src/HOL/Spec_Check/Examples.thy

+theory Examples
+imports Spec_Check
+begin
+
+section {* List examples *}
+
+ML {*
+check_property @{context} "ALL xs. rev xs = xs";
+*}
+
+ML {*
+check_property @{context} "ALL xs. rev (rev xs) = xs";
+*}
+
+
+section {* AList Specification *}
+
+ML {*
+(* map_entry applies the function to the element *)
+check_property @{context} "ALL k f xs. AList.lookup (op =) (AList.map_entry (op =) k f xs) k = Option.map f (AList.lookup (op =) xs k)";
+
+(* update always results in an entry *)
+check_property @{context} "ALL k v xs. AList.defined (op =) (AList.update (op =) (k, v) xs) k";
+
+(* update always writes the value *)
+check_property @{context} "ALL k v xs. AList.lookup (op =) (AList.update (op =) (k, v) xs) k = SOME v";
+
+(* default always results in an entry *)
+check_property @{context} "ALL k v xs. AList.defined (op =) (AList.default (op =) (k, v) xs) k";
+
+(* delete always removes the entry *)
+check_property @{context} "ALL k xs. not (AList.defined (op =) (AList.delete (op =) k xs) k)";
+
+(* default writes the entry iff it didn't exist *)
+check_property @{context} "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))";
+*}
+
+section {* Examples on Types and Terms *}
+
+ML {*
+check_property @{context} "ALL f g t. map_types (g o f) t = (map_types f o map_types g) t";
+*}
+
+ML {*
+check_property @{context} "ALL f g t. map_types (f o g) t = (map_types f o map_types g) t";
+*}
+
+text {* One would think this holds: *}
+
+ML {*
+check_property @{context} "ALL t ts. strip_comb (list_comb (t, ts)) = (t, ts)"
+*}
+
+text {* But it only holds with this precondition: *}
+
+ML {*
+check_property @{context} "ALL t ts. case t of _ $ _ => true | _ => strip_comb (list_comb (t, ts)) = (t, ts)"
+*}
+
+section {* Some surprises *}
+
+ML {*
+check_property @{context} "ALL Ts t. type_of1 (Ts, t) = fastype_of1 (Ts, t)"
+*}
+
+
+
+ML {* val thy = @{theory}; *}
+ML {*
+  check_property @{context} "ALL t u. if Pattern.matches thy (t, u) then Term.could_unify (t, u) else true"
+*}
+
+end