(* Title: HOL/Tools/BNF/bnf_lfp_size.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2014
Generation of size functions for new-style datatypes.
*)
structure BNF_LFP_Size : sig end =
struct
open BNF_Util
open BNF_Def
open BNF_FP_Def_Sugar
val size_N = "size_"
val sizeN = "size"
val size_mapN = "size_map"
structure Data = Theory_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;
);
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 generate_size (fp_sugars as ({T = Type (_, As), BT = Type (_, Bs),
fp_res = {bnfs = fp_bnfs, ...}, common_co_inducts = common_inducts, ...} : fp_sugar) :: _) thy =
let
val data = Data.get thy;
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 = map fastype_of recs;
val Cs = map body_type rec_Ts;
val Cs_rho = map (rpair HOLogic.natT) Cs;
val substCT = 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;
val f_names = map (prefix "f" o string_of_int) (1 upto num_As);
val fs = map2 (curry Free) f_names f_Ts;
val fsB = map2 (curry Free) f_names f_TsB;
val As_fs = As ~~ fs;
val gen_size_names = map (Long_Name.map_base_name (prefix size_N)) 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) Ts then
(case Symtab.lookup data s of
SOME (gen_size_name, (_, gen_size_maps)) =>
let
val (args, gen_size_mapss') = split_list (map (fn T => mk_size_of_typ T []) Ts);
val gen_size_const = Const (gen_size_name, map fastype_of args ---> mk_to_natT T);
in
fold (union Thm.eq_thm) (gen_size_maps :: gen_size_mapss')
#> pair (Term.list_comb (gen_size_const, args))
end
| NONE => 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 => substCT (betapply (s, t)));
fun mk_gen_size_arg arg_T gen_size_maps =
let
val x_Ts = binder_types arg_T;
val m = length x_Ts;
val x_names = map (prefix "x" o string_of_int) (1 upto m);
val xs = map2 (curry Free) x_names x_Ts;
val (summands, gen_size_maps') =
fold_map mk_size_of_arg xs gen_size_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 substCT xs) sum, gen_size_maps')
end;
fun mk_gen_size_rhs rec_T recx gen_size_maps =
let
val arg_Ts = binder_fun_types rec_T;
val (args, gen_size_maps') = fold_map mk_gen_size_arg arg_Ts gen_size_maps;
in
(fold_rev Term.lambda fs (Term.list_comb (substCT recx, args)), gen_size_maps')
end;
fun mk_def_binding f = Binding.conceal o Binding.name o Thm.def_name o f o Long_Name.base_name;
val (gen_size_rhss, nested_gen_size_maps) = fold_map2 mk_gen_size_rhs rec_Ts recs [];
val gen_size_Ts = map fastype_of gen_size_rhss;
val gen_size_consts = map2 (curry Const) gen_size_names gen_size_Ts;
val gen_size_constsB = map (Term.map_types B_ify) gen_size_consts;
val gen_size_def_bs = map (mk_def_binding I) gen_size_names;
val (gen_size_defs, thy2) =
thy
|> Sign.add_consts (map (fn (s, T) => (Binding.name (Long_Name.base_name s), T, NoSyn))
(gen_size_names ~~ gen_size_Ts))
|> Global_Theory.add_defs false (map Thm.no_attributes (gen_size_def_bs ~~
map Logic.mk_equals (gen_size_consts ~~ gen_size_rhss)));
val zeros = map mk_abs_zero_nat As;
val spec_size_rhss = map (fn c => Term.list_comb (c, zeros)) gen_size_consts;
val spec_size_Ts = map fastype_of spec_size_rhss;
val spec_size_consts = map (curry Const @{const_name size}) spec_size_Ts;
val spec_size_def_bs = map (mk_def_binding (suffix "_overloaded")) gen_size_names;
fun define_spec_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 (spec_size_defs, thy3) = thy2
|> Class.instantiation (T_names, map dest_TFree As, [HOLogic.class_size])
|> fold_map3 define_spec_size spec_size_def_bs spec_size_consts spec_size_rhss
||> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
||> Local_Theory.exit_global;
val thy3_ctxt = Proof_Context.init_global thy3;
val gen_size_defs' =
map (mk_unabs_def (num_As + 1) o (fn thm => thm RS meta_eq_to_obj_eq)) gen_size_defs;
val spec_size_defs' =
map (mk_unabs_def 1 o (fn thm => thm RS meta_eq_to_obj_eq)) spec_size_defs;
fun derive_size_simp unfolds folds size_def' simp0 =
fold_thms thy3_ctxt folds (unfold_thms thy3_ctxt unfolds (trans OF [size_def', simp0]));
val derive_gen_size_simp =
derive_size_simp (@{thm snd_o_convol} :: nested_gen_size_maps) gen_size_defs';
val derive_spec_size_simp = derive_size_simp @{thms add_0_left add_0_right} spec_size_defs';
val gen_size_simpss = map2 (map o derive_gen_size_simp) gen_size_defs' rec_thmss;
val gen_size_simps = flat gen_size_simpss;
val spec_size_simpss = map2 (map o derive_spec_size_simp) spec_size_defs' gen_size_simpss;
val ABs = As ~~ Bs;
val g_names = map (prefix "g" o string_of_int) (1 upto num_As);
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 u_names = map (prefix "u" o string_of_int) (1 upto nn);
val us = map2 (curry Free) u_names Ts;
val maps0 = map map_of_bnf fp_bnfs;
val map_thms = maps #maps fp_sugars;
fun mk_gen_size_map_tac ctxt =
HEADGOAL (rtac (co_induct_of common_inducts)) THEN
ALLGOALS (asm_simp_tac (ss_only (o_apply :: map_thms @ gen_size_simps) ctxt));
val gen_size_map_thmss =
if live = 0 then
replicate nn []
else if null nested_gen_size_maps then
let
val xgmaps =
map2 (fn map0 => fn u => Term.list_comb (mk_map live As Bs map0, live_gs) $ u) maps0 us;
val fsizes =
map (fn gen_size_constB => Term.list_comb (gen_size_constB, fsB)) gen_size_constsB;
val lhss = map2 (curry (op $)) fsizes xgmaps;
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 rhss = map2 (fn gen_size_const => fn u => Term.list_comb (gen_size_const, fgs) $ u)
gen_size_consts us;
val goal = Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) lhss rhss)
|> HOLogic.mk_Trueprop;
in
Goal.prove_global thy3 [] [] goal (mk_gen_size_map_tac o #context)
|> Thm.close_derivation
|> conj_dests nn
|> map single
end
else
(* TODO: implement general case, with nesting of datatypes that themselves nest other
types *)
replicate nn [];
val (_, thy4) = thy3
|> fold_map3 (fn T_name => fn size_simps => fn gen_size_map_thms =>
let val qualify = Binding.qualify true (Long_Name.base_name T_name) in
Global_Theory.note_thmss ""
([((qualify (Binding.name sizeN),
[Simplifier.simp_add, Nitpick_Simps.add, Thm.declaration_attribute
(fn thm => Context.mapping (Code.add_default_eqn thm) I)]),
[(size_simps, [])]),
((qualify (Binding.name size_mapN), []), [(gen_size_map_thms, [])])]
|> filter_out (forall (null o fst) o snd))
end)
T_names (map2 append gen_size_simpss spec_size_simpss) gen_size_map_thmss
||> Spec_Rules.add_global Spec_Rules.Equational (gen_size_consts, gen_size_simps);
in
thy4
|> Data.map (fold2 (fn T_name => fn gen_size_name =>
Symtab.update_new (T_name, (gen_size_name, (gen_size_simps, flat gen_size_map_thmss))))
T_names gen_size_names)
end;
val _ = Theory.setup (fp_sugar_interpretation generate_size);
end;