# HG changeset patch
# User huffman
# Date 1315087791 25200
# Node ID a9635943a3e969539d5fdfbaddbb16f18eaad54d
# Parent  67b78d5dea5b231807652147327bd6a25d3bb6f3# Parent  ccfc7c193d2b998079e8a0e643662ef6d7d3ca48
merged

diff -r ccfc7c193d2b -r a9635943a3e9 src/HOL/Nominal/Examples/Pattern.thy
--- a/src/HOL/Nominal/Examples/Pattern.thy	Sat Sep 03 14:52:40 2011 -0700
+++ b/src/HOL/Nominal/Examples/Pattern.thy	Sat Sep 03 15:09:51 2011 -0700
@@ -1,7 +1,7 @@
 header {* Simply-typed lambda-calculus with let and tuple patterns *}
 
 theory Pattern
-imports Nominal
+imports "../Nominal"
 begin
 
 no_syntax
@@ -622,7 +622,7 @@
     (auto simp add: Cons_eq_append_conv fresh_star_def
      fresh_list_nil fresh_list_cons supp_list_nil supp_list_cons fresh_list_append
      supp_prod fresh_prod supp_atm fresh_atm
-     dest: notE [OF iffD1 [OF fresh_def [THEN meta_eq_to_obj_eq]]])
+     dest: notE [OF iffD1 [OF fresh_def]])
 
 lemma perm_mem_left: "(x::name) \<in> ((pi::name prm) \<bullet> A) \<Longrightarrow> (rev pi \<bullet> x) \<in> A"
   by (drule perm_boolI [of _ "rev pi"]) (simp add: eqvts perm_pi_simp)
diff -r ccfc7c193d2b -r a9635943a3e9 src/HOL/Nominal/Nominal.thy
--- a/src/HOL/Nominal/Nominal.thy	Sat Sep 03 14:52:40 2011 -0700
+++ b/src/HOL/Nominal/Nominal.thy	Sat Sep 03 15:09:51 2011 -0700
@@ -32,7 +32,7 @@
 (* an auxiliary constant for the decision procedure involving *) 
 (* permutations (to avoid loops when using perm-compositions)  *)
 definition
-  "perm_aux pi x \<equiv> pi\<bullet>x"
+  "perm_aux pi x = pi\<bullet>x"
 
 (* overloaded permutation operations *)
 overloading
@@ -51,61 +51,42 @@
 begin
 
 definition
-  perm_fun_def: "perm_fun pi (f::'a\<Rightarrow>'b) \<equiv> (\<lambda>x. pi\<bullet>f((rev pi)\<bullet>x))"
-
-fun
-  perm_bool :: "'x prm \<Rightarrow> bool \<Rightarrow> bool"
-where
+  perm_fun_def: "perm_fun pi (f::'a\<Rightarrow>'b) = (\<lambda>x. pi\<bullet>f((rev pi)\<bullet>x))"
+
+primrec perm_bool :: "'x prm \<Rightarrow> bool \<Rightarrow> bool" where
   true_eqvt:  "perm_bool pi True  = True"
 | false_eqvt: "perm_bool pi False = False"
 
-fun
-  perm_unit :: "'x prm \<Rightarrow> unit \<Rightarrow> unit" 
-where 
+primrec perm_unit :: "'x prm \<Rightarrow> unit \<Rightarrow> unit"  where 
   "perm_unit pi () = ()"
   
-fun
-  perm_prod :: "'x prm \<Rightarrow> ('a\<times>'b) \<Rightarrow> ('a\<times>'b)"
-where
+primrec perm_prod :: "'x prm \<Rightarrow> ('a\<times>'b) \<Rightarrow> ('a\<times>'b)" where
   "perm_prod pi (x,y) = (pi\<bullet>x,pi\<bullet>y)"
 
-fun
-  perm_list :: "'x prm \<Rightarrow> 'a list \<Rightarrow> 'a list"
-where
+primrec perm_list :: "'x prm \<Rightarrow> 'a list \<Rightarrow> 'a list" where
   nil_eqvt:  "perm_list pi []     = []"
 | cons_eqvt: "perm_list pi (x#xs) = (pi\<bullet>x)#(pi\<bullet>xs)"
 
-fun
-  perm_option :: "'x prm \<Rightarrow> 'a option \<Rightarrow> 'a option"
-where
+primrec perm_option :: "'x prm \<Rightarrow> 'a option \<Rightarrow> 'a option" where
   some_eqvt:  "perm_option pi (Some x) = Some (pi\<bullet>x)"
 | none_eqvt:  "perm_option pi None     = None"
 
-definition
-  perm_char :: "'x prm \<Rightarrow> char \<Rightarrow> char"
-where
-  perm_char_def: "perm_char pi c \<equiv> c"
-
-definition
-  perm_nat :: "'x prm \<Rightarrow> nat \<Rightarrow> nat"
-where
-  perm_nat_def: "perm_nat pi i \<equiv> i"
-
-definition
-  perm_int :: "'x prm \<Rightarrow> int \<Rightarrow> int"
-where
-  perm_int_def: "perm_int pi i \<equiv> i"
-
-fun
-  perm_noption :: "'x prm \<Rightarrow> 'a noption \<Rightarrow> 'a noption"
-where
+definition perm_char :: "'x prm \<Rightarrow> char \<Rightarrow> char" where
+  perm_char_def: "perm_char pi c = c"
+
+definition perm_nat :: "'x prm \<Rightarrow> nat \<Rightarrow> nat" where
+  perm_nat_def: "perm_nat pi i = i"
+
+definition perm_int :: "'x prm \<Rightarrow> int \<Rightarrow> int" where
+  perm_int_def: "perm_int pi i = i"
+
+primrec perm_noption :: "'x prm \<Rightarrow> 'a noption \<Rightarrow> 'a noption" where
   nsome_eqvt:  "perm_noption pi (nSome x) = nSome (pi\<bullet>x)"
 | nnone_eqvt:  "perm_noption pi nNone     = nNone"
 
-fun
-  perm_nprod :: "'x prm \<Rightarrow> ('a, 'b) nprod \<Rightarrow> ('a, 'b) nprod"
-where
+primrec perm_nprod :: "'x prm \<Rightarrow> ('a, 'b) nprod \<Rightarrow> ('a, 'b) nprod" where
   "perm_nprod pi (nPair x y) = nPair (pi\<bullet>x) (pi\<bullet>y)"
+
 end
 
 
@@ -188,18 +169,18 @@
 (*==============================*)
 
 definition prm_eq :: "'x prm \<Rightarrow> 'x prm \<Rightarrow> bool" (" _ \<triangleq> _ " [80,80] 80) where
-  "pi1 \<triangleq> pi2 \<equiv> \<forall>a::'x. pi1\<bullet>a = pi2\<bullet>a"
+  "pi1 \<triangleq> pi2 \<longleftrightarrow> (\<forall>a::'x. pi1\<bullet>a = pi2\<bullet>a)"
 
 section {* Support, Freshness and Supports*}
 (*========================================*)
 definition supp :: "'a \<Rightarrow> ('x set)" where  
-   "supp x \<equiv> {a . (infinite {b . [(a,b)]\<bullet>x \<noteq> x})}"
+   "supp x = {a . (infinite {b . [(a,b)]\<bullet>x \<noteq> x})}"
 
 definition fresh :: "'x \<Rightarrow> 'a \<Rightarrow> bool" ("_ \<sharp> _" [80,80] 80) where
-   "a \<sharp> x \<equiv> a \<notin> supp x"
+   "a \<sharp> x \<longleftrightarrow> a \<notin> supp x"
 
 definition supports :: "'x set \<Rightarrow> 'a \<Rightarrow> bool" (infixl "supports" 80) where
-   "S supports x \<equiv> \<forall>a b. (a\<notin>S \<and> b\<notin>S \<longrightarrow> [(a,b)]\<bullet>x=x)"
+   "S supports x \<longleftrightarrow> (\<forall>a b. (a\<notin>S \<and> b\<notin>S \<longrightarrow> [(a,b)]\<bullet>x=x))"
 
 (* lemmas about supp *)
 lemma supp_fresh_iff: 
@@ -1731,7 +1712,7 @@
   hence "infinite ({c. [(a,c)]\<bullet>x = x \<and> [(b,c)]\<bullet>x = x}-{a,b})" 
     by (force dest: Diff_infinite_finite)
   hence "({c. [(a,c)]\<bullet>x = x \<and> [(b,c)]\<bullet>x = x}-{a,b}) \<noteq> {}"
-    by (metis Collect_def finite_set set_empty2)
+    by (metis finite_set set_empty2)
   hence "\<exists>c. c\<in>({c. [(a,c)]\<bullet>x = x \<and> [(b,c)]\<bullet>x = x}-{a,b})" by (force)
   then obtain c 
     where eq1: "[(a,c)]\<bullet>x = x" 
diff -r ccfc7c193d2b -r a9635943a3e9 src/HOL/Nominal/nominal_atoms.ML
--- a/src/HOL/Nominal/nominal_atoms.ML	Sat Sep 03 14:52:40 2011 -0700
+++ b/src/HOL/Nominal/nominal_atoms.ML	Sat Sep 03 15:09:51 2011 -0700
@@ -714,48 +714,48 @@
              fold (fn ak_name => fn thy =>
              let
                val qu_class = Sign.full_bname thy ("pt_"^ak_name);
-               val simp_s = HOL_basic_ss addsimps [defn];
+               val simp_s = HOL_basic_ss addsimps [Simpdata.mk_eq defn];
                val proof = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
              in 
-               AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
+               AxClass.prove_arity (discrete_ty, [], [qu_class]) proof thy
              end) ak_names;
 
           fun discrete_fs_inst discrete_ty defn = 
              fold (fn ak_name => fn thy =>
              let
                val qu_class = Sign.full_bname thy ("fs_"^ak_name);
-               val supp_def = @{thm "Nominal.supp_def"};
-               val simp_s = HOL_ss addsimps [supp_def,Collect_const,finite_emptyI,defn];
+               val supp_def = Simpdata.mk_eq @{thm "Nominal.supp_def"};
+               val simp_s = HOL_ss addsimps [supp_def, Collect_const, finite_emptyI, Simpdata.mk_eq defn];
                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
              in 
-               AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
+               AxClass.prove_arity (discrete_ty, [], [qu_class]) proof thy
              end) ak_names;
 
           fun discrete_cp_inst discrete_ty defn = 
              fold (fn ak_name' => (fold (fn ak_name => fn thy =>
              let
                val qu_class = Sign.full_bname thy ("cp_"^ak_name^"_"^ak_name');
-               val supp_def = @{thm "Nominal.supp_def"};
-               val simp_s = HOL_ss addsimps [defn];
+               val supp_def = Simpdata.mk_eq @{thm "Nominal.supp_def"};
+               val simp_s = HOL_ss addsimps [Simpdata.mk_eq defn];
                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
              in
-               AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
+               AxClass.prove_arity (discrete_ty, [], [qu_class]) proof thy
              end) ak_names)) ak_names;
 
         in
          thy26
-         |> discrete_pt_inst @{type_name nat}  @{thm "perm_nat_def"}
-         |> discrete_fs_inst @{type_name nat}  @{thm "perm_nat_def"}
-         |> discrete_cp_inst @{type_name nat}  @{thm "perm_nat_def"}
-         |> discrete_pt_inst @{type_name bool} @{thm "perm_bool"}
-         |> discrete_fs_inst @{type_name bool} @{thm "perm_bool"}
-         |> discrete_cp_inst @{type_name bool} @{thm "perm_bool"}
-         |> discrete_pt_inst @{type_name int} @{thm "perm_int_def"}
-         |> discrete_fs_inst @{type_name int} @{thm "perm_int_def"}
-         |> discrete_cp_inst @{type_name int} @{thm "perm_int_def"}
-         |> discrete_pt_inst @{type_name char} @{thm "perm_char_def"}
-         |> discrete_fs_inst @{type_name char} @{thm "perm_char_def"}
-         |> discrete_cp_inst @{type_name char} @{thm "perm_char_def"}
+         |> discrete_pt_inst @{type_name nat} @{thm perm_nat_def}
+         |> discrete_fs_inst @{type_name nat} @{thm perm_nat_def}
+         |> discrete_cp_inst @{type_name nat} @{thm perm_nat_def}
+         |> discrete_pt_inst @{type_name bool} @{thm perm_bool}
+         |> discrete_fs_inst @{type_name bool} @{thm perm_bool}
+         |> discrete_cp_inst @{type_name bool} @{thm perm_bool}
+         |> discrete_pt_inst @{type_name int} @{thm perm_int_def}
+         |> discrete_fs_inst @{type_name int} @{thm perm_int_def}
+         |> discrete_cp_inst @{type_name int} @{thm perm_int_def}
+         |> discrete_pt_inst @{type_name char} @{thm perm_char_def}
+         |> discrete_fs_inst @{type_name char} @{thm perm_char_def}
+         |> discrete_cp_inst @{type_name char} @{thm perm_char_def}
         end;
 
 
diff -r ccfc7c193d2b -r a9635943a3e9 src/HOL/Nominal/nominal_datatype.ML
--- a/src/HOL/Nominal/nominal_datatype.ML	Sat Sep 03 14:52:40 2011 -0700
+++ b/src/HOL/Nominal/nominal_datatype.ML	Sat Sep 03 15:09:51 2011 -0700
@@ -155,9 +155,9 @@
 val supp_prod = @{thm supp_prod};
 val fresh_prod = @{thm fresh_prod};
 val supports_fresh = @{thm supports_fresh};
-val supports_def = @{thm Nominal.supports_def};
-val fresh_def = @{thm fresh_def};
-val supp_def = @{thm supp_def};
+val supports_def = Simpdata.mk_eq @{thm Nominal.supports_def};
+val fresh_def = Simpdata.mk_eq @{thm fresh_def};
+val supp_def = Simpdata.mk_eq @{thm supp_def};
 val rev_simps = @{thms rev.simps};
 val app_simps = @{thms append.simps};
 val at_fin_set_supp = @{thm at_fin_set_supp};
@@ -306,7 +306,7 @@
     val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
 
     val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types);
-    val perm_fun_def = Global_Theory.get_thm thy2 "perm_fun_def";
+    val perm_fun_def = Simpdata.mk_eq @{thm perm_fun_def};
 
     val unfolded_perm_eq_thms =
       if length descr = length new_type_names then []
diff -r ccfc7c193d2b -r a9635943a3e9 src/HOL/Nominal/nominal_permeq.ML
--- a/src/HOL/Nominal/nominal_permeq.ML	Sat Sep 03 14:52:40 2011 -0700
+++ b/src/HOL/Nominal/nominal_permeq.ML	Sat Sep 03 15:09:51 2011 -0700
@@ -56,10 +56,10 @@
 val finite_Un     = @{thm "finite_Un"};
 val conj_absorb   = @{thm "conj_absorb"};
 val not_false     = @{thm "not_False_eq_True"}
-val perm_fun_def  = @{thm "Nominal.perm_fun_def"};
+val perm_fun_def  = Simpdata.mk_eq @{thm "Nominal.perm_fun_def"};
 val perm_eq_app   = @{thm "Nominal.pt_fun_app_eq"};
-val supports_def  = @{thm "Nominal.supports_def"};
-val fresh_def     = @{thm "Nominal.fresh_def"};
+val supports_def  = Simpdata.mk_eq @{thm "Nominal.supports_def"};
+val fresh_def     = Simpdata.mk_eq @{thm "Nominal.fresh_def"};
 val fresh_prod    = @{thm "Nominal.fresh_prod"};
 val fresh_unit    = @{thm "Nominal.fresh_unit"};
 val supports_rule = @{thm "supports_finite"};
@@ -130,7 +130,7 @@
      case redex of 
        (* case pi o f == (%x. pi o (f ((rev pi)o x))) *)     
        (Const("Nominal.perm",_) $ pi $ f)  => 
-          (if (applicable_fun f) then SOME (perm_fun_def) else NONE)
+          (if (applicable_fun f) then SOME perm_fun_def else NONE)
       | _ => NONE
    end