author  wenzelm 
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permissions  rwrr 
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(* Title: Tools/case_product.ML 
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Author: Lars Noschinski, TU Muenchen 

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Combine two case rules into a single one. 
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Assumes that the theorems are of the form 
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"[ C1; ...; Cm; A1 ==> P; ...; An ==> P ] ==> P" 
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where m is given by the "consumes" attribute of the theorem. 
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*) 
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signature CASE_PRODUCT = 
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sig 
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val combine: Proof.context > thm > thm > thm 
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val combine_annotated: Proof.context > thm > thm > thm 
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val setup: theory > theory 
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end 
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structure Case_Product: CASE_PRODUCT = 
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struct 
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(*instantiate the conclusion of thm2 to the one of thm1*) 
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fun inst_concl thm1 thm2 = 
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let 
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val cconcl_of = Drule.strip_imp_concl o Thm.cprop_of 
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in Thm.instantiate (Thm.match (cconcl_of thm2, cconcl_of thm1)) thm2 end 
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fun inst_thms thm1 thm2 ctxt = 
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let 
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val import = yield_singleton (apfst snd oo Variable.import true) 
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val (i_thm1, ctxt') = import thm1 ctxt 
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val (i_thm2, ctxt'') = import (inst_concl i_thm1 thm2) ctxt' 
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in ((i_thm1, i_thm2), ctxt'') end 
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(* 
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Return list of prems, where loose bounds have been replaced by frees. 
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FIXME: Focus 
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*) 
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fun free_prems t ctxt = 
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let 
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val bs = Term.strip_all_vars t 
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val (names, ctxt') = Variable.variant_fixes (map fst bs) ctxt 
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val subst = map Free (names ~~ map snd bs) 
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val t' = map (Term.subst_bounds o pair (rev subst)) (Logic.strip_assums_hyp t) 
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in ((t', subst), ctxt') end 
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fun build_concl_prems thm1 thm2 ctxt = 
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let 
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val concl = Thm.concl_of thm1 
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fun is_consumes t = not (Logic.strip_assums_concl t aconv concl) 
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val (p_cons1, p_cases1) = chop_while is_consumes (Thm.prems_of thm1) 
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val (p_cons2, p_cases2) = chop_while is_consumes (Thm.prems_of thm2) 
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val p_cases_prod = map (fn p1 => map (fn p2 => 
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let 
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val (((t1, subst1), (t2, subst2)), _) = ctxt 
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> free_prems p1 >> free_prems p2 
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in 
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Logic.list_implies (t1 @ t2, concl) 
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> fold_rev Logic.all (subst1 @ subst2) 
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end) p_cases2) p_cases1 
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val prems = p_cons1 :: p_cons2 :: p_cases_prod 
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in 
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(concl, prems) 
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end 
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fun case_product_tac prems struc thm1 thm2 = 
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let 
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val (p_cons1 :: p_cons2 :: premss) = unflat struc prems 
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val thm2' = thm2 OF p_cons2 
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in 
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Tactic.rtac (thm1 OF p_cons1) 
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THEN' EVERY' (map (fn p => 
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Tactic.rtac thm2' 
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THEN' EVERY' (map (Proof_Context.fact_tac o single) p)) premss) 
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end 
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fun combine ctxt thm1 thm2 = 
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let 
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val ((i_thm1, i_thm2), ctxt') = inst_thms thm1 thm2 ctxt 
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val (concl, prems_rich) = build_concl_prems i_thm1 i_thm2 ctxt' 
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in 
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Goal.prove ctxt' [] (flat prems_rich) concl (fn {prems, ...} => 
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case_product_tac prems prems_rich i_thm1 i_thm2 1) 
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> singleton (Variable.export ctxt' ctxt) 
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end 
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fun annotation_rule thm1 thm2 = 
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let 
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infrastructure for attaching names to hypothesis in cases; realised via the same tag mechanism as case names
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val (cases1, cons1) = apfst (map fst) (Rule_Cases.get thm1) 
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val (cases2, cons2) = apfst (map fst) (Rule_Cases.get thm2) 
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val names = map_product (fn (x, _) => fn (y, _) => x ^ "_" ^ y) cases1 cases2 
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in 
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Rule_Cases.name names o Rule_Cases.put_consumes (SOME (cons1 + cons2)) 
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end 
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fun annotation thm1 thm2 = Thm.rule_attribute (K (annotation_rule thm1 thm2)) 
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fun combine_annotated ctxt thm1 thm2 = 
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combine ctxt thm1 thm2 
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> annotation_rule thm1 thm2 
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(* attribute setup *) 
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val case_prod_attr = 
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let 

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fun combine_list ctxt = fold (fn x => fn y => combine_annotated ctxt y x) 
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in 
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Attrib.thms >> (fn thms => Thm.rule_attribute (fn ctxt => fn thm => 
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combine_list (Context.proof_of ctxt) thms thm)) 
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end 
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val setup = 
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Attrib.setup @{binding case_product} case_prod_attr "product with other case rules" 
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end 