src/Tools/Spec_Check/Examples.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Tools/Spec_Check/Examples.thy	Fri Jul 09 10:36:20 2021 +0200
@@ -0,0 +1,83 @@
+theory Examples
+imports Spec_Check
+begin
+
+section \<open>List examples\<close>
+
+ML_command \<open>
+check_property "ALL xs. rev xs = xs";
+\<close>
+
+ML_command \<open>
+check_property "ALL xs. rev (rev xs) = xs";
+\<close>
+
+
+section \<open>AList Specification\<close>
+
+ML_command \<open>
+(* map_entry applies the function to the element *)
+check_property "ALL k f xs. AList.lookup (op =) (AList.map_entry (op =) k f xs) k = Option.map f (AList.lookup (op =) xs k)";
+\<close>
+
+ML_command \<open>
+(* update always results in an entry *)
+check_property "ALL k v xs. AList.defined (op =) (AList.update (op =) (k, v) xs) k";
+\<close>
+
+ML_command \<open>
+(* update always writes the value *)
+check_property "ALL k v xs. AList.lookup (op =) (AList.update (op =) (k, v) xs) k = SOME v";
+\<close>
+
+ML_command \<open>
+(* default always results in an entry *)
+check_property "ALL k v xs. AList.defined (op =) (AList.default (op =) (k, v) xs) k";
+\<close>
+
+ML_command \<open>
+(* delete always removes the entry *)
+check_property "ALL k xs. not (AList.defined (op =) (AList.delete (op =) k xs) k)";
+\<close>
+
+ML_command \<open>
+(* default writes the entry iff it didn't exist *)
+check_property "ALL k v xs. (AList.lookup (op =) (AList.default (op =) (k, v) xs) k = (if AList.defined (op =) xs k then AList.lookup (op =) xs k else SOME v))";
+\<close>
+
+section \<open>Examples on Types and Terms\<close>
+
+ML_command \<open>
+check_property "ALL f g t. map_types (g o f) t = (map_types f o map_types g) t";
+\<close>
+
+ML_command \<open>
+check_property "ALL f g t. map_types (f o g) t = (map_types f o map_types g) t";
+\<close>
+
+
+text \<open>One would think this holds:\<close>
+
+ML_command \<open>
+check_property "ALL t ts. strip_comb (list_comb (t, ts)) = (t, ts)"
+\<close>
+
+text \<open>But it only holds with this precondition:\<close>
+
+ML_command \<open>
+check_property "ALL t ts. case t of _ $ _ => true | _ => strip_comb (list_comb (t, ts)) = (t, ts)"
+\<close>
+
+section \<open>Some surprises\<close>
+
+ML_command \<open>
+check_property "ALL Ts t. type_of1 (Ts, t) = fastype_of1 (Ts, t)"
+\<close>
+
+
+ML_command \<open>
+val thy = \<^theory>;
+check_property "ALL t u. if Pattern.matches thy (t, u) then Term.could_unify (t, u) else true"
+\<close>
+
+end