(* Title: HOL/Tools/BNF/bnf_lfp_size.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2014
Generation of size functions for new-style datatypes.
*)
signature BNF_LFP_SIZE =
sig
val register_size: string -> string -> thm list -> thm list -> local_theory -> local_theory
val register_size_global: string -> string -> thm list -> thm list -> theory -> theory
val lookup_size: Proof.context -> string -> (string * (thm list * thm list)) option
val lookup_size_global: theory -> string -> (string * (thm list * thm list)) option
val generate_lfp_size: BNF_FP_Util.fp_sugar list -> local_theory -> local_theory
end;
structure BNF_LFP_Size : BNF_LFP_SIZE =
struct
open BNF_Util
open BNF_Tactics
open BNF_Def
open BNF_FP_Util
val size_N = "size_"
val rec_o_mapN = "rec_o_map"
val sizeN = "size"
val size_o_mapN = "size_o_map"
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;
structure Data = Generic_Data
(
type T = (string * (thm list * thm list)) Symtab.table;
val empty = Symtab.empty;
val extend = I
fun merge data = Symtab.merge (K true) data;
);
fun register_size T_name size_name size_simps size_o_maps =
Context.proof_map (Data.map (Symtab.update (T_name, (size_name, (size_simps, size_o_maps)))));
fun register_size_global T_name size_name size_simps size_o_maps =
Context.theory_map (Data.map (Symtab.update (T_name, (size_name, (size_simps, size_o_maps)))));
val lookup_size = Symtab.lookup o Data.get o Context.Proof;
val lookup_size_global = Symtab.lookup o Data.get o Context.Theory;
val zero_nat = @{const zero_class.zero (nat)};
fun mk_plus_nat (t1, t2) = Const (@{const_name Groups.plus},
HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
fun mk_to_natT T = T --> HOLogic.natT;
fun mk_abs_zero_nat T = Term.absdummy T zero_nat;
fun pointfill ctxt th = unfold_thms ctxt [o_apply] (th RS fun_cong);
fun mk_unabs_def_unused_0 n =
funpow n (fn thm => thm RS @{thm fun_cong_unused_0} handle THM _ => thm RS fun_cong);
val rec_o_map_simp_thms =
@{thms o_def id_def case_prod_app case_sum_map_sum case_prod_map_prod BNF_Comp.id_bnf_comp_def};
fun mk_rec_o_map_tac ctxt rec_def pre_map_defs live_nesting_map_ident0s abs_inverses
ctor_rec_o_map =
unfold_thms_tac ctxt [rec_def] THEN
HEADGOAL (rtac (ctor_rec_o_map RS trans)) THEN
PRIMITIVE (Conv.fconv_rule Thm.eta_long_conversion) THEN
HEADGOAL (asm_simp_tac (ss_only (pre_map_defs @
distinct Thm.eq_thm_prop (live_nesting_map_ident0s @ abs_inverses) @ rec_o_map_simp_thms) ctxt));
val size_o_map_simp_thms = @{thms prod_inj_map inj_on_id snd_comp_apfst[unfolded apfst_def]};
fun mk_size_o_map_tac ctxt size_def rec_o_map inj_maps size_maps =
unfold_thms_tac ctxt [size_def] THEN
HEADGOAL (rtac (rec_o_map RS trans) THEN'
asm_simp_tac (ss_only (inj_maps @ size_maps @ size_o_map_simp_thms) ctxt)) THEN
IF_UNSOLVED (unfold_thms_tac ctxt @{thms o_def} THEN HEADGOAL (rtac refl));
fun generate_lfp_size (fp_sugars as ({T = Type (_, As), BT = Type (_, Bs),
fp_res = {bnfs = fp_bnfs, xtor_co_rec_o_map_thms = ctor_rec_o_maps, ...}, fp_nesting_bnfs,
live_nesting_bnfs, ...} : fp_sugar) :: _) lthy0 =
let
val data = Data.get (Context.Proof lthy0);
val Ts = map #T fp_sugars
val T_names = map (fst o dest_Type) Ts;
val nn = length Ts;
val B_ify = Term.typ_subst_atomic (As ~~ Bs);
val recs = map #co_rec fp_sugars;
val rec_thmss = map #co_rec_thms fp_sugars;
val rec_Ts as rec_T1 :: _ = map fastype_of recs;
val rec_arg_Ts = binder_fun_types rec_T1;
val Cs = map body_type rec_Ts;
val Cs_rho = map (rpair HOLogic.natT) Cs;
val substCnatT = Term.subst_atomic_types Cs_rho;
val f_Ts = map mk_to_natT As;
val f_TsB = map mk_to_natT Bs;
val num_As = length As;
fun variant_names n pre = fst (Variable.variant_fixes (replicate n pre) lthy0);
val f_names = variant_names num_As "f";
val fs = map2 (curry Free) f_names f_Ts;
val fsB = map2 (curry Free) f_names f_TsB;
val As_fs = As ~~ fs;
val size_bs =
map ((fn base => Binding.qualify false base (Binding.name (prefix size_N base))) o
Long_Name.base_name) T_names;
fun is_pair_C @{type_name prod} [_, T'] = member (op =) Cs T'
| is_pair_C _ _ = false;
fun mk_size_of_typ (T as TFree _) =
pair (case AList.lookup (op =) As_fs T of
SOME f => f
| NONE => if member (op =) Cs T then Term.absdummy T (Bound 0) else mk_abs_zero_nat T)
| mk_size_of_typ (T as Type (s, Ts)) =
if is_pair_C s Ts then
pair (snd_const T)
else if exists (exists_subtype_in (As @ Cs)) Ts then
(case Symtab.lookup data s of
SOME (size_name, (_, size_o_maps)) =>
let
val (args, size_o_mapss') = split_list (map (fn T => mk_size_of_typ T []) Ts);
val size_const = Const (size_name, map fastype_of args ---> mk_to_natT T);
in
fold (union Thm.eq_thm_prop) (size_o_maps :: size_o_mapss')
#> pair (Term.list_comb (size_const, args))
end
| _ => pair (mk_abs_zero_nat T))
else
pair (mk_abs_zero_nat T);
fun mk_size_of_arg t =
mk_size_of_typ (fastype_of t) #>> (fn s => substCnatT (betapply (s, t)));
fun mk_size_arg rec_arg_T size_o_maps =
let
val x_Ts = binder_types rec_arg_T;
val m = length x_Ts;
val x_names = variant_names m "x";
val xs = map2 (curry Free) x_names x_Ts;
val (summands, size_o_maps') =
fold_map mk_size_of_arg xs size_o_maps
|>> remove (op =) zero_nat;
val sum =
if null summands then HOLogic.zero
else foldl1 mk_plus_nat (summands @ [HOLogic.Suc_zero]);
in
(fold_rev Term.lambda (map substCnatT xs) sum, size_o_maps')
end;
fun mk_size_rhs recx size_o_maps =
fold_map mk_size_arg rec_arg_Ts size_o_maps
|>> (fn args => fold_rev Term.lambda fs (Term.list_comb (substCnatT recx, args)));
val maybe_conceal_def_binding = Thm.def_binding
#> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
val (size_rhss, nested_size_o_maps) = fold_map mk_size_rhs recs [];
val size_Ts = map fastype_of size_rhss;
val ((raw_size_consts, raw_size_defs), (lthy1', lthy1)) = lthy0
|> apfst split_list o fold_map2 (fn b => fn rhs =>
Local_Theory.define ((b, NoSyn), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
size_bs size_rhss
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy1 lthy1';
val size_defs = map (Morphism.thm phi) raw_size_defs;
val size_consts0 = map (Morphism.term phi) raw_size_consts;
val size_consts = map2 retype_const_or_free size_Ts size_consts0;
val size_constsB = map (Term.map_types B_ify) size_consts;
val zeros = map mk_abs_zero_nat As;
val overloaded_size_rhss = map (fn c => Term.list_comb (c, zeros)) size_consts;
val overloaded_size_Ts = map fastype_of overloaded_size_rhss;
val overloaded_size_consts = map (curry Const @{const_name size}) overloaded_size_Ts;
val overloaded_size_def_bs =
map (maybe_conceal_def_binding o Binding.suffix_name "_overloaded") size_bs;
fun define_overloaded_size def_b lhs0 rhs lthy =
let
val Free (c, _) = Syntax.check_term lthy lhs0;
val (thm, lthy') = lthy
|> Local_Theory.define ((Binding.name c, NoSyn), ((def_b, []), rhs))
|-> (fn (t, (_, thm)) => Spec_Rules.add Spec_Rules.Equational ([t], [thm]) #> pair thm);
val ctxt_thy = Proof_Context.init_global (Proof_Context.theory_of lthy');
val thm' = singleton (Proof_Context.export lthy' ctxt_thy) thm;
in (thm', lthy') end;
val (overloaded_size_defs, lthy2) = lthy1
|> Local_Theory.background_theory_result
(Class.instantiation (T_names, map dest_TFree As, [HOLogic.class_size])
#> fold_map3 define_overloaded_size overloaded_size_def_bs overloaded_size_consts
overloaded_size_rhss
##> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
##> Local_Theory.exit_global);
val size_defs' =
map (mk_unabs_def (num_As + 1) o (fn thm => thm RS meta_eq_to_obj_eq)) size_defs;
val size_defs_unused_0 =
map (mk_unabs_def_unused_0 (num_As + 1) o (fn thm => thm RS meta_eq_to_obj_eq)) size_defs;
val overloaded_size_defs' =
map (mk_unabs_def 1 o (fn thm => thm RS meta_eq_to_obj_eq)) overloaded_size_defs;
val all_overloaded_size_defs = overloaded_size_defs @
(Spec_Rules.retrieve lthy0 @{const size ('a)}
|> map_filter (try (fn (Spec_Rules.Equational, (_, [thm])) => thm)));
val nested_size_maps = map (pointfill lthy2) nested_size_o_maps @ nested_size_o_maps;
val all_inj_maps = map inj_map_of_bnf (fp_bnfs @ fp_nesting_bnfs @ live_nesting_bnfs)
|> distinct Thm.eq_thm_prop;
fun derive_size_simp size_def' simp0 =
(trans OF [size_def', simp0])
|> Simplifier.asm_full_simplify (ss_only (@{thms inj_on_convol_ident id_def o_def snd_conv} @
all_inj_maps @ nested_size_maps) lthy2)
|> fold_thms lthy2 size_defs_unused_0;
fun derive_overloaded_size_simp overloaded_size_def' simp0 =
(trans OF [overloaded_size_def', simp0])
|> unfold_thms lthy2 @{thms add_0_left add_0_right}
|> fold_thms lthy2 all_overloaded_size_defs;
val size_simpss = map2 (map o derive_size_simp) size_defs' rec_thmss;
val size_simps = flat size_simpss;
val overloaded_size_simpss =
map2 (map o derive_overloaded_size_simp) overloaded_size_defs' size_simpss;
val size_thmss = map2 append size_simpss overloaded_size_simpss;
val ABs = As ~~ Bs;
val g_names = variant_names num_As "g";
val gs = map2 (curry Free) g_names (map (op -->) ABs);
val liveness = map (op <>) ABs;
val live_gs = AList.find (op =) (gs ~~ liveness) true;
val live = length live_gs;
val maps0 = map map_of_bnf fp_bnfs;
val (rec_o_map_thmss, size_o_map_thmss) =
if live = 0 then
`I (replicate nn [])
else
let
val pre_bnfs = map #pre_bnf fp_sugars;
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs;
val abs_inverses = map (#abs_inverse o #absT_info) fp_sugars;
val rec_defs = map #co_rec_def fp_sugars;
val gmaps = map (fn map0 => Term.list_comb (mk_map live As Bs map0, live_gs)) maps0;
val num_rec_args = length rec_arg_Ts;
val h_Ts = map B_ify rec_arg_Ts;
val h_names = variant_names num_rec_args "h";
val hs = map2 (curry Free) h_names h_Ts;
val hrecs = map (fn recx => Term.list_comb (Term.map_types B_ify recx, hs)) recs;
val rec_o_map_lhss = map2 (curry HOLogic.mk_comp) hrecs gmaps;
val ABgs = ABs ~~ gs;
fun mk_rec_arg_arg (x as Free (_, T)) =
let val U = B_ify T in
if T = U then x else build_map lthy2 [] (the o AList.lookup (op =) ABgs) (T, U) $ x
end;
fun mk_rec_o_map_arg rec_arg_T h =
let
val x_Ts = binder_types rec_arg_T;
val m = length x_Ts;
val x_names = variant_names m "x";
val xs = map2 (curry Free) x_names x_Ts;
val xs' = map mk_rec_arg_arg xs;
in
fold_rev Term.lambda xs (Term.list_comb (h, xs'))
end;
fun mk_rec_o_map_rhs recx =
let val args = map2 mk_rec_o_map_arg rec_arg_Ts hs in
Term.list_comb (recx, args)
end;
val rec_o_map_rhss = map mk_rec_o_map_rhs recs;
val rec_o_map_goals =
map2 (fold_rev (fold_rev Logic.all) [gs, hs] o HOLogic.mk_Trueprop oo
curry HOLogic.mk_eq) rec_o_map_lhss rec_o_map_rhss;
val rec_o_map_thms =
map3 (fn goal => fn rec_def => fn ctor_rec_o_map =>
Goal.prove lthy2 [] [] goal (fn {context = ctxt, ...} =>
mk_rec_o_map_tac ctxt rec_def pre_map_defs live_nesting_map_ident0s abs_inverses
ctor_rec_o_map)
|> Thm.close_derivation)
rec_o_map_goals rec_defs ctor_rec_o_maps;
val size_o_map_conds =
if exists (can Logic.dest_implies o Thm.prop_of) nested_size_o_maps then
map (HOLogic.mk_Trueprop o mk_inj) live_gs
else
[];
val fsizes = map (fn size_constB => Term.list_comb (size_constB, fsB)) size_constsB;
val size_o_map_lhss = map2 (curry HOLogic.mk_comp) fsizes gmaps;
val fgs = map2 (fn fB => fn g as Free (_, Type (_, [A, B])) =>
if A = B then fB else HOLogic.mk_comp (fB, g)) fsB gs;
val size_o_map_rhss = map (fn c => Term.list_comb (c, fgs)) size_consts;
val size_o_map_goals =
map2 (fold_rev (fold_rev Logic.all) [fsB, gs] o
curry Logic.list_implies size_o_map_conds o HOLogic.mk_Trueprop oo
curry HOLogic.mk_eq) size_o_map_lhss size_o_map_rhss;
(* The "size o map" theorem generation will fail if 'nested_size_maps' is incomplete,
which occurs when there is recursion through non-datatypes. In this case, we simply
avoid generating the theorem. The resulting characteristic lemmas are then expressed
in terms of "map", which is not the end of the world. *)
val size_o_map_thmss =
map3 (fn goal => fn size_def => the_list o try (fn rec_o_map =>
Goal.prove lthy2 [] [] goal (fn {context = ctxt, ...} =>
mk_size_o_map_tac ctxt size_def rec_o_map all_inj_maps nested_size_maps)
|> Thm.close_derivation))
size_o_map_goals size_defs rec_o_map_thms
in
(map single rec_o_map_thms, size_o_map_thmss)
end;
val massage_multi_notes =
maps (fn (thmN, thmss, attrs) =>
map2 (fn T_name => fn thms =>
((Binding.qualify true (Long_Name.base_name T_name) (Binding.name thmN), attrs),
[(thms, [])]))
T_names thmss)
#> filter_out (null o fst o hd o snd);
val notes =
[(rec_o_mapN, rec_o_map_thmss, []),
(sizeN, size_thmss, code_nitpicksimp_simp_attrs),
(size_o_mapN, size_o_map_thmss, [])]
|> massage_multi_notes;
in
lthy2
|> Local_Theory.notes notes |> snd
|> Spec_Rules.add Spec_Rules.Equational (size_consts, size_simps)
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (fold2 (fn T_name => fn Const (size_name, _) =>
Symtab.update (T_name, (size_name,
pairself (map (Morphism.thm phi)) (size_simps, flat size_o_map_thmss))))
T_names size_consts))
end;
end;