diff -r 6088fea1c8b1 -r 8a1c8dc72b5c Quot/Quotients.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Quot/Quotients.thy	Mon Dec 07 14:09:50 2009 +0100
@@ -0,0 +1,80 @@
+theory Quotients
+imports Main
+begin
+
+(* Other quotients that have not been proved yet *)
+
+fun
+  option_rel
+where
+  "option_rel R None None = True"
+| "option_rel R (Some x) None = False"
+| "option_rel R None (Some x) = False"
+| "option_rel R (Some x) (Some y) = R x y"
+
+fun
+  option_map
+where
+  "option_map f None = None"
+| "option_map f (Some x) = Some (f x)"
+
+fun
+  prod_rel
+where
+  "prod_rel R1 R2 (a1,a2) (b1,b2) = (R1 a1 b1 \<and> R2 a2 b2)"
+
+fun
+  prod_map
+where
+  "prod_map f1 f2 (a,b) = (f1 a, f2 b)"
+
+fun
+  sum_rel
+where
+  "sum_rel R1 R2 (Inl a1) (Inl b1) = R1 a1 b1"
+| "sum_rel R1 R2 (Inl a1) (Inr b2) = False"
+| "sum_rel R1 R2 (Inr a2) (Inl b1) = False"
+| "sum_rel R1 R2 (Inr a2) (Inr b2) = R2 a2 b2"
+
+fun
+  sum_map
+where
+  "sum_map f1 f2 (Inl a) = Inl (f1 a)"
+| "sum_map f1 f2 (Inr a) = Inr (f2 a)"
+
+
+
+
+
+fun
+  noption_map::"('a \<Rightarrow> 'b) \<Rightarrow> ('a noption) \<Rightarrow> ('b noption)"
+where
+  "noption_map f (nSome x) = nSome (f x)"
+| "noption_map f nNone = nNone"
+
+fun
+  noption_rel
+where
+  "noption_rel r (nSome x) (nSome y) = r x y"
+| "noption_rel r _ _ = False"
+
+declare [[map noption = (noption_map, noption_rel)]]
+
+lemma "noption_map id = id"
+sorry
+
+lemma noption_Quotient:
+  assumes q: "Quotient R Abs Rep"
+  shows "Quotient (noption_rel R) (noption_map Abs) (noption_map Rep)"
+  apply (unfold Quotient_def)
+  apply (auto)
+  using q
+  apply (unfold Quotient_def)
+  apply (case_tac "a :: 'b noption")
+  apply (simp)
+  apply (simp)
+  apply (case_tac "a :: 'b noption")
+  apply (simp only: option_map.simps)
+  apply (subst option_rel.simps)
+  (* Simp starts hanging so don't know how to continue *)
+  sorry