
diff -r 0fea8b7a14a1 -r 01e71cddf6a3 ProgTutorial/General.thy
--- a/ProgTutorial/General.thy	Tue Oct 13 22:57:25 2009 +0200
+++ b/ProgTutorial/General.thy	Wed Oct 14 02:32:53 2009 +0200
@@ -11,7 +11,7 @@
 (*>*)
 
 
-chapter {* Isabelle in More Detail \mbox{or, the Good, the Bad and the Ugly} *}
+chapter {* Isabelle in More Detail *}
 
 text {*
   Isabelle is build around a few central ideas. One central idea is the
@@ -693,7 +693,7 @@
   val zero = @{term \"0::nat\"}
 in
   cterm_of @{theory} 
-      (Const (@{const_name plus}, natT --> natT --> natT) $ zero $ zero)
+      (Const (@{const_name plus}, [natT, natT] ---> natT) $ zero $ zero)
 end" "0 + 0"}
 
   In Isabelle not just terms need to be certified, but also types. For example, 
@@ -779,7 +779,8 @@
   final statement of the theorem.
 
   @{ML_response_fake [display, gray]
-  "string_of_thm @{context} my_thm |> tracing"
+  "string_of_thm @{context} my_thm 
+|> tracing"
   "\<lbrakk>\<And>x. P x \<Longrightarrow> Q x; P t\<rbrakk> \<Longrightarrow> Q t"}
 
   However, internally the code-snippet constructs the following 
@@ -811,24 +812,26 @@
 text {*
   The first argument @{ML_ind theoremK in Thm} is a kind indicator, which
   classifies the theorem. For a theorem arising from a definition we should
-  state @{ML_ind definitionK in Thm}, instead. The second argument is the 
-  name under which we store the theorem or theorems. The third can contain 
-  a list of (theorem) attributes. Above it is empty, but if we want to store
-  the theorem and at the same time add it to the simpset we have to declare:
+  use @{ML_ind definitionK in Thm}, for an axiom @{ML_ind axiomK in Thm}, for
+  ``normal'' theorems the kinds @{ML_ind theoremK in Thm} or @{ML_ind lemmaK
+  in Thm}.  The second argument is the name under which we store the theorem
+  or theorems. The third can contain a list of (theorem) attributes. We will
+  explain them in detail in Section~\ref{sec:attributes}. Below we
+  use such an attribute in order add the theorem to the simpset. 
+  have to declare:
 *}
 
 local_setup %gray {*
   LocalTheory.note Thm.theoremK
-     ((@{binding "my_thm_simp"}, 
-          [Attrib.internal (K Simplifier.simp_add)]), 
-             [my_thm]) #> snd *}
+    ((@{binding "my_thm_simp"}, 
+       [Attrib.internal (K Simplifier.simp_add)]), [my_thm]) #> snd *}
 
 text {*
   Note that we have to use another name for the theorem, since Isabelle does
-  not allow to add another theorem under the same name.  The attribute can be
-  given @{ML_ind internal in Attrib}. If we use the function @{ML
-  get_thm_names_from_ss} from the previous chapter, we can check whether the
-  theorem has been added.
+  not allow to store another theorem under the same name. The attribute needs to
+  be wrapped inside the function @{ML_ind internal in Attrib}. If we use the 
+  function @{ML get_thm_names_from_ss} from the previous chapter, we can check 
+  whether the theorem has actually been added.
 
   @{ML_response [display,gray]
   "let
@@ -838,20 +841,23 @@
 end"
   "true"}
 
-  Now the theorems @{thm [source] my_thm} and @{thm [source] my_thm_simp} can 
-  also be referenced  with the \isacommand{thm}-command on the user-level of 
-  Isabelle
+  The main point of storing the theorems @{thm [source] my_thm} and @{thm
+  [source] my_thm_simp} is that they can now also be referenced with the
+  \isacommand{thm}-command on the user-level of Isabelle
+
 
   \begin{isabelle}
   \isacommand{thm}~@{text "my_thm"}\isanewline
    @{text ">"}~@{prop "\<lbrakk>\<And>x. P x \<Longrightarrow> Q x; P t\<rbrakk> \<Longrightarrow> Q t"}
   \end{isabelle}
 
-  or with the @{text "@{thm \<dots>}"}-antiquotation on the ML-level. Note that the
-  theorem does not have any meta-variables that would be present if we proved
-  this theorem on the user-level. As we shall see later on, we have to construct
-  meta-variables explicitly.
+  or with the @{text "@{thm \<dots>}"}-antiquotation on the ML-level. As can be seen
+  the theorem does not have any meta-variables that would be present if we proved
+  this theorem on the user-level. We will see later on, we have to construct
+  meta-variables in a theorem explicitly.
+*}
 
+text {*
   There is a multitude of functions that manage or manipulate theorems. For example 
   we can test theorems for (alpha) equality. Suppose you proved the following three 
   facts.
@@ -922,6 +928,16 @@
   @{ML_file "Pure/thm.ML"}, @{ML_file "Pure/more_thm.ML"} and @{ML_file "Pure/drule.ML"}. 
   \end{readmore}
 
+  The simplifier can be used to unfold definition in theorms. To show
+  this we build the theorem @{term "True \<equiv> True"} (Line 1) and then 
+  unfold the constant according to its definition (Line 2).
+
+  @{ML_response_fake [display,gray,linenos]
+  "Thm.reflexive @{cterm \"True\"}
+  |> Simplifier.rewrite_rule [@{thm True_def}]
+  |> string_of_thm @{context}
+  |> tracing"
+  "(\<lambda>x. x) = (\<lambda>x. x) \<equiv> (\<lambda>x. x) = (\<lambda>x. x)"}
 
   Often it is necessary to transform theorems to and from the object 
   logic.  For example, the function @{ML_ind rulify in ObjectLogic}
@@ -946,10 +962,32 @@
 
   In this code the function @{ML atomize in ObjectLogic} produces 
   a meta-equation between the given theorem and the theorem transformed
-  into the object logic. The function @{ML_ind rewrite_rule in MetaSimplifier}
-  unfolds this meta-equation in the given theorem. The result is
-  the theorem with object logic connectives.
-x
+  into the object logic. The result is the theorem with object logic 
+  connectives. However, in order to completely transform a theorem
+  such as @{thm [source] list.induct}
+
+  @{thm [display] list.induct}
+
+  we have to first abstract over the variables @{text "?P"} and 
+  @{text "?list"}. For this we can use the function 
+  @{ML_ind forall_intr_vars in Drule}. 
+*}
+
+ML{*fun atomize_thm thm =
+let
+  val thm' = forall_intr_vars thm
+  val thm'' = ObjectLogic.atomize (cprop_of thm')
+in
+  MetaSimplifier.rewrite_rule [thm''] thm'
+end*}
+
+text {*
+  For @{thm [source] list.induct} it produces:
+
+  @{ML_response_fake [display, gray]
+  "atomize_thm @{thm list.induct}"
+  "\<forall>P list. P [] \<longrightarrow> (\<forall>a list. P list \<longrightarrow> P (a # list)) \<longrightarrow> P list"}
+
   Theorems can also be produced from terms by giving an explicit proof. 
   One way to achive this is by using the function @{ML_ind prove in Goal}. 
   For example




