src/HOL/Metis_Examples/Typings.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Metis_Examples/Typings.thy	Mon Jun 06 20:36:34 2011 +0200
@@ -0,0 +1,73 @@
+(*  Title:      HOL/Metis_Examples/Typings.thy
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Testing the new Metis's (and hence Sledgehammer's) type translations.
+*)
+
+theory Typings
+imports Main
+begin
+
+
+text {* Setup for testing Metis exhaustively *}
+
+lemma fork: "P \<Longrightarrow> P \<Longrightarrow> P" by assumption
+
+ML {*
+open ATP_Translate
+
+val polymorphisms = [Polymorphic, Monomorphic, Mangled_Monomorphic]
+val levels =
+  [All_Types, Nonmonotonic_Types, Finite_Types, Const_Arg_Types, No_Types]
+val heaviness = [Heavyweight, Lightweight]
+val type_syss =
+  (levels |> map Simple_Types) @
+  (map_product pair levels heaviness
+   |> map_product pair polymorphisms
+   |> map_product (fn constr => fn (poly, (level, heaviness)) =>
+                      constr (poly, level, heaviness))
+                  [Preds, Tags])
+
+fun metis_exhaust_tac ctxt ths =
+  let
+    fun tac [] = all_tac
+      | tac (type_sys :: type_syss) =
+        (if null type_syss then all_tac else rtac @{thm fork} 1)
+        THEN Metis_Tactics.metisX_tac ctxt (SOME type_sys) ths 1
+        THEN COND (has_fewer_prems 2) all_tac no_tac
+        THEN tac type_syss
+  in tac end
+*}
+
+method_setup metis_exhaust = {*
+  Attrib.thms >>
+    (fn ths => fn ctxt => SIMPLE_METHOD (metis_exhaust_tac ctxt ths type_syss))
+*} "exhaustively run the new Metis with all type encodings"
+
+
+text {* Metis tests *}
+
+lemma "x = y \<Longrightarrow> y = x"
+by metis_exhaust
+
+lemma "[a] = [1 + 1] \<Longrightarrow> a = 1 + (1::int)"
+by (metis_exhaust last.simps)
+
+lemma "map Suc [0] = [Suc 0]"
+by (metis_exhaust map.simps)
+
+lemma "map Suc [1 + 1] = [Suc 2]"
+by (metis_exhaust map.simps nat_1_add_1)
+
+lemma "map Suc [2] = [Suc (1 + 1)]"
+by (metis_exhaust map.simps nat_1_add_1)
+
+definition "null xs = (xs = [])"
+
+lemma "P (null xs) \<Longrightarrow> null xs \<Longrightarrow> xs = []"
+by (metis_exhaust null_def)
+
+lemma "(0::nat) + 0 = 0"
+by (metis_exhaust arithmetic_simps(38))
+
+end