--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Tools/case_product.ML Wed Dec 08 18:18:36 2010 +0100
@@ -0,0 +1,117 @@
+(* 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+Returns list of prems, where loose bounds have been replaced by frees.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;