--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/activities/tphols09/IDW/MW-Ex3.thy	Wed Mar 30 17:27:34 2016 +0100
@@ -0,0 +1,142 @@
+theory Ex1
+imports Main
+begin
+
+lemma True
+proof
+
+  subsect {* Basic context elements *}
+
+  {
+    fix x
+    have "B x" sorry
+  }
+  thm this
+
+  {
+    assume A
+    have B sorry
+  }
+  thm this
+
+  {
+    def x == a
+    have "B x" sorry
+  }
+  thm this
+
+  {
+    obtain a where "B a" sorry
+    have C sorry
+  }
+  thm this
+
+
+  subsect {* Contexts vs. rules *}
+
+  {
+    fix A B
+    fix x :: 'a
+    assume "A x"
+    have "B x" sorry
+  }
+  note r = this
+
+  {
+    ML_prf {* val ctxt = @{context} *}
+    ML_prf {* val (((Ts, ts), [th']), ctxt') =
+      Variable.import_thms true [@{thm r}] ctxt *}
+  }
+
+qed
+
+
+section {* Building up contexts in ML *}
+
+subsection {* Variables *}
+
+lemma True
+proof
+
+  ML_prf {* val ctxt0 = @{context} *}
+  ML_prf {* val (xs, ctxt1) = ctxt0 |> Variable.add_fixes ["x", "y", "z"] *}
+  ML_prf {* val t = Syntax.read_term ctxt1 "(x::nat) = y + z" *}
+  ML_prf {* val ctxt2 = ctxt1 |> Variable.declare_term t *}
+  ML_prf {* Syntax.read_term ctxt2 "x" *}
+
+qed
+
+ML {* val ctxt0 = @{context} *}
+ML {* val (xs, ctxt1) = ctxt0 |> Variable.add_fixes ["x", "y", "z"] *}
+ML {* val (xs, ctxt1) = ctxt0 |> Variable.variant_fixes ["x", "y", "z"] *}
+
+ML {* Variable.focus (Thm.cprem_of @{thm exE} 2) @{context} *}
+
+
+subsection {* Assumptions *}
+
+lemma True
+proof
+
+ML_prf {* val ctxt0 = @{context} *}
+ML_prf {*
+  val (asms, ctxt1) = ctxt0
+    |> Assumption.add_assumes [@{cprop "x = y"}, @{cprop "y = z"}]
+*}
+ML_prf {* Assumption.export false ctxt1 ctxt0 (@{thm trans} OF asms) *}
+
+
+ML_prf {* val ctxt0 = @{context} *}
+ML_prf {* val (_, ctxt1) = ctxt0 |> Variable.add_fixes ["x", "y", "z"] *}
+ML_prf {* val ts = Syntax.read_props ctxt1 ["x = y", "y = z"] *}
+ML_prf {* val ctxt2 = ctxt1 |> fold Variable.declare_term ts *}
+
+ML_prf {*
+  val (asms, ctxt3) =
+    ctxt2
+    |> Assumption.add_assumes (map (cterm_of (ProofContext.theory_of ctxt2)) ts)
+*}
+ML_prf {* Assumption.export false ctxt3 ctxt0 (@{thm trans} OF asms) *}
+ML_prf {* ProofContext.export ctxt3 ctxt0 [@{thm trans} OF asms] *}
+
+qed
+
+
+subsection {* Local definitions (non-polymorphic) *}
+
+lemma True
+proof
+  fix x y z :: nat
+
+  ML_prf {* val ctxt0 = @{context} *}
+  ML_prf {* val ((a, a_def), ctxt1) =
+    ctxt0 |> LocalDefs.add_def ((@{binding a}, NoSyn), @{term "x + y"})
+  *}
+  ML_prf {* val ((b, b_def), ctxt2) =
+    ctxt1 |> LocalDefs.add_def ((@{binding b}, NoSyn), @{term "y + z"})
+  *}
+
+  ML_prf {*
+    Goal.prove ctxt2 [] [] (Syntax.read_prop ctxt2 "a + b = x + 2 * y + z")
+      (fn _ => asm_full_simp_tac (local_simpset_of ctxt2 addsimps [a_def, b_def]) 1)
+  *}
+
+qed
+
+
+subsection {* Local elimination *}
+
+lemma True
+proof
+  assume ex: "EX x. B x"
+
+  ML_prf {* val ctxt0 = @{context} *}
+  ML_prf {* val (([x], [B]), ctxt1) = ctxt0
+    |> Obtain.result (fn _ => etac @{thm exE} 1) @{thms ex} *}
+  ML_prf {*
+    ProofContext.export ctxt1 ctxt0 [Thm.reflexive x]
+      handle ERROR msg => (warning msg; []) *}
+
+qed
+
+end