1.1 --- a/src/HOL/Quotient.thy	Fri Mar 23 14:21:41 2012 +0100
     1.2 +++ b/src/HOL/Quotient.thy	Fri Mar 23 14:25:31 2012 +0100
     1.3 @@ -9,6 +9,7 @@
     1.4  keywords
     1.5    "print_quotmaps" "print_quotients" "print_quotconsts" :: diag and
     1.6    "quotient_type" :: thy_goal and "/" and
     1.7 +  "setup_lifting" :: thy_decl and
     1.8    "quotient_definition" :: thy_goal
     1.9  uses
    1.10    ("Tools/Quotient/quotient_info.ML")
    1.11 @@ -137,6 +138,18 @@
    1.12    unfolding Quotient_def
    1.13    by blast
    1.14  
    1.15 +lemma Quotient_refl1: 
    1.16 +  assumes a: "Quotient R Abs Rep" 
    1.17 +  shows "R r s \<Longrightarrow> R r r"
    1.18 +  using a unfolding Quotient_def 
    1.19 +  by fast
    1.20 +
    1.21 +lemma Quotient_refl2: 
    1.22 +  assumes a: "Quotient R Abs Rep" 
    1.23 +  shows "R r s \<Longrightarrow> R s s"
    1.24 +  using a unfolding Quotient_def 
    1.25 +  by fast
    1.26 +
    1.27  lemma Quotient_rel_rep:
    1.28    assumes a: "Quotient R Abs Rep"
    1.29    shows "R (Rep a) (Rep b) \<longleftrightarrow> a = b"
    1.30 @@ -263,6 +276,15 @@
    1.31    shows "R2 (f x) (g y)"
    1.32    using a by (auto elim: fun_relE)
    1.33  
    1.34 +lemma apply_rsp'':
    1.35 +  assumes "Quotient R Abs Rep"
    1.36 +  and "(R ===> S) f f"
    1.37 +  shows "S (f (Rep x)) (f (Rep x))"
    1.38 +proof -
    1.39 +  from assms(1) have "R (Rep x) (Rep x)" by (rule Quotient_rep_reflp)
    1.40 +  then show ?thesis using assms(2) by (auto intro: apply_rsp')
    1.41 +qed
    1.42 +
    1.43  subsection {* lemmas for regularisation of ball and bex *}
    1.44  
    1.45  lemma ball_reg_eqv:
    1.46 @@ -679,6 +701,153 @@
    1.47  
    1.48  end
    1.49  
    1.50 +subsection {* Quotient composition *}
    1.51 +
    1.52 +lemma OOO_quotient:
    1.53 +  fixes R1 :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
    1.54 +  fixes Abs1 :: "'a \<Rightarrow> 'b" and Rep1 :: "'b \<Rightarrow> 'a"
    1.55 +  fixes Abs2 :: "'b \<Rightarrow> 'c" and Rep2 :: "'c \<Rightarrow> 'b"
    1.56 +  fixes R2' :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
    1.57 +  fixes R2 :: "'b \<Rightarrow> 'b \<Rightarrow> bool"
    1.58 +  assumes R1: "Quotient R1 Abs1 Rep1"
    1.59 +  assumes R2: "Quotient R2 Abs2 Rep2"
    1.60 +  assumes Abs1: "\<And>x y. R2' x y \<Longrightarrow> R1 x x \<Longrightarrow> R1 y y \<Longrightarrow> R2 (Abs1 x) (Abs1 y)"
    1.61 +  assumes Rep1: "\<And>x y. R2 x y \<Longrightarrow> R2' (Rep1 x) (Rep1 y)"
    1.62 +  shows "Quotient (R1 OO R2' OO R1) (Abs2 \<circ> Abs1) (Rep1 \<circ> Rep2)"
    1.63 +apply (rule QuotientI)
    1.64 +   apply (simp add: o_def Quotient_abs_rep [OF R2] Quotient_abs_rep [OF R1])
    1.65 +  apply simp
    1.66 +  apply (rule_tac b="Rep1 (Rep2 a)" in pred_compI)
    1.67 +   apply (rule Quotient_rep_reflp [OF R1])
    1.68 +  apply (rule_tac b="Rep1 (Rep2 a)" in pred_compI [rotated])
    1.69 +   apply (rule Quotient_rep_reflp [OF R1])
    1.70 +  apply (rule Rep1)
    1.71 +  apply (rule Quotient_rep_reflp [OF R2])
    1.72 + apply safe
    1.73 +    apply (rename_tac x y)
    1.74 +    apply (drule Abs1)
    1.75 +      apply (erule Quotient_refl2 [OF R1])
    1.76 +     apply (erule Quotient_refl1 [OF R1])
    1.77 +    apply (drule Quotient_refl1 [OF R2], drule Rep1)
    1.78 +    apply (subgoal_tac "R1 r (Rep1 (Abs1 x))")
    1.79 +     apply (rule_tac b="Rep1 (Abs1 x)" in pred_compI, assumption)
    1.80 +     apply (erule pred_compI)
    1.81 +     apply (erule Quotient_symp [OF R1, THEN sympD])
    1.82 +    apply (rule Quotient_rel[symmetric, OF R1, THEN iffD2])
    1.83 +    apply (rule conjI, erule Quotient_refl1 [OF R1])
    1.84 +    apply (rule conjI, rule Quotient_rep_reflp [OF R1])
    1.85 +    apply (subst Quotient_abs_rep [OF R1])
    1.86 +    apply (erule Quotient_rel_abs [OF R1])
    1.87 +   apply (rename_tac x y)
    1.88 +   apply (drule Abs1)
    1.89 +     apply (erule Quotient_refl2 [OF R1])
    1.90 +    apply (erule Quotient_refl1 [OF R1])
    1.91 +   apply (drule Quotient_refl2 [OF R2], drule Rep1)
    1.92 +   apply (subgoal_tac "R1 s (Rep1 (Abs1 y))")
    1.93 +    apply (rule_tac b="Rep1 (Abs1 y)" in pred_compI, assumption)
    1.94 +    apply (erule pred_compI)
    1.95 +    apply (erule Quotient_symp [OF R1, THEN sympD])
    1.96 +   apply (rule Quotient_rel[symmetric, OF R1, THEN iffD2])
    1.97 +   apply (rule conjI, erule Quotient_refl2 [OF R1])
    1.98 +   apply (rule conjI, rule Quotient_rep_reflp [OF R1])
    1.99 +   apply (subst Quotient_abs_rep [OF R1])
   1.100 +   apply (erule Quotient_rel_abs [OF R1, THEN sym])
   1.101 +  apply simp
   1.102 +  apply (rule Quotient_rel_abs [OF R2])
   1.103 +  apply (rule Quotient_rel_abs [OF R1, THEN ssubst], assumption)
   1.104 +  apply (rule Quotient_rel_abs [OF R1, THEN subst], assumption)
   1.105 +  apply (erule Abs1)
   1.106 +   apply (erule Quotient_refl2 [OF R1])
   1.107 +  apply (erule Quotient_refl1 [OF R1])
   1.108 + apply (rename_tac a b c d)
   1.109 + apply simp
   1.110 + apply (rule_tac b="Rep1 (Abs1 r)" in pred_compI)
   1.111 +  apply (rule Quotient_rel[symmetric, OF R1, THEN iffD2])
   1.112 +  apply (rule conjI, erule Quotient_refl1 [OF R1])
   1.113 +  apply (simp add: Quotient_abs_rep [OF R1] Quotient_rep_reflp [OF R1])
   1.114 + apply (rule_tac b="Rep1 (Abs1 s)" in pred_compI [rotated])
   1.115 +  apply (rule Quotient_rel[symmetric, OF R1, THEN iffD2])
   1.116 +  apply (simp add: Quotient_abs_rep [OF R1] Quotient_rep_reflp [OF R1])
   1.117 +  apply (erule Quotient_refl2 [OF R1])
   1.118 + apply (rule Rep1)
   1.119 + apply (drule Abs1)
   1.120 +   apply (erule Quotient_refl2 [OF R1])
   1.121 +  apply (erule Quotient_refl1 [OF R1])
   1.122 + apply (drule Abs1)
   1.123 +  apply (erule Quotient_refl2 [OF R1])
   1.124 + apply (erule Quotient_refl1 [OF R1])
   1.125 + apply (drule Quotient_rel_abs [OF R1])
   1.126 + apply (drule Quotient_rel_abs [OF R1])
   1.127 + apply (drule Quotient_rel_abs [OF R1])
   1.128 + apply (drule Quotient_rel_abs [OF R1])
   1.129 + apply simp
   1.130 + apply (rule Quotient_rel[symmetric, OF R2, THEN iffD2])
   1.131 + apply simp
   1.132 +done
   1.133 +
   1.134 +lemma OOO_eq_quotient:
   1.135 +  fixes R1 :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
   1.136 +  fixes Abs1 :: "'a \<Rightarrow> 'b" and Rep1 :: "'b \<Rightarrow> 'a"
   1.137 +  fixes Abs2 :: "'b \<Rightarrow> 'c" and Rep2 :: "'c \<Rightarrow> 'b"
   1.138 +  assumes R1: "Quotient R1 Abs1 Rep1"
   1.139 +  assumes R2: "Quotient op= Abs2 Rep2"
   1.140 +  shows "Quotient (R1 OOO op=) (Abs2 \<circ> Abs1) (Rep1 \<circ> Rep2)"
   1.141 +using assms
   1.142 +by (rule OOO_quotient) auto
   1.143 +
   1.144 +subsection {* Invariant *}
   1.145 +
   1.146 +definition invariant :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" 
   1.147 +  where "invariant R = (\<lambda>x y. R x \<and> x = y)"
   1.148 +
   1.149 +lemma invariant_to_eq:
   1.150 +  assumes "invariant P x y"
   1.151 +  shows "x = y"
   1.152 +using assms by (simp add: invariant_def)
   1.153 +
   1.154 +lemma fun_rel_eq_invariant:
   1.155 +  shows "((invariant R) ===> S) = (\<lambda>f g. \<forall>x. R x \<longrightarrow> S (f x) (g x))"
   1.156 +by (auto simp add: invariant_def fun_rel_def)
   1.157 +
   1.158 +lemma invariant_same_args:
   1.159 +  shows "invariant P x x \<equiv> P x"
   1.160 +using assms by (auto simp add: invariant_def)
   1.161 +
   1.162 +lemma copy_type_to_Quotient:
   1.163 +  assumes "type_definition Rep Abs UNIV"
   1.164 +  shows "Quotient (op =) Abs Rep"
   1.165 +proof -
   1.166 +  interpret type_definition Rep Abs UNIV by fact
   1.167 +  from Abs_inject Rep_inverse show ?thesis by (auto intro!: QuotientI)
   1.168 +qed
   1.169 +
   1.170 +lemma copy_type_to_equivp:
   1.171 +  fixes Abs :: "'a \<Rightarrow> 'b"
   1.172 +  and Rep :: "'b \<Rightarrow> 'a"
   1.173 +  assumes "type_definition Rep Abs (UNIV::'a set)"
   1.174 +  shows "equivp (op=::'a\<Rightarrow>'a\<Rightarrow>bool)"
   1.175 +by (rule identity_equivp)
   1.176 +
   1.177 +lemma invariant_type_to_Quotient:
   1.178 +  assumes "type_definition Rep Abs {x. P x}"
   1.179 +  shows "Quotient (invariant P) Abs Rep"
   1.180 +proof -
   1.181 +  interpret type_definition Rep Abs "{x. P x}" by fact
   1.182 +  from Rep Abs_inject Rep_inverse show ?thesis by (auto intro!: QuotientI simp: invariant_def)
   1.183 +qed
   1.184 +
   1.185 +lemma invariant_type_to_part_equivp:
   1.186 +  assumes "type_definition Rep Abs {x. P x}"
   1.187 +  shows "part_equivp (invariant P)"
   1.188 +proof (intro part_equivpI)
   1.189 +  interpret type_definition Rep Abs "{x. P x}" by fact
   1.190 +  show "\<exists>x. invariant P x x" using Rep by (auto simp: invariant_def)
   1.191 +next
   1.192 +  show "symp (invariant P)" by (auto intro: sympI simp: invariant_def)
   1.193 +next
   1.194 +  show "transp (invariant P)" by (auto intro: transpI simp: invariant_def)
   1.195 +qed
   1.196 +
   1.197  subsection {* ML setup *}
   1.198  
   1.199  text {* Auxiliary data for the quotient package *}

     2.1 --- a/src/HOL/Tools/Quotient/quotient_def.ML	Fri Mar 23 14:21:41 2012 +0100
     2.2 +++ b/src/HOL/Tools/Quotient/quotient_def.ML	Fri Mar 23 14:25:31 2012 +0100
     2.3 @@ -27,6 +27,130 @@
     2.4  
     2.5  (** Interface and Syntax Setup **)
     2.6  
     2.7 +(* Generation of the code certificate from the rsp theorem *)
     2.8 +
     2.9 +infix 0 MRSL
    2.10 +
    2.11 +fun ants MRSL thm = fold (fn rl => fn thm => rl RS thm) ants thm
    2.12 +
    2.13 +fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
    2.14 +  | get_body_types (U, V)  = (U, V)
    2.15 +
    2.16 +fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
    2.17 +  | get_binder_types _ = []
    2.18 +
    2.19 +fun unabs_def ctxt def = 
    2.20 +  let
    2.21 +    val (_, rhs) = Thm.dest_equals (cprop_of def)
    2.22 +    fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
    2.23 +      | dest_abs tm = raise TERM("get_abs_var",[tm])
    2.24 +    val (var_name, T) = dest_abs (term_of rhs)
    2.25 +    val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
    2.26 +    val thy = Proof_Context.theory_of ctxt'
    2.27 +    val refl_thm = Thm.reflexive (cterm_of thy (Free (hd new_var_names, T)))
    2.28 +  in
    2.29 +    Thm.combination def refl_thm |>
    2.30 +    singleton (Proof_Context.export ctxt' ctxt)
    2.31 +  end
    2.32 +
    2.33 +fun unabs_all_def ctxt def = 
    2.34 +  let
    2.35 +    val (_, rhs) = Thm.dest_equals (cprop_of def)
    2.36 +    val xs = strip_abs_vars (term_of rhs)
    2.37 +  in  
    2.38 +    fold (K (unabs_def ctxt)) xs def
    2.39 +  end
    2.40 +
    2.41 +val map_fun_unfolded = 
    2.42 +  @{thm map_fun_def[abs_def]} |>
    2.43 +  unabs_def @{context} |>
    2.44 +  unabs_def @{context} |>
    2.45 +  Local_Defs.unfold @{context} [@{thm comp_def}]
    2.46 +
    2.47 +fun unfold_fun_maps ctm =
    2.48 +  let
    2.49 +    fun unfold_conv ctm =
    2.50 +      case (Thm.term_of ctm) of
    2.51 +        Const (@{const_name "map_fun"}, _) $ _ $ _ => 
    2.52 +          (Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
    2.53 +        | _ => Conv.all_conv ctm
    2.54 +    val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
    2.55 +  in
    2.56 +    (Conv.arg_conv (Conv.fun_conv unfold_conv then_conv try_beta_conv)) ctm
    2.57 +  end
    2.58 +
    2.59 +fun prove_rel ctxt rsp_thm (rty, qty) =
    2.60 +  let
    2.61 +    val ty_args = get_binder_types (rty, qty)
    2.62 +    fun disch_arg args_ty thm = 
    2.63 +      let
    2.64 +        val quot_thm = Quotient_Term.prove_quot_theorem ctxt args_ty
    2.65 +      in
    2.66 +        [quot_thm, thm] MRSL @{thm apply_rsp''}
    2.67 +      end
    2.68 +  in
    2.69 +    fold disch_arg ty_args rsp_thm
    2.70 +  end
    2.71 +
    2.72 +exception CODE_CERT_GEN of string
    2.73 +
    2.74 +fun simplify_code_eq ctxt def_thm = 
    2.75 +  Local_Defs.unfold ctxt [@{thm o_def}, @{thm map_fun_def}, @{thm id_def}] def_thm
    2.76 +
    2.77 +fun generate_code_cert ctxt def_thm rsp_thm (rty, qty) =
    2.78 +  let
    2.79 +    val quot_thm = Quotient_Term.prove_quot_theorem ctxt (get_body_types (rty, qty))
    2.80 +    val fun_rel = prove_rel ctxt rsp_thm (rty, qty)
    2.81 +    val abs_rep_thm = [quot_thm, fun_rel] MRSL @{thm Quotient_rep_abs}
    2.82 +    val abs_rep_eq = 
    2.83 +      case (HOLogic.dest_Trueprop o prop_of) fun_rel of
    2.84 +        Const (@{const_name HOL.eq}, _) $ _ $ _ => abs_rep_thm
    2.85 +        | Const (@{const_name invariant}, _) $ _ $ _ $ _ => abs_rep_thm RS @{thm invariant_to_eq}
    2.86 +        | _ => raise CODE_CERT_GEN "relation is neither equality nor invariant"
    2.87 +    val unfolded_def = Conv.fconv_rule unfold_fun_maps def_thm
    2.88 +    val unabs_def = unabs_all_def ctxt unfolded_def
    2.89 +    val rep = (snd o Thm.dest_comb o snd o Thm.dest_comb o cprop_of) quot_thm
    2.90 +    val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
    2.91 +    val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
    2.92 +    val code_cert = [repped_eq, abs_rep_eq] MRSL @{thm trans}
    2.93 +  in
    2.94 +    simplify_code_eq ctxt code_cert
    2.95 +  end
    2.96 +
    2.97 +fun define_code_cert def_thm rsp_thm (rty, qty) lthy = 
    2.98 +  let
    2.99 +    val quot_thm = Quotient_Term.prove_quot_theorem lthy (get_body_types (rty, qty))
   2.100 +  in
   2.101 +    if Quotient_Type.can_generate_code_cert quot_thm then
   2.102 +      let
   2.103 +        val code_cert = generate_code_cert lthy def_thm rsp_thm (rty, qty)
   2.104 +        val add_abs_eqn_attribute = 
   2.105 +          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abs_eqn thm) I)
   2.106 +        val add_abs_eqn_attrib = Attrib.internal (K add_abs_eqn_attribute);
   2.107 +      in
   2.108 +        lthy
   2.109 +          |> (snd oo Local_Theory.note) ((Binding.empty, [add_abs_eqn_attrib]), [code_cert])
   2.110 +      end
   2.111 +    else
   2.112 +      lthy
   2.113 +  end
   2.114 +
   2.115 +fun define_code_eq def_thm lthy =
   2.116 +  let
   2.117 +    val unfolded_def = Conv.fconv_rule unfold_fun_maps def_thm
   2.118 +    val code_eq = unabs_all_def lthy unfolded_def
   2.119 +    val simp_code_eq = simplify_code_eq lthy code_eq
   2.120 +  in
   2.121 +    lthy
   2.122 +      |> (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [simp_code_eq])
   2.123 +  end
   2.124 +
   2.125 +fun define_code def_thm rsp_thm (rty, qty) lthy =
   2.126 +  if body_type rty = body_type qty then 
   2.127 +    define_code_eq def_thm lthy
   2.128 +  else 
   2.129 +    define_code_cert def_thm rsp_thm (rty, qty) lthy
   2.130 +
   2.131  (* The ML-interface for a quotient definition takes
   2.132     as argument:
   2.133  
   2.134 @@ -52,17 +176,19 @@
   2.135  
   2.136  fun add_quotient_def ((var, (name, atts)), (lhs, rhs)) rsp_thm lthy =
   2.137    let
   2.138 +    val rty = fastype_of rhs
   2.139 +    val qty = fastype_of lhs
   2.140      val absrep_trm = 
   2.141 -      Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (fastype_of rhs, fastype_of lhs) $ rhs
   2.142 +      Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (rty, qty) $ rhs
   2.143      val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm))
   2.144      val (_, prop') = Local_Defs.cert_def lthy prop
   2.145      val (_, newrhs) = Local_Defs.abs_def prop'
   2.146  
   2.147 -    val ((trm, (_ , thm)), lthy') =
   2.148 +    val ((trm, (_ , def_thm)), lthy') =
   2.149        Local_Theory.define (var, ((Thm.def_binding_optional (#1 var) name, atts), newrhs)) lthy
   2.150  
   2.151      (* data storage *)
   2.152 -    val qconst_data = {qconst = trm, rconst = rhs, def = thm}
   2.153 +    val qconst_data = {qconst = trm, rconst = rhs, def = def_thm}
   2.154      fun get_rsp_thm_name (lhs_name, _) = Binding.suffix_name "_rsp" lhs_name
   2.155      
   2.156      val lthy'' = lthy'
   2.157 @@ -75,6 +201,7 @@
   2.158        |> (snd oo Local_Theory.note) 
   2.159          ((get_rsp_thm_name var, [Attrib.internal (K Quotient_Info.rsp_rules_add)]),
   2.160          [rsp_thm])
   2.161 +      |> define_code def_thm rsp_thm (rty, qty)
   2.162  
   2.163    in
   2.164      (qconst_data, lthy'')
   2.165 @@ -99,7 +226,8 @@
   2.166      fun simp_arrows_conv ctm =
   2.167        let
   2.168          val unfold_conv = Conv.rewrs_conv 
   2.169 -          [@{thm fun_rel_eq_rel[THEN eq_reflection]}, @{thm fun_rel_def[THEN eq_reflection]}]
   2.170 +          [@{thm fun_rel_eq_invariant[THEN eq_reflection]}, @{thm fun_rel_eq_rel[THEN eq_reflection]}, 
   2.171 +            @{thm fun_rel_def[THEN eq_reflection]}]
   2.172          val left_conv = simp_arrows_conv then_conv Conv.try_conv norm_fun_eq
   2.173          fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
   2.174        in
   2.175 @@ -109,11 +237,14 @@
   2.176            | _ => Conv.all_conv ctm
   2.177        end
   2.178  
   2.179 +    val unfold_ret_val_invs = Conv.bottom_conv 
   2.180 +      (K (Conv.try_conv (Conv.rewr_conv @{thm invariant_same_args}))) lthy 
   2.181      val simp_conv = Conv.arg_conv (Conv.fun2_conv simp_arrows_conv)
   2.182      val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
   2.183      val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
   2.184 +    val beta_conv = Thm.beta_conversion true
   2.185      val eq_thm = 
   2.186 -      (simp_conv then_conv univq_prenex_conv then_conv Thm.beta_conversion true) ctm
   2.187 +      (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs) ctm
   2.188    in
   2.189      Object_Logic.rulify(eq_thm RS Drule.equal_elim_rule2)
   2.190    end

     3.1 --- a/src/HOL/Tools/Quotient/quotient_term.ML	Fri Mar 23 14:21:41 2012 +0100
     3.2 +++ b/src/HOL/Tools/Quotient/quotient_term.ML	Fri Mar 23 14:25:31 2012 +0100
     3.3 @@ -20,6 +20,9 @@
     3.4    val equiv_relation: Proof.context -> typ * typ -> term
     3.5    val equiv_relation_chk: Proof.context -> typ * typ -> term
     3.6  
     3.7 +  val get_rel_from_quot_thm: thm -> term
     3.8 +  val prove_quot_theorem: Proof.context -> typ * typ -> thm
     3.9 +
    3.10    val regularize_trm: Proof.context -> term * term -> term
    3.11    val regularize_trm_chk: Proof.context -> term * term -> term
    3.12  
    3.13 @@ -331,6 +334,78 @@
    3.14    equiv_relation ctxt (rty, qty)
    3.15    |> Syntax.check_term ctxt
    3.16  
    3.17 +(* generation of the Quotient theorem  *)
    3.18 +
    3.19 +fun get_quot_thm ctxt s =
    3.20 +  let
    3.21 +    val thy = Proof_Context.theory_of ctxt
    3.22 +  in
    3.23 +    (case Quotient_Info.lookup_quotients_global thy s of
    3.24 +      SOME qdata => #quot_thm qdata
    3.25 +    | NONE => raise LIFT_MATCH ("No quotient type " ^ quote s ^ " found."))
    3.26 +  end
    3.27 +
    3.28 +fun get_rel_quot_thm thy s =
    3.29 +  (case Quotient_Info.lookup_quotmaps thy s of
    3.30 +    SOME map_data => #quot_thm map_data
    3.31 +  | NONE => raise LIFT_MATCH ("get_relmap (no relation map function found for type " ^ s ^ ")"));
    3.32 +
    3.33 +fun is_id_quot thm = (prop_of thm = prop_of @{thm identity_quotient})
    3.34 +
    3.35 +infix 0 MRSL
    3.36 +
    3.37 +fun ants MRSL thm = fold (fn rl => fn thm => rl RS thm) ants thm
    3.38 +
    3.39 +exception NOT_IMPL of string
    3.40 +
    3.41 +fun get_rel_from_quot_thm quot_thm = 
    3.42 +  let
    3.43 +    val (_ $ rel $ _ $ _) = (HOLogic.dest_Trueprop o prop_of) quot_thm
    3.44 +  in
    3.45 +    rel
    3.46 +  end
    3.47 +
    3.48 +fun mk_quot_thm_compose (rel_quot_thm, quot_thm) = 
    3.49 +  let
    3.50 +    val quot_thm_rel = get_rel_from_quot_thm quot_thm
    3.51 +  in
    3.52 +    if is_eq quot_thm_rel then [rel_quot_thm, quot_thm] MRSL @{thm OOO_eq_quotient}
    3.53 +    else raise NOT_IMPL "nested quotients: not implemented yet"
    3.54 +  end
    3.55 +
    3.56 +fun prove_quot_theorem ctxt (rty, qty) =
    3.57 +  if rty = qty
    3.58 +  then @{thm identity_quotient}
    3.59 +  else
    3.60 +    case (rty, qty) of
    3.61 +      (Type (s, tys), Type (s', tys')) =>
    3.62 +        if s = s'
    3.63 +        then
    3.64 +          let
    3.65 +            val args = map (prove_quot_theorem ctxt) (tys ~~ tys')
    3.66 +          in
    3.67 +            args MRSL (get_rel_quot_thm ctxt s)
    3.68 +          end
    3.69 +        else
    3.70 +          let
    3.71 +            val (Type (_, rtys), qty_pat) = get_rty_qty ctxt s'
    3.72 +            val qtyenv = match ctxt equiv_match_err qty_pat qty
    3.73 +            val rtys' = map (Envir.subst_type qtyenv) rtys
    3.74 +            val args = map (prove_quot_theorem ctxt) (tys ~~ rtys')
    3.75 +            val quot_thm = get_quot_thm ctxt s'
    3.76 +          in
    3.77 +            if forall is_id_quot args
    3.78 +            then
    3.79 +              quot_thm
    3.80 +            else
    3.81 +              let
    3.82 +                val rel_quot_thm = args MRSL (get_rel_quot_thm ctxt s)
    3.83 +              in
    3.84 +                mk_quot_thm_compose (rel_quot_thm, quot_thm)
    3.85 +             end
    3.86 +          end
    3.87 +    | _ => @{thm identity_quotient}
    3.88 +
    3.89  
    3.90  
    3.91  (*** Regularization ***)

     4.1 --- a/src/HOL/Tools/Quotient/quotient_type.ML	Fri Mar 23 14:21:41 2012 +0100
     4.2 +++ b/src/HOL/Tools/Quotient/quotient_type.ML	Fri Mar 23 14:25:31 2012 +0100
     4.3 @@ -6,6 +6,8 @@
     4.4  
     4.5  signature QUOTIENT_TYPE =
     4.6  sig
     4.7 +  val can_generate_code_cert: thm -> bool
     4.8 +  
     4.9    val add_quotient_type: ((string list * binding * mixfix) * (typ * term * bool) * 
    4.10      ((binding * binding) option)) * thm -> local_theory -> Quotient_Info.quotients * local_theory
    4.11  
    4.12 @@ -76,6 +78,44 @@
    4.13      Goal.prove lthy [] [] goal
    4.14        (K (typedef_quot_type_tac equiv_thm typedef_info))
    4.15    end
    4.16 +   
    4.17 +fun can_generate_code_cert quot_thm  =
    4.18 +   case Quotient_Term.get_rel_from_quot_thm quot_thm of
    4.19 +      Const (@{const_name HOL.eq}, _) => true
    4.20 +      | Const (@{const_name invariant}, _) $ _  => true
    4.21 +      | _ => false
    4.22 +
    4.23 +fun define_abs_type quot_thm lthy =
    4.24 +  if can_generate_code_cert quot_thm then
    4.25 +    let
    4.26 +      val abs_type_thm = quot_thm RS @{thm Quotient_abs_rep}
    4.27 +      val add_abstype_attribute = 
    4.28 +          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abstype thm) I)
    4.29 +        val add_abstype_attrib = Attrib.internal (K add_abstype_attribute);
    4.30 +    in
    4.31 +      lthy
    4.32 +        |> (snd oo Local_Theory.note) ((Binding.empty, [add_abstype_attrib]), [abs_type_thm])
    4.33 +    end
    4.34 +  else
    4.35 +    lthy
    4.36 +
    4.37 +fun init_quotient_infr quot_thm equiv_thm lthy =
    4.38 +  let
    4.39 +    val (_ $ rel $ abs $ rep) = (HOLogic.dest_Trueprop o prop_of) quot_thm
    4.40 +    val (qtyp, rtyp) = (dest_funT o fastype_of) rep
    4.41 +    val qty_full_name = (fst o dest_Type) qtyp
    4.42 +    val quotients = {qtyp = qtyp, rtyp = rtyp, equiv_rel = rel, equiv_thm = equiv_thm, 
    4.43 +      quot_thm = quot_thm }
    4.44 +    fun quot_info phi = Quotient_Info.transform_quotients phi quotients
    4.45 +    val abs_rep = {abs = abs, rep = rep}
    4.46 +    fun abs_rep_info phi = Quotient_Info.transform_abs_rep phi abs_rep
    4.47 +  in
    4.48 +    lthy
    4.49 +      |> Local_Theory.declaration {syntax = false, pervasive = true}
    4.50 +        (fn phi => Quotient_Info.update_quotients qty_full_name (quot_info phi)
    4.51 +          #> Quotient_Info.update_abs_rep qty_full_name (abs_rep_info phi))
    4.52 +      |> define_abs_type quot_thm
    4.53 +  end
    4.54  
    4.55  (* main function for constructing a quotient type *)
    4.56  fun add_quotient_type (((vs, qty_name, mx), (rty, rel, partial), opt_morphs), equiv_thm) lthy =
    4.57 @@ -86,7 +126,7 @@
    4.58        else equiv_thm RS @{thm equivp_implies_part_equivp}
    4.59  
    4.60      (* generates the typedef *)
    4.61 -    val ((qty_full_name, typedef_info), lthy1) =
    4.62 +    val ((_, typedef_info), lthy1) =
    4.63        typedef_make (vs, qty_name, mx, rel, rty) part_equiv lthy
    4.64  
    4.65      (* abs and rep functions from the typedef *)
    4.66 @@ -108,9 +148,9 @@
    4.67          NONE => (Binding.prefix_name "rep_" qty_name, Binding.prefix_name "abs_" qty_name)
    4.68        | SOME morphs => morphs)
    4.69  
    4.70 -    val ((abs_t, (_, abs_def)), lthy2) = lthy1
    4.71 +    val ((_, (_, abs_def)), lthy2) = lthy1
    4.72        |> Local_Theory.define ((abs_name, NoSyn), ((Thm.def_binding abs_name, []), abs_trm))
    4.73 -    val ((rep_t, (_, rep_def)), lthy3) = lthy2
    4.74 +    val ((_, (_, rep_def)), lthy3) = lthy2
    4.75        |> Local_Theory.define ((rep_name, NoSyn), ((Thm.def_binding rep_name, []), rep_trm))
    4.76  
    4.77      (* quot_type theorem *)
    4.78 @@ -129,13 +169,8 @@
    4.79      val quotients = {qtyp = Abs_ty, rtyp = rty, equiv_rel = rel, equiv_thm = equiv_thm, 
    4.80        quot_thm = quotient_thm}
    4.81  
    4.82 -    fun qinfo phi = Quotient_Info.transform_quotients phi quotients
    4.83 -    fun abs_rep phi = Quotient_Info.transform_abs_rep phi {abs = abs_t, rep = rep_t}
    4.84 -
    4.85      val lthy4 = lthy3
    4.86 -      |> Local_Theory.declaration {syntax = false, pervasive = true}
    4.87 -        (fn phi => Quotient_Info.update_quotients qty_full_name (qinfo phi)
    4.88 -           #> Quotient_Info.update_abs_rep qty_full_name (abs_rep phi))
    4.89 +      |> init_quotient_infr quotient_thm equiv_thm
    4.90        |> (snd oo Local_Theory.note)
    4.91          ((equiv_thm_name,
    4.92            if partial then [] else [Attrib.internal (K Quotient_Info.equiv_rules_add)]),
    4.93 @@ -276,6 +311,32 @@
    4.94  val _ =
    4.95    Outer_Syntax.local_theory_to_proof @{command_spec "quotient_type"}
    4.96      "quotient type definitions (require equivalence proofs)"
    4.97 -    (quotspec_parser >> quotient_type_cmd)
    4.98 +      (quotspec_parser >> quotient_type_cmd)
    4.99 +
   4.100 +(* Setup lifting using type_def_thm *)
   4.101 +
   4.102 +exception SETUP_LIFT_TYPE of string
   4.103 +
   4.104 +fun setup_lift_type typedef_thm =
   4.105 +  let
   4.106 +    val typedef_set = (snd o dest_comb o HOLogic.dest_Trueprop o prop_of) typedef_thm
   4.107 +    val (quot_thm, equivp_thm) = (case typedef_set of
   4.108 +      Const ("Orderings.top_class.top", _) => 
   4.109 +        (typedef_thm RS @{thm copy_type_to_Quotient}, 
   4.110 +         typedef_thm RS @{thm copy_type_to_equivp})
   4.111 +      | Const (@{const_name "Collect"}, _) $ Abs (_, _, _ $ Bound 0) => 
   4.112 +        (typedef_thm RS @{thm invariant_type_to_Quotient}, 
   4.113 +         typedef_thm RS @{thm invariant_type_to_part_equivp})
   4.114 +      | _ => raise SETUP_LIFT_TYPE "unsupported typedef theorem")
   4.115 +  in
   4.116 +    init_quotient_infr quot_thm equivp_thm
   4.117 +  end
   4.118 +
   4.119 +fun setup_lift_type_aux xthm lthy = setup_lift_type (singleton (Attrib.eval_thms lthy) xthm) lthy
   4.120 +
   4.121 +val _ = 
   4.122 +  Outer_Syntax.local_theory @{command_spec "setup_lifting"}
   4.123 +    "Setup lifting infrastracture" 
   4.124 +      (Parse_Spec.xthm >> (fn xthm => setup_lift_type_aux xthm))
   4.125  
   4.126  end;