diff -r 835b5443b978 -r 3d060f43accb src/HOL/Tools/SMT2/smt2_normalize.ML --- a/src/HOL/Tools/SMT2/smt2_normalize.ML Thu Aug 28 00:40:38 2014 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,441 +0,0 @@ -(* Title: HOL/Tools/SMT2/smt2_normalize.ML - Author: Sascha Boehme, TU Muenchen - -Normalization steps on theorems required by SMT solvers. -*) - -signature SMT2_NORMALIZE = -sig - val drop_fact_warning: Proof.context -> thm -> unit - val atomize_conv: Proof.context -> conv - - val special_quant_table: (string * thm) list - val case_bool_entry: string * thm - val abs_min_max_table: (string * thm) list - - type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list - val add_extra_norm: SMT2_Util.class * extra_norm -> Context.generic -> Context.generic - val normalize: Proof.context -> thm list -> (int * thm) list -end; - -structure SMT2_Normalize: SMT2_NORMALIZE = -struct - -fun drop_fact_warning ctxt = - SMT2_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o - Display.string_of_thm ctxt) - - -(* general theorem normalizations *) - -(** instantiate elimination rules **) - -local - val (cpfalse, cfalse) = `SMT2_Util.mk_cprop (Thm.cterm_of @{theory} @{const False}) - - fun inst f ct thm = - let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm)) - in Thm.instantiate ([], [(cv, ct)]) thm end -in - -fun instantiate_elim thm = - (case Thm.concl_of thm of - @{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm - | Var _ => inst I cpfalse thm - | _ => thm) - -end - - -(** normalize definitions **) - -fun norm_def thm = - (case Thm.prop_of thm of - @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) => - norm_def (thm RS @{thm fun_cong}) - | Const (@{const_name Pure.eq}, _) $ _ $ Abs _ => norm_def (thm RS @{thm meta_eq_to_obj_eq}) - | _ => thm) - - -(** atomization **) - -fun atomize_conv ctxt ct = - (case Thm.term_of ct of - @{const Pure.imp} $ _ $ _ => - Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_imp} - | Const (@{const_name Pure.eq}, _) $ _ $ _ => - Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_eq} - | Const (@{const_name Pure.all}, _) $ Abs _ => - Conv.binder_conv (atomize_conv o snd) ctxt then_conv Conv.rewr_conv @{thm atomize_all} - | _ => Conv.all_conv) ct - -val setup_atomize = - fold SMT2_Builtin.add_builtin_fun_ext'' [@{const_name Pure.imp}, @{const_name Pure.eq}, - @{const_name Pure.all}, @{const_name Trueprop}] - - -(** unfold special quantifiers **) - -val special_quant_table = [ - (@{const_name Ex1}, @{thm Ex1_def_raw}), - (@{const_name Ball}, @{thm Ball_def_raw}), - (@{const_name Bex}, @{thm Bex_def_raw})] - -local - fun special_quant (Const (n, _)) = AList.lookup (op =) special_quant_table n - | special_quant _ = NONE - - fun special_quant_conv _ ct = - (case special_quant (Thm.term_of ct) of - SOME thm => Conv.rewr_conv thm - | NONE => Conv.all_conv) ct -in - -fun unfold_special_quants_conv ctxt = - SMT2_Util.if_exists_conv (is_some o special_quant) (Conv.top_conv special_quant_conv ctxt) - -val setup_unfolded_quants = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) special_quant_table - -end - - -(** trigger inference **) - -local - (*** check trigger syntax ***) - - fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true - | dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false - | dest_trigger _ = NONE - - fun eq_list [] = false - | eq_list (b :: bs) = forall (equal b) bs - - fun proper_trigger t = - t - |> these o try SMT2_Util.dest_symb_list - |> map (map_filter dest_trigger o these o try SMT2_Util.dest_symb_list) - |> (fn [] => false | bss => forall eq_list bss) - - fun proper_quant inside f t = - (case t of - Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u - | Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u - | @{const trigger} $ p $ u => - (if inside then f p else false) andalso proper_quant false f u - | Abs (_, _, u) => proper_quant false f u - | u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2 - | _ => true) - - fun check_trigger_error ctxt t = - error ("SMT triggers must only occur under quantifier and multipatterns " ^ - "must have the same kind: " ^ Syntax.string_of_term ctxt t) - - fun check_trigger_conv ctxt ct = - if proper_quant false proper_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct - else check_trigger_error ctxt (Thm.term_of ct) - - - (*** infer simple triggers ***) - - fun dest_cond_eq ct = - (case Thm.term_of ct of - Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct - | @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct) - | _ => raise CTERM ("no equation", [ct])) - - fun get_constrs thy (Type (n, _)) = these (Datatype_Data.get_constrs thy n) - | get_constrs _ _ = [] - - fun is_constr thy (n, T) = - let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U) - in can (the o find_first match o get_constrs thy o Term.body_type) T end - - fun is_constr_pat thy t = - (case Term.strip_comb t of - (Free _, []) => true - | (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts - | _ => false) - - fun is_simp_lhs ctxt t = - (case Term.strip_comb t of - (Const c, ts as _ :: _) => - not (SMT2_Builtin.is_builtin_fun_ext ctxt c ts) andalso - forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts - | _ => false) - - fun has_all_vars vs t = - subset (op aconv) (vs, map Free (Term.add_frees t [])) - - fun minimal_pats vs ct = - if has_all_vars vs (Thm.term_of ct) then - (case Thm.term_of ct of - _ $ _ => - (case pairself (minimal_pats vs) (Thm.dest_comb ct) of - ([], []) => [[ct]] - | (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss') - | _ => []) - else [] - - fun proper_mpat _ _ _ [] = false - | proper_mpat thy gen u cts = - let - val tps = (op ~~) (`gen (map Thm.term_of cts)) - fun some_match u = tps |> exists (fn (t', t) => - Pattern.matches thy (t', u) andalso not (t aconv u)) - in not (Term.exists_subterm some_match u) end - - val pat = SMT2_Util.mk_const_pat @{theory} @{const_name pat} SMT2_Util.destT1 - fun mk_pat ct = Thm.apply (SMT2_Util.instT' ct pat) ct - - fun mk_clist T = - pairself (Thm.cterm_of @{theory}) (SMT2_Util.symb_cons_const T, SMT2_Util.symb_nil_const T) - fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil - val mk_pat_list = mk_list (mk_clist @{typ pattern}) - val mk_mpat_list = mk_list (mk_clist @{typ "pattern symb_list"}) - fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss - - val trigger_eq = mk_meta_eq @{lemma "p = trigger t p" by (simp add: trigger_def)} - - fun insert_trigger_conv [] ct = Conv.all_conv ct - | insert_trigger_conv ctss ct = - let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct - in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end - - fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct = - let - val (lhs, rhs) = dest_cond_eq ct - - val vs = map Thm.term_of cvs - val thy = Proof_Context.theory_of ctxt - - fun get_mpats ct = - if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct - else [] - val gen = Variable.export_terms ctxt outer_ctxt - val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs)) - - in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end - - fun has_trigger (@{const trigger} $ _ $ _) = true - | has_trigger _ = false - - fun try_trigger_conv cv ct = - if SMT2_Util.under_quant has_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct - else Conv.try_conv cv ct - - fun infer_trigger_conv ctxt = - if Config.get ctxt SMT2_Config.infer_triggers then - try_trigger_conv (SMT2_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt) - else Conv.all_conv -in - -fun trigger_conv ctxt = - SMT2_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt) - -val setup_trigger = - fold SMT2_Builtin.add_builtin_fun_ext'' - [@{const_name pat}, @{const_name nopat}, @{const_name trigger}] - -end - - -(** combined general normalizations **) - -fun gen_normalize1_conv ctxt = - atomize_conv ctxt then_conv - unfold_special_quants_conv ctxt then_conv - Thm.beta_conversion true then_conv - trigger_conv ctxt - -fun gen_normalize1 ctxt = - instantiate_elim #> - norm_def #> - Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #> - Drule.forall_intr_vars #> - Conv.fconv_rule (gen_normalize1_conv ctxt) #> - (* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *) - Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]} - -fun gen_norm1_safe ctxt (i, thm) = - (case try (gen_normalize1 ctxt) thm of - SOME thm' => SOME (i, thm') - | NONE => (drop_fact_warning ctxt thm; NONE)) - -fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms - - -(* unfolding of definitions and theory-specific rewritings *) - -fun expand_head_conv cv ct = - (case Thm.term_of ct of - _ $ _ => - Conv.fun_conv (expand_head_conv cv) then_conv - Conv.try_conv (Thm.beta_conversion false) - | _ => cv) ct - - -(** rewrite bool case expressions as if expressions **) - -val case_bool_entry = (@{const_name "bool.case_bool"}, @{thm case_bool_if}) - -local - fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true - | is_case_bool _ = false - - fun unfold_conv _ = - SMT2_Util.if_true_conv (is_case_bool o Term.head_of) - (expand_head_conv (Conv.rewr_conv @{thm case_bool_if})) -in - -fun rewrite_case_bool_conv ctxt = - SMT2_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt) - -val setup_case_bool = SMT2_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"} - -end - - -(** unfold abs, min and max **) - -val abs_min_max_table = [ - (@{const_name min}, @{thm min_def_raw}), - (@{const_name max}, @{thm max_def_raw}), - (@{const_name abs}, @{thm abs_if_raw})] - -local - fun abs_min_max ctxt (Const (n, Type (@{type_name fun}, [T, _]))) = - (case AList.lookup (op =) abs_min_max_table n of - NONE => NONE - | SOME thm => if SMT2_Builtin.is_builtin_typ_ext ctxt T then SOME thm else NONE) - | abs_min_max _ _ = NONE - - fun unfold_amm_conv ctxt ct = - (case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of - SOME thm => expand_head_conv (Conv.rewr_conv thm) - | NONE => Conv.all_conv) ct -in - -fun unfold_abs_min_max_conv ctxt = - SMT2_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt) - -val setup_abs_min_max = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) abs_min_max_table - -end - - -(** normalize numerals **) - -local - (* - rewrite Numeral1 into 1 - rewrite - 0 into 0 - *) - - fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) = - true - | is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) = - true - | is_irregular_number _ = false - - fun is_strange_number ctxt t = is_irregular_number t andalso SMT2_Builtin.is_builtin_num ctxt t - - val proper_num_ss = - simpset_of (put_simpset HOL_ss @{context} addsimps @{thms Num.numeral_One minus_zero}) - - fun norm_num_conv ctxt = - SMT2_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt)) - Conv.no_conv -in - -fun normalize_numerals_conv ctxt = - SMT2_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt) - -end - - -(** combined unfoldings and rewritings **) - -fun unfold_conv ctxt = - rewrite_case_bool_conv ctxt then_conv - unfold_abs_min_max_conv ctxt then_conv - Thm.beta_conversion true - -fun unfold_polymorph ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt))) -fun unfold_monomorph ctxt = map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt))) - - -(* overall normalization *) - -fun burrow_ids f ithms = - let - val (is, thms) = split_list ithms - val (thms', extra_thms) = f thms - in (is ~~ thms') @ map (pair ~1) extra_thms end - -type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list - -structure Extra_Norms = Generic_Data -( - type T = extra_norm SMT2_Util.dict - val empty = [] - val extend = I - fun merge data = SMT2_Util.dict_merge fst data -) - -fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT2_Util.dict_update (cs, norm)) - -fun apply_extra_norms ctxt ithms = - let - val cs = SMT2_Config.solver_class_of ctxt - val es = SMT2_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs - in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end - -local - val ignored = member (op =) [@{const_name All}, @{const_name Ex}, - @{const_name Let}, @{const_name If}, @{const_name HOL.eq}] - - val schematic_consts_of = - let - fun collect (@{const trigger} $ p $ t) = collect_trigger p #> collect t - | collect (t $ u) = collect t #> collect u - | collect (Abs (_, _, t)) = collect t - | collect (t as Const (n, _)) = - if not (ignored n) then Monomorph.add_schematic_consts_of t else I - | collect _ = I - and collect_trigger t = - let val dest = these o try SMT2_Util.dest_symb_list - in fold (fold collect_pat o dest) (dest t) end - and collect_pat (Const (@{const_name pat}, _) $ t) = collect t - | collect_pat (Const (@{const_name nopat}, _) $ t) = collect t - | collect_pat _ = I - in (fn t => collect t Symtab.empty) end -in - -fun monomorph ctxt xthms = - let val (xs, thms) = split_list xthms - in - map (pair 1) thms - |> Monomorph.monomorph schematic_consts_of ctxt - |> maps (uncurry (map o pair)) o map2 pair xs o map (map snd) - end - -end - -fun normalize ctxt wthms = - wthms - |> map_index I - |> gen_normalize ctxt - |> unfold_polymorph ctxt - |> monomorph ctxt - |> unfold_monomorph ctxt - |> apply_extra_norms ctxt - -val _ = Theory.setup (Context.theory_map ( - setup_atomize #> - setup_unfolded_quants #> - setup_trigger #> - setup_case_bool #> - setup_abs_min_max)) - -end;