src/Tools/case_product.ML

+(*   Title: case_product.ML
+     Author: Lars Noschinski
+
+Combines two case rules into a single one.
+
+Assumes that the theorems are of the form
+  "[| C1; ...; Cm; A1 ==> P; ...; An ==> P |] ==> P"
+where m is given by the "consumes" attribute of the theorem.
+*)
+
+signature CASE_PRODUCT =
+  sig
+
+  val combine: Proof.context -> thm -> thm -> thm
+  val combine_annotated: Proof.context -> thm -> thm -> thm
+  val setup: theory -> theory
+end;
+
+structure Case_Product: CASE_PRODUCT =
+struct
+
+(*Instantiates the conclusion of thm2 to the one of thm1.*)
+fun inst_concl thm1 thm2 =
+  let
+    val cconcl_of = Drule.strip_imp_concl o Thm.cprop_of
+  in Thm.instantiate (Thm.match (cconcl_of thm2, cconcl_of thm1)) thm2 end
+
+fun inst_thms thm1 thm2 ctxt =
+  let
+    val import = yield_singleton (apfst snd oo Variable.import true)
+    val (i_thm1, ctxt') = import thm1 ctxt
+    val (i_thm2, ctxt'') = import (inst_concl i_thm1 thm2) ctxt'
+  in ((i_thm1, i_thm2), ctxt'') end
+
+(*
+Returns list of prems, where loose bounds have been replaced by frees.
+FIXME: Focus
+*)
+fun free_prems t ctxt =
+  let
+    val bs = Term.strip_all_vars t
+    val (names, ctxt') = Variable.variant_fixes (map fst bs) ctxt
+    val subst = map Free (names ~~ map snd bs)
+    val t' = map (Term.subst_bounds o pair (rev subst)) (Logic.strip_assums_hyp t)
+  in ((t', subst), ctxt') end
+
+fun build_concl_prems thm1 thm2 ctxt =
+  let
+    val concl = Thm.concl_of thm1
+
+    fun is_consumes t = not (Logic.strip_assums_concl t aconv concl)
+    val (p_cons1, p_cases1) = chop_while is_consumes (Thm.prems_of thm1)
+    val (p_cons2, p_cases2) = chop_while is_consumes (Thm.prems_of thm2)
+
+    val p_cases_prod = map (fn p1 => map (fn p2 =>
+      let
+        val (((t1, subst1), (t2, subst2)), _) = ctxt
+          |> free_prems p1 ||>> free_prems p2
+      in
+        Logic.list_implies (t1 @ t2, concl)
+        |> fold_rev Logic.all (subst1 @ subst2)
+      end
+      ) p_cases2) p_cases1
+
+    val prems = p_cons1 :: p_cons2 :: p_cases_prod
+  in
+    (concl, prems)
+  end
+
+fun case_product_tac prems struc thm1 thm2 =
+  let
+    val (p_cons1 :: p_cons2 :: premss) = unflat struc prems
+    val thm2' = thm2 OF p_cons2
+  in
+    (Tactic.rtac (thm1 OF p_cons1)
+     THEN' EVERY' (map (fn p =>
+       Tactic.rtac thm2'
+       THEN' EVERY' (map (ProofContext.fact_tac o single) p)) premss)
+    )
+  end
+
+fun combine ctxt thm1 thm2 =
+  let
+    val ((i_thm1, i_thm2), ctxt') = inst_thms thm1 thm2 ctxt
+    val (concl, prems_rich) = build_concl_prems i_thm1 i_thm2 ctxt'
+  in
+    Goal.prove ctxt' [] (flat prems_rich) concl (fn {prems, ...} =>
+      case_product_tac prems prems_rich i_thm1 i_thm2 1)
+    |> singleton (Variable.export ctxt' ctxt)
+  end;
+
+fun annotation thm1 thm2 =
+  let
+    val (names1, cons1) = apfst (map fst) (Rule_Cases.get thm1)
+    val (names2, cons2) = apfst (map fst) (Rule_Cases.get thm2)
+    val names = map_product (fn x => fn y => x ^ "_" ^y) names1 names2
+  in
+    Rule_Cases.case_names names o Rule_Cases.consumes (cons1 + cons2)
+  end
+
+fun combine_annotated ctxt thm1 thm2 =
+  combine ctxt thm1 thm2
+  |> snd o annotation thm1 thm2 o pair (Context.Proof ctxt)
+
+(* Attribute setup *)
+
+val case_prod_attr = let
+    fun combine_list ctxt = fold (fn x => fn y => combine_annotated ctxt y x)
+  in
+    Attrib.thms >> (fn thms => Thm.rule_attribute (fn ctxt => fn thm =>
+      combine_list (Context.proof_of ctxt) thms thm))
+  end
+
+val setup =
+ Attrib.setup @{binding "case_product"} case_prod_attr "product with other case rules"
+
+end;