generate size instances for new-style datatypes
authorblanchet
Wed, 23 Apr 2014 10:23:26 +0200
changeset 56638 092a306bcc3d
parent 56637 d1d55f1bbc8a
child 56639 c9d6b581bd3b
generate size instances for new-style datatypes
src/HOL/BNF_LFP.thy
src/HOL/Tools/BNF/bnf_fp_def_sugar.ML
src/HOL/Tools/BNF/bnf_fp_n2m.ML
src/HOL/Tools/BNF/bnf_fp_n2m_sugar.ML
src/HOL/Tools/BNF/bnf_lfp.ML
src/HOL/Tools/BNF/bnf_lfp_rec_sugar.ML
src/HOL/Tools/BNF/bnf_lfp_rec_sugar_more.ML
src/HOL/Tools/BNF/bnf_lfp_size.ML
src/HOL/Tools/BNF/bnf_lfp_tactics.ML
src/HOL/Tools/BNF/bnf_lfp_util.ML
--- a/src/HOL/BNF_LFP.thy	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/BNF_LFP.thy	Wed Apr 23 10:23:26 2014 +0200
@@ -186,12 +186,78 @@
 lemma ssubst_Pair_rhs: "\<lbrakk>(r, s) \<in> R; s' = s\<rbrakk> \<Longrightarrow> (r, s') \<in> R"
   by (rule ssubst)
 
+lemma snd_o_convol: "(snd \<circ> (\<lambda>x. (f x, g x))) = g"
+  by (rule ext) simp
+
+lemma inj_on_convol_id: "inj_on (\<lambda>x. (x, f x)) X"
+  unfolding inj_on_def by simp
+
 ML_file "Tools/BNF/bnf_lfp_util.ML"
 ML_file "Tools/BNF/bnf_lfp_tactics.ML"
 ML_file "Tools/BNF/bnf_lfp.ML"
 ML_file "Tools/BNF/bnf_lfp_compat.ML"
 ML_file "Tools/BNF/bnf_lfp_rec_sugar_more.ML"
+ML_file "Tools/BNF/bnf_lfp_size.ML"
 
 hide_fact (open) id_transfer
 
+datatype_new x = X nat
+thm x.size
+
+datatype_new 'a l = N | C 'a "'a l"
+thm l.size
+thm l.size_map
+thm size_l_def size_l_overloaded_def
+
+datatype_new
+  'a tl = TN | TC "'a mt" "'a tl" and
+  'a mt = MT 'a "'a tl"
+
+thm size_tl_def size_tl_overloaded_def
+thm size_mt_def size_mt_overloaded_def
+
+datatype_new 'a t = T 'a "'a t l"
+thm t.size
+
+lemma size_l_cong: "(ALL x : set_l t. f x = g x) --> size_l f t = size_l g t"
+  apply (induct_tac t)
+  apply (simp only: l.size simp_thms)
+  apply (simp add: l.set l.size simp_thms)
+  done
+
+lemma t_size_map_t: "size_t g (map_t f t) = size_t (g \<circ> f) t"
+  apply (rule t.induct)
+  apply (simp_all only: t.map t.size comp_def l.size_map)
+  apply (auto intro: size_l_cong)
+  apply (subst size_l_cong[rule_format], assumption)
+  apply (rule refl)
+  done
+
+
+thm t.size
+
+lemmas size_t_def' =
+  size_t_def[THEN meta_eq_to_obj_eq, THEN fun_cong, THEN fun_cong]
+
+thm trans[OF size_t_def' t.rec(1), unfolded l.size_map snd_o_convol, folded size_t_def']
+
+lemma "size_t f (T x ts) = f x + size_l (size_t f) ts + Suc 0"
+  unfolding size_t_def t.rec l.size_map snd_o_convol
+  by rule
+
+
+lemma "       (\<And>x2aa. x2aa \<in> set_l x2a \<Longrightarrow>
+                size_t f1 (map_t g1 x2aa) = size_t (f1 \<circ> g1) x2aa) \<Longrightarrow>
+       f1 (g1 x1a) +
+       size_l snd (map_l (\<lambda>t. (t, size_t f1 t)) (map_l (map_t g1) x2a)) +
+       Suc 0 =
+       f1 (g1 x1a) + size_l snd (map_l (\<lambda>t. (t, size_t (\<lambda>x1. f1 (g1 x1)) t)) x2a) +
+       Suc 0"
+apply (simp only: l.size_map comp_def snd_conv t.size_map snd_o_convol)
+
+thm size_t_def size_t_overloaded_def
+
+xdatatype_new ('a, 'b, 'c) x = XN 'c | XC 'a "('a, 'b, 'c) x"
+thm size_x_def size_x_overloaded_def
+
 end
--- a/src/HOL/Tools/BNF/bnf_fp_def_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_fp_def_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -9,6 +9,7 @@
 sig
   type fp_sugar =
     {T: typ,
+     BT: typ,
      X: typ,
      fp: BNF_Util.fp_kind,
      fp_res_index: int,
@@ -123,6 +124,7 @@
 
 type fp_sugar =
   {T: typ,
+   BT: typ,
    X: typ,
    fp: fp_kind,
    fp_res_index: int,
@@ -1086,6 +1088,7 @@
     val dtors = map (mk_dtor As) dtors0;
 
     val fpTs = map (domain_type o fastype_of) dtors;
+    val fpBTs = map B_ify fpTs;
 
     fun massage_simple_notes base =
       filter_out (null o #2)
@@ -1215,7 +1218,7 @@
                 end;
 
               val cxIns = map2 (mk_cIn ctor) ks xss;
-              val cyIns = map2 (mk_cIn (map_types B_ify ctor)) ks yss;
+              val cyIns = map2 (mk_cIn (Term.map_types B_ify ctor)) ks yss;
 
               fun mk_map_thm ctr_def' cxIn =
                 fold_thms lthy [ctr_def']
--- a/src/HOL/Tools/BNF/bnf_fp_n2m.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_fp_n2m.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -25,7 +25,7 @@
 open BNF_FP_N2M_Tactics
 
 fun force_typ ctxt T =
-  map_types Type_Infer.paramify_vars
+  Term.map_types Type_Infer.paramify_vars
   #> Type.constraint T
   #> Syntax.check_term ctxt
   #> singleton (Variable.polymorphic ctxt);
--- a/src/HOL/Tools/BNF/bnf_fp_n2m_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_fp_n2m_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -276,10 +276,11 @@
 
         fun mk_target_fp_sugar T X kk pre_bnf absT_info ctrXs_Tss ctr_defs ctr_sugar co_rec maps
             co_inducts co_rec_thms disc_corec_thms sel_corec_thmss rel_injects =
-          {T = T, X = X, fp = fp, fp_res = fp_res, fp_res_index = kk, pre_bnf = pre_bnf,
-           absT_info = absT_info, nested_bnfs = nested_bnfs, nesting_bnfs = nesting_bnfs,
-           ctrXs_Tss = ctrXs_Tss, ctr_defs = ctr_defs, ctr_sugar = ctr_sugar, co_rec = co_rec,
-           maps = maps, common_co_inducts = common_co_inducts, co_inducts = co_inducts,
+          {T = T, BT = Term.dummyT (*wrong but harmless*), X = X, fp = fp, fp_res = fp_res,
+           fp_res_index = kk, pre_bnf = pre_bnf, absT_info = absT_info, nested_bnfs = nested_bnfs,
+           nesting_bnfs = nesting_bnfs, ctrXs_Tss = ctrXs_Tss, ctr_defs = ctr_defs,
+           ctr_sugar = ctr_sugar, co_rec = co_rec, maps = maps,
+           common_co_inducts = common_co_inducts, co_inducts = co_inducts,
            co_rec_thms = co_rec_thms, disc_co_recs = disc_corec_thms,
            sel_co_recss = sel_corec_thmss, rel_injects = rel_injects}
           |> morph_fp_sugar phi;
--- a/src/HOL/Tools/BNF/bnf_lfp.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_lfp.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -3,7 +3,7 @@
     Author:     Andrei Popescu, TU Muenchen
     Copyright   2012
 
-Datatype construction.
+New-style datatype construction.
 *)
 
 signature BNF_LFP =
--- a/src/HOL/Tools/BNF/bnf_lfp_rec_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_lfp_rec_sugar.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -3,7 +3,7 @@
     Author:     Jasmin Blanchette, TU Muenchen
     Copyright   2013
 
-Recursor sugar ("primrec").
+New-style recursor sugar ("primrec").
 *)
 
 signature BNF_LFP_REC_SUGAR =
--- a/src/HOL/Tools/BNF/bnf_lfp_rec_sugar_more.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_lfp_rec_sugar_more.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -3,7 +3,7 @@
     Author:     Jasmin Blanchette, TU Muenchen
     Copyright   2013
 
-More recursor sugar.
+More new-style recursor sugar.
 *)
 
 structure BNF_LFP_Rec_Sugar_More : sig end =
@@ -141,14 +141,14 @@
         in
           if ctr_pos >= 0 then
             if d = SOME ~1 andalso length vs = ctr_pos then
-              list_comb (permute_args ctr_pos (snd_const pT), vs)
+              Term.list_comb (permute_args ctr_pos (snd_const pT), vs)
             else if length vs > ctr_pos andalso is_some d andalso
                 d = try (fn Bound n => n) (nth vs ctr_pos) then
-              list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
+              Term.list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
             else
               raise PRIMREC ("recursive call not directly applied to constructor argument", [t])
           else
-            list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
+            Term.list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
         end
   in
     subst (SOME ~1)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/BNF/bnf_lfp_size.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -0,0 +1,241 @@
+(*  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;
--- a/src/HOL/Tools/BNF/bnf_lfp_tactics.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_lfp_tactics.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -3,7 +3,7 @@
     Author:     Andrei Popescu, TU Muenchen
     Copyright   2012
 
-Tactics for the datatype construction.
+Tactics for the new-style datatype construction.
 *)
 
 signature BNF_LFP_TACTICS =
--- a/src/HOL/Tools/BNF/bnf_lfp_util.ML	Wed Apr 23 10:23:26 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_lfp_util.ML	Wed Apr 23 10:23:26 2014 +0200
@@ -3,7 +3,7 @@
     Author:     Jasmin Blanchette, TU Muenchen
     Copyright   2012
 
-Library for the datatype construction.
+Library for the new-style datatype construction.
 *)
 
 signature BNF_LFP_UTIL =