wenzelm@41883: (*  Title:      Tools/case_product.ML
wenzelm@41883:     Author:     Lars Noschinski, TU Muenchen
noschinl@41826: 
noschinl@41826: Combines two case rules into a single one.
noschinl@41826: 
noschinl@41826: Assumes that the theorems are of the form
noschinl@41826:   "[| C1; ...; Cm; A1 ==> P; ...; An ==> P |] ==> P"
noschinl@41826: where m is given by the "consumes" attribute of the theorem.
noschinl@41826: *)
noschinl@41826: 
noschinl@41826: signature CASE_PRODUCT =
wenzelm@41883: sig
noschinl@41826:   val combine: Proof.context -> thm -> thm -> thm
noschinl@41826:   val combine_annotated: Proof.context -> thm -> thm -> thm
noschinl@41826:   val setup: theory -> theory
noschinl@41826: end;
noschinl@41826: 
noschinl@41826: structure Case_Product: CASE_PRODUCT =
noschinl@41826: struct
noschinl@41826: 
noschinl@41826: (*Instantiates the conclusion of thm2 to the one of thm1.*)
noschinl@41826: fun inst_concl thm1 thm2 =
noschinl@41826:   let
noschinl@41826:     val cconcl_of = Drule.strip_imp_concl o Thm.cprop_of
noschinl@41826:   in Thm.instantiate (Thm.match (cconcl_of thm2, cconcl_of thm1)) thm2 end
noschinl@41826: 
noschinl@41826: fun inst_thms thm1 thm2 ctxt =
noschinl@41826:   let
noschinl@41826:     val import = yield_singleton (apfst snd oo Variable.import true)
noschinl@41826:     val (i_thm1, ctxt') = import thm1 ctxt
noschinl@41826:     val (i_thm2, ctxt'') = import (inst_concl i_thm1 thm2) ctxt'
noschinl@41826:   in ((i_thm1, i_thm2), ctxt'') end
noschinl@41826: 
noschinl@41826: (*
noschinl@41826: Returns list of prems, where loose bounds have been replaced by frees.
noschinl@41826: FIXME: Focus
noschinl@41826: *)
noschinl@41826: fun free_prems t ctxt =
noschinl@41826:   let
noschinl@41826:     val bs = Term.strip_all_vars t
noschinl@41826:     val (names, ctxt') = Variable.variant_fixes (map fst bs) ctxt
noschinl@41826:     val subst = map Free (names ~~ map snd bs)
noschinl@41826:     val t' = map (Term.subst_bounds o pair (rev subst)) (Logic.strip_assums_hyp t)
noschinl@41826:   in ((t', subst), ctxt') end
noschinl@41826: 
noschinl@41826: fun build_concl_prems thm1 thm2 ctxt =
noschinl@41826:   let
noschinl@41826:     val concl = Thm.concl_of thm1
noschinl@41826: 
noschinl@41826:     fun is_consumes t = not (Logic.strip_assums_concl t aconv concl)
noschinl@41826:     val (p_cons1, p_cases1) = chop_while is_consumes (Thm.prems_of thm1)
noschinl@41826:     val (p_cons2, p_cases2) = chop_while is_consumes (Thm.prems_of thm2)
noschinl@41826: 
noschinl@41826:     val p_cases_prod = map (fn p1 => map (fn p2 =>
noschinl@41826:       let
noschinl@41826:         val (((t1, subst1), (t2, subst2)), _) = ctxt
noschinl@41826:           |> free_prems p1 ||>> free_prems p2
noschinl@41826:       in
noschinl@41826:         Logic.list_implies (t1 @ t2, concl)
noschinl@41826:         |> fold_rev Logic.all (subst1 @ subst2)
noschinl@41826:       end
noschinl@41826:       ) p_cases2) p_cases1
noschinl@41826: 
noschinl@41826:     val prems = p_cons1 :: p_cons2 :: p_cases_prod
noschinl@41826:   in
noschinl@41826:     (concl, prems)
noschinl@41826:   end
noschinl@41826: 
noschinl@41826: fun case_product_tac prems struc thm1 thm2 =
noschinl@41826:   let
noschinl@41826:     val (p_cons1 :: p_cons2 :: premss) = unflat struc prems
noschinl@41826:     val thm2' = thm2 OF p_cons2
noschinl@41826:   in
noschinl@41826:     (Tactic.rtac (thm1 OF p_cons1)
noschinl@41826:      THEN' EVERY' (map (fn p =>
noschinl@41826:        Tactic.rtac thm2'
wenzelm@42361:        THEN' EVERY' (map (Proof_Context.fact_tac o single) p)) premss)
noschinl@41826:     )
noschinl@41826:   end
noschinl@41826: 
noschinl@41826: fun combine ctxt thm1 thm2 =
noschinl@41826:   let
noschinl@41826:     val ((i_thm1, i_thm2), ctxt') = inst_thms thm1 thm2 ctxt
noschinl@41826:     val (concl, prems_rich) = build_concl_prems i_thm1 i_thm2 ctxt'
noschinl@41826:   in
noschinl@41826:     Goal.prove ctxt' [] (flat prems_rich) concl (fn {prems, ...} =>
noschinl@41826:       case_product_tac prems prems_rich i_thm1 i_thm2 1)
noschinl@41826:     |> singleton (Variable.export ctxt' ctxt)
noschinl@41826:   end;
noschinl@41826: 
noschinl@41826: fun annotation thm1 thm2 =
noschinl@41826:   let
nipkow@44045:     val (cases1, cons1) = apfst (map fst) (Rule_Cases.get thm1)
nipkow@44045:     val (cases2, cons2) = apfst (map fst) (Rule_Cases.get thm2)
nipkow@44045:     val names = map_product (fn (x,_) => fn (y,_) => x ^ "_" ^y) cases1 cases2
noschinl@41826:   in
noschinl@41826:     Rule_Cases.case_names names o Rule_Cases.consumes (cons1 + cons2)
noschinl@41826:   end
noschinl@41826: 
noschinl@41826: fun combine_annotated ctxt thm1 thm2 =
noschinl@41826:   combine ctxt thm1 thm2
noschinl@41826:   |> snd o annotation thm1 thm2 o pair (Context.Proof ctxt)
noschinl@41826: 
noschinl@41826: (* Attribute setup *)
noschinl@41826: 
wenzelm@41883: val case_prod_attr =
wenzelm@41883:   let
noschinl@41826:     fun combine_list ctxt = fold (fn x => fn y => combine_annotated ctxt y x)
noschinl@41826:   in
noschinl@41826:     Attrib.thms >> (fn thms => Thm.rule_attribute (fn ctxt => fn thm =>
noschinl@41826:       combine_list (Context.proof_of ctxt) thms thm))
noschinl@41826:   end
noschinl@41826: 
noschinl@41826: val setup =
noschinl@41826:  Attrib.setup @{binding "case_product"} case_prod_attr "product with other case rules"
noschinl@41826: 
noschinl@41826: end;