(* 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 =
{lfp: bool,
index: int,
pre_bnfs: BNF_Def.bnf list,
fp_res: BNF_FP.fp_result,
ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
xxfolds: term list,
xxrecs: term list,
xxfold_thmss: thm list list,
xxrec_thmss: thm list list};
val fp_sugar_of: Proof.context -> string -> fp_sugar option
val mk_fp_iter_fun_types: term -> typ list
val mk_fun_arg_typess: int -> int list -> typ -> typ list list
val unzip_recT: typ list -> typ -> typ list * typ list
val mk_fold_fun_typess: typ list list list -> typ list list -> typ list list
val mk_rec_fun_typess: typ list -> typ list list list -> typ list list -> typ list list
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 ->
typ list -> term list list -> thm list list -> term list -> term list -> thm list -> thm list ->
Proof.context ->
(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 -> Proof.context ->
(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 datatypes: bool ->
(mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
binding list list -> typ list * typ list list -> BNF_Def.bnf list -> local_theory ->
BNF_FP.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_datatype_cmd: bool ->
(mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
binding list list -> typ list * typ list list -> BNF_Def.bnf list -> local_theory ->
BNF_FP.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
open BNF_FP_Def_Sugar_Tactics
val EqN = "Eq_";
type fp_sugar =
{lfp: bool,
index: int,
pre_bnfs: bnf list,
fp_res: fp_result,
ctr_sugars: ctr_sugar list,
xxfolds: term list,
xxrecs: term list,
xxfold_thmss: thm list list,
xxrec_thmss: thm list list};
fun eq_fp_sugar ({lfp = lfp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
{lfp = lfp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
lfp1 = lfp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
fun morph_fp_sugar phi {lfp, index, pre_bnfs, fp_res, ctr_sugars, xxfolds, xxrecs, xxfold_thmss,
xxrec_thmss} =
{lfp = lfp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
fp_res = morph_fp_result phi fp_res, ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars,
xxfolds = map (Morphism.term phi) xxfolds, xxrecs = map (Morphism.term phi) xxrecs,
xxfold_thmss = map (map (Morphism.thm phi)) xxfold_thmss,
xxrec_thmss = map (map (Morphism.thm phi)) xxrec_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 lfp pre_bnfs (fp_res as {ctors, ...}) ctr_sugars xxfolds xxrecs xxfold_thmss
xxrec_thmss lthy =
(0, lthy)
|> fold (fn ctor => fn (kk, lthy) => (kk + 1,
register_fp_sugar (fp_name_of_ctor ctor) {lfp = lfp, index = kk,
pre_bnfs = pre_bnfs, fp_res = fp_res, ctr_sugars = ctr_sugars, xxfolds = xxfolds,
xxrecs = xxrecs, xxfold_thmss = xxfold_thmss, xxrec_thmss = xxrec_thmss} lthy)) ctors
|> 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 split_list4 [] = ([], [], [], [])
| split_list4 ((x1, x2, x3, x4) :: xs) =
let val (xs1, xs2, xs3, xs4) = split_list4 xs;
in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end;
fun add_components_of_typ (Type (s, Ts)) =
fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
| add_components_of_typ _ = I;
fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
fun exists_subtype_in Ts = exists_subtype (member (op =) Ts);
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);
fun variant_types ss Ss ctxt =
let
val (tfrees, _) =
fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt);
val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
in (tfrees, ctxt') end;
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
fun 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: *)
(*
maps (op @) ps
*)
maps fst ps @ maps snd 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_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_xxiter lfp Ts Us t =
let
val (bindings, body) = strip_type (fastype_of t);
val (f_Us, prebody) = split_last bindings;
val Type (_, Ts0) = if lfp then prebody else body;
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
in
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
end;
val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
fun mk_fp_iter lfp As Cs fp_iters0 =
map (mk_xxiter lfp As Cs) fp_iters0
|> (fn ts => (ts, mk_fp_iter_fun_types (hd ts)));
fun unzip_recT fpTs T =
let
fun project_recT proj =
let
fun project (Type (s as @{type_name prod}, Ts as [T, U])) =
if member (op =) fpTs T 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;
in
if exists_subtype_in fpTs T then ([project_recT fst T], [project_recT snd T]) else ([T], [])
end;
val massage_rec_fun_arg_typesss = map o map o flat_rec o unzip_recT;
val mk_fold_fun_typess = map2 (map2 (curry (op --->)));
val mk_rec_fun_typess = mk_fold_fun_typess oo massage_rec_fun_arg_typesss;
fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
fun mk_fold_rec_terms_types fpTs Css ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy =
let
val y_Tsss = map3 mk_fun_arg_typess ns mss ctor_fold_fun_Ts;
val g_Tss = mk_fold_fun_typess y_Tsss Css;
val ((gss, ysss), lthy) =
lthy
|> mk_Freess "f" g_Tss
||>> mk_Freesss "x" y_Tsss;
val z_Tsss = map3 mk_fun_arg_typess ns mss ctor_rec_fun_Ts;
val h_Tss = mk_rec_fun_typess fpTs z_Tsss Css;
val hss = map2 (map2 retype_free) h_Tss gss;
val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
in
(((gss, g_Tss, ysss), (hss, h_Tss, zsss)), lthy)
end;
fun mk_unfold_corec_terms_types fpTs 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 project_corecT proj =
let
fun project (Type (s as @{type_name sum}, Ts as [T, U])) =
if member (op =) fpTs T 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;
fun unzip_corecT T =
if exists_subtype_in fpTs T then [project_corecT fst T, project_corecT 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 [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single dtor_unfold_fun_Ts;
val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) = 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_terms 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_terms = mk_terms rssss gssss;
val corec_terms = mk_terms sssss hssss;
in
((cs, cpss, (unfold_terms, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
(corec_terms, (h_sum_prod_Ts, h_Tsss, ph_Tss))), 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 build_map_step lthy build_arg (Type (s, Ts)) (Type (_, Us)) =
let
val bnf = the (bnf_of lthy s);
val live = live_of_bnf bnf;
val mapx = mk_map live Ts Us (map_of_bnf bnf);
val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
in Term.list_comb (mapx, map build_arg TUs') end;
fun build_rel_step lthy build_arg (Type (s, Ts)) =
let
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_arg Ts') end;
fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_folds0 ctor_recs0 ctor_induct ctor_fold_thms
ctor_rec_thms nesting_bnfs nested_bnfs fpTs Cs As 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 Css = map2 replicate ns Cs;
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_comp's = map 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 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 true As Cs ctor_folds0;
val (_, ctor_rec_fun_Ts) = mk_fp_iter true As Cs ctor_recs0;
val (((gss, _, _), (hss, _, _)), names_lthy0) =
mk_fold_rec_terms_types fpTs Css 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)));
fun build_iter fiters (T, U) =
if T = U then
id_const T
else
(case find_index (curry (op =) T) fpTs of
~1 => build_map_step lthy (build_iter fiters) T U
| kk => nth fiters kk);
val mk_U = typ_subst_nonatomic (map2 pair fpTs Cs);
fun unzip_iters fiters combine (x as Free (_, T)) =
if exists_subtype_in fpTs T then
combine (x, build_iter fiters (T, mk_U T) $ x)
else
([x], []);
val gxsss = map (map (flat_rec (unzip_iters gfolds (fn (_, t) => ([t], []))))) xsss;
val hxsss = map (map (flat_rec (unzip_iters hrecs (pairself single)))) 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_comp's
(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_unfolds0 dtor_corecs0 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 false As Cs dtor_unfolds0;
val (_, dtor_corec_fun_Ts) = mk_fp_iter false As Cs dtor_corecs0;
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_terms_types fpTs 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 build_rel_step lthy (build_rel rs') T
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'))));
fun build_coiter fcoiters (T, U) =
if T = U then
id_const T
else
(case find_index (curry (op =) U) fpTs of
~1 => build_map_step lthy (build_coiter fcoiters) T U
| kk => nth fcoiters kk);
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_coiter 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_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
(wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
let
(* TODO: sanity checks on arguments *)
val _ = if not lfp 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
||>> apfst (map TFree) o
variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS);
(* TODO: cleaner handling of fake contexts, without "background_theory" *)
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
locale and shadows an existing global type*)
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,
folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_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, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) =
fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs
no_defs_lthy0;
val timer = time (Timer.startRealTimer ());
fun add_nesty_bnf_names Us =
let
fun add (Type (s, Ts)) ss =
let val (needs, ss') = fold_map add Ts ss in
if exists I needs then (true, insert (op =) s ss') else (false, ss')
end
| add T ss = (member (op =) Us T, ss);
in snd oo add end;
fun nesty_bnfs Us =
map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []);
val nesting_bnfs = nesty_bnfs As;
val nested_bnfs = nesty_bnfs 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 Css = map2 replicate ns Cs;
val (fp_folds, fp_fold_fun_Ts) = mk_fp_iter lfp As Cs fp_folds0;
val (fp_recs, fp_rec_fun_Ts) = mk_fp_iter lfp As Cs fp_recs0;
val (((fold_only, rec_only),
(cs, cpss, unfold_only as ((_, crssss, cgssss), (_, g_Tsss, _)),
corec_only as ((_, csssss, chssss), (_, h_Tsss, _)))), _) =
if lfp then
mk_fold_rec_terms_types fpTs Css ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
|>> rpair ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))
else
mk_unfold_corec_terms_types fpTs Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
|>> pair (([], [], []), ([], [], []));
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 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 lfp 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 (not lfp ? 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 lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
(cterm_instantiate_pos (nones @ [SOME cxIn])
(if lfp 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 lfp 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 lfp 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 define_fold_rec no_defs_lthy =
let
val fpT_to_C = fpT --> C;
fun build_prod_proj mk_proj (T, U) =
if T = U then
id_const T
else
(case (T, U) of
(Type (s, _), Type (s', _)) =>
if s = s' then build_map_step lthy (build_prod_proj mk_proj) T U else mk_proj T
| _ => mk_proj T);
(* TODO: Avoid these complications; cf. corec case *)
fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
| mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
| mk_U _ T = T;
fun unzip_rec (x as Free (_, T)) =
if exists_subtype_in fpTs T then
([build_prod_proj fst_const (T, mk_U fst T) $ x],
[build_prod_proj snd_const (T, mk_U snd T) $ x])
else
([x], []);
fun mk_iter_arg f xs =
mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
fun generate_iter (suf, ctor_iter, (fss, f_Tss, xsss)) =
let
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
val spec =
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
Term.list_comb (ctor_iter,
map2 (mk_sum_caseN_balanced oo map2 mk_iter_arg) fss xsss));
in (binding, spec) end;
val iter_infos =
[(foldN, fp_fold, fold_only),
(recN, fp_rec, rec_only)];
val (bindings, specs) = map generate_iter iter_infos |> split_list;
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map2 (fn b => fn spec =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) bindings specs
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val [fold_def, rec_def] = map (Morphism.thm phi) defs;
val [foldx, recx] = map (mk_xxiter lfp As Cs o Morphism.term phi) csts;
in
((foldx, recx, fold_def, rec_def), lthy')
end;
fun define_unfold_corec no_defs_lthy =
let
val B_to_fpT = C --> fpT;
fun build_sum_inj mk_inj (T, U) =
if T = U then
id_const T
else
(case (T, U) of
(Type (s, _), Type (s', _)) =>
if s = s' then build_map_step lthy (build_sum_inj mk_inj) T U
else uncurry mk_inj (dest_sumT U)
| _ => uncurry mk_inj (dest_sumT U));
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 crgsss = map3 (map3 (map3 build_dtor_coiter_arg)) g_Tsss crssss cgssss;
val cshsss = map3 (map3 (map3 build_dtor_coiter_arg)) h_Tsss csssss chssss;
fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
Term.lambda c (mk_IfN sum_prod_T cps
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
fun generate_coiter (suf, dtor_coiter, (cqfsss, ((pfss, _, _),
(f_sum_prod_Ts, _, pf_Tss)))) =
let
val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
val spec =
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
Term.list_comb (dtor_coiter,
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
in (binding, spec) end;
val coiter_infos =
[(unfoldN, fp_fold, (crgsss, unfold_only)),
(corecN, fp_rec, (cshsss, corec_only))];
val (bindings, specs) = map generate_coiter coiter_infos |> split_list;
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map2 (fn b => fn spec =>
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
#>> apsnd snd) bindings specs
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
val [unfold, corec] = map (mk_xxiter lfp As Cs o Morphism.term phi) csts;
in
((unfold, corec, unfold_def, corec_def), lthy')
end;
fun massage_res (((maps_sets_rels, ctr_sugar), xxiter_res), lthy) =
(((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), xxiter_res), lthy);
in
(wrap
#> derive_maps_sets_rels
##>> (if lfp then define_fold_rec else define_unfold_corec)
#> 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 xxfolds => fn xxrecs =>
fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
injects @ distincts @ case_thms @ xxrecs @ xxfolds @ 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_folds0 fp_recs0 fp_induct fp_fold_thms
fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As 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 true pre_bnfs fp_res ctr_sugars folds recs fold_thmss rec_thmss
end;
fun derive_and_note_coinduct_unfold_corec_thms_for_types
((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, 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_folds0 fp_recs0 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 false pre_bnfs fp_res ctr_sugars unfolds corecs 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 lfp 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 " ^
(if lfp then "" else "co") ^ "datatype"));
in
timer; lthy'
end;
val datatypes = define_datatypes (K I) (K I) (K I);
val datatype_cmd = define_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_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
end;