diff -r b8a1c3cdf739 -r c5f7cba2a675 src/HOL/Nominal/Examples/Class.thy
--- a/src/HOL/Nominal/Examples/Class.thy	Tue Jan 31 18:19:36 2006 +0100
+++ b/src/HOL/Nominal/Examples/Class.thy	Wed Feb 01 01:03:41 2006 +0100
@@ -3,16 +3,43 @@
 imports "../nominal" 
 begin
 
+section {* Term-Calculus from Urban's PhD *}
+
 atom_decl name coname
 
-section {* Term-Calculus from my PHD *}
+nominal_datatype trm = 
+    Ax   "name" "coname"
+  | Cut  "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm"            ("Cut <_>._ (_)._" [100,100,100,100] 100)
+  | NotR "\<guillemotleft>name\<guillemotright>trm" "coname"                 ("NotR (_)._ _" [100,100,100] 100)
+  | NotL "\<guillemotleft>coname\<guillemotright>trm" "name"                 ("NotL <_>._ _" [100,100,100] 100)
+  | AndR "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>coname\<guillemotright>trm" "coname" ("AndR <_>._ <_>._ _" [100,100,100,100,100] 100)
+  | AndL1 "\<guillemotleft>name\<guillemotright>trm" "name"                  ("AndL1 (_)._ _" [100,100,100] 100)
+  | AndL2 "\<guillemotleft>name\<guillemotright>trm" "name"                  ("AndL2 (_)._ _" [100,100,100] 100)
+  | OrR1 "\<guillemotleft>coname\<guillemotright>trm" "coname"               ("OrR1 <_>._ _" [100,100,100] 100)
+  | OrR2 "\<guillemotleft>coname\<guillemotright>trm" "coname"               ("OrR2 <_>._ _" [100,100,100] 100)
+  | OrL "\<guillemotleft>name\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm" "name"        ("OrL (_)._ (_)._ _" [100,100,100,100,100] 100)
+  | ImpR "\<guillemotleft>name\<guillemotright>(\<guillemotleft>coname\<guillemotright>trm)" "coname"       ("ImpR (_).<_>._ _" [100,100,100,100] 100)
+  | ImpL "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm" "name"     ("ImpL <_>._ (_)._ _" [100,100,100,100,100] 100)
+  
+  
+text {* Induction principles *}
 
-nominal_datatype trm = Ax  "name" "coname"
-                 | ImpR "\<guillemotleft>name\<guillemotright>(\<guillemotleft>coname\<guillemotright>trm)" "coname"  ("ImpR [_].[_]._ _" [100,100,100,100] 100)
-                 | ImpL "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm" "name"("ImpL [_]._ [_]._ _" [100,100,100,100,100] 100)
-                 | Cut "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm"        ("Cut [_]._ [_]._" [100,100,100,100] 100)
+thm trm.induct_weak --"weak"
+thm trm.induct      --"strong"
+thm trm.induct'     --"strong with explicit context (rarely needed)"
+
+text {* named terms *}
+
+nominal_datatype ntrm = N "\<guillemotleft>name\<guillemotright>trm" ("N (_)._" [100,100] 100)
+
+text {* conamed terms *}
 
-thm trm.induct
-thm trm.inducts
-thm trm.induct'
+nominal_datatype ctrm = C "\<guillemotleft>coname\<guillemotright>trm" ("C <_>._" [100,100] 100)
+
+text {* We should now define the two forms of substitition :o( *}
 
+consts
+  substn :: "trm \<Rightarrow> name   \<Rightarrow> ctrm \<Rightarrow> trm" ("_[_::=_]" [100,100,100] 100) 
+  substc :: "trm \<Rightarrow> coname \<Rightarrow> ntrm \<Rightarrow> trm" ("_[_::=_]" [100,100,100] 100)
+
+text {* does not work yet *}
\ No newline at end of file