fp Ts)
| kk => nth Xs kk)
| freeze_fp T = T;
val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
val fp_eqs =
map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects,
dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms, xtor_co_iter_thmss, ...},
lthy)) =
fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
no_defs_lthy0
handle BAD_DEAD (X, X_backdrop) =>
(case X_backdrop of
Type (bad_tc, _) =>
let
val qsoty = quote o Syntax.string_of_typ fake_lthy;
val fake_T = qsoty (unfreeze_fp X);
val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
fun register_hint () =
"\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
\it";
in
if is_some (bnf_of no_defs_lthy bad_tc) orelse
is_some (fp_sugar_of no_defs_lthy bad_tc) then
error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
" in type expression " ^ fake_T_backdrop)
else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
bad_tc) then
error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
" via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
fake_T_backdrop ^ register_hint ())
else
error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
" via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
register_hint ())
end);
val time = time lthy;
val timer = time (Timer.startRealTimer ());
val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss 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 _ =
if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
warning ("Map function and relator names ignored")
else
();
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)))) ctrXs_Tsss;
val ns = map length ctr_Tsss;
val kss = map (fn n => 1 upto n) ns;
val mss = map (map length) ctr_Tsss;
val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy;
fun define_ctrs_dtrs_for_type (((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
xtor_co_iters), 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 ((((w, xss), yss), u'), names_lthy) =
no_defs_lthy
|> yield_singleton (mk_Frees "w") dtorT
||>> 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 ((raw_ctrs, 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)
ctr_bindings ctr_mixfixes 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 ctrs0 = map (Morphism.term phi) raw_ctrs;
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 unit_all_eq1}
(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 tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
in
wrap_free_constructors tacss (((wrap_opts, ctrs0), standard_binding), (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_iters [foldN, recN] (the iters_args_types)
else define_coiters [unfoldN, corecN] (the coiters_args_types))
mk_binding fpTs Cs xtor_co_iters
#> massage_res, lthy')
end;
fun wrap_types_etc (wrap_types_etcs, lthy) =
fold_map I wrap_types_etcs lthy
|>> apsnd split_list 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_iters_thms_for_types
((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
(iterss, iter_defss)), lthy) =
let
val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, fold_attrs),
(rec_thmss, rec_attrs)) =
derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss
iter_defss 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 pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars iterss
[induct_thm] (transpose [fold_thmss, rec_thmss])
end;
fun derive_and_note_coinduct_coiters_thms_for_types
((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
(coiterss, coiter_defss)), lthy) =
let
val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
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_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
dtor_injects dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs kss mss ns ctr_defss
ctr_sugars coiterss coiter_defss (Proof_Context.export lthy' no_defs_lthy) 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 pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars coiterss
[coinduct_thm, strong_coinduct_thm] (transpose [unfold_thmss, corec_thmss])
end;
val lthy'' = lthy'
|> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
sel_bindingsss ~~ raw_sel_defaultsss)
|> wrap_types_etc
|> fp_case fp derive_and_note_induct_iters_thms_for_types
derive_and_note_coinduct_coiters_thms_for_types;
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
co_prefix fp ^ "datatype"));
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_free_constructors_options -- Parse.and_list1 parse_spec;
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
end;