author | wenzelm |
Fri, 06 Mar 2015 23:44:57 +0100 | |
changeset 59632 | 5980e75a204e |
parent 59621 | 291934bac95e |
child 60642 | 48dd1cefb4ae |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT/smt_normalize.ML |
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Author: Sascha Boehme, TU Muenchen |
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Normalization steps on theorems required by SMT solvers. |
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*) |
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signature SMT_NORMALIZE = |
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sig |
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val drop_fact_warning: Proof.context -> thm -> unit |
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val atomize_conv: Proof.context -> conv |
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val special_quant_table: (string * thm) list |
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val case_bool_entry: string * thm |
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val abs_min_max_table: (string * thm) list |
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type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list |
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val add_extra_norm: SMT_Util.class * extra_norm -> Context.generic -> Context.generic |
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val normalize: Proof.context -> thm list -> (int * thm) list |
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end; |
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structure SMT_Normalize: SMT_NORMALIZE = |
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struct |
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fun drop_fact_warning ctxt = |
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SMT_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o |
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Display.string_of_thm ctxt) |
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(* general theorem normalizations *) |
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(** instantiate elimination rules **) |
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local |
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val (cpfalse, cfalse) = `SMT_Util.mk_cprop (Thm.cterm_of @{context} @{const False}) |
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fun inst f ct thm = |
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let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm)) |
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in Thm.instantiate ([], [(cv, ct)]) thm end |
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in |
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fun instantiate_elim thm = |
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(case Thm.concl_of thm of |
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@{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm |
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| Var _ => inst I cpfalse thm |
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| _ => thm) |
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end |
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(** normalize definitions **) |
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fun norm_def thm = |
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(case Thm.prop_of thm of |
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@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) => |
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norm_def (thm RS @{thm fun_cong}) |
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| Const (@{const_name Pure.eq}, _) $ _ $ Abs _ => norm_def (thm RS @{thm meta_eq_to_obj_eq}) |
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| _ => thm) |
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(** atomization **) |
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fun atomize_conv ctxt ct = |
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(case Thm.term_of ct of |
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@{const Pure.imp} $ _ $ _ => |
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Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_imp} |
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| Const (@{const_name Pure.eq}, _) $ _ $ _ => |
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Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_eq} |
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| Const (@{const_name Pure.all}, _) $ Abs _ => |
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Conv.binder_conv (atomize_conv o snd) ctxt then_conv Conv.rewr_conv @{thm atomize_all} |
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| _ => Conv.all_conv) ct |
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val setup_atomize = |
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fold SMT_Builtin.add_builtin_fun_ext'' [@{const_name Pure.imp}, @{const_name Pure.eq}, |
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@{const_name Pure.all}, @{const_name Trueprop}] |
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(** unfold special quantifiers **) |
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val special_quant_table = [ |
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(@{const_name Ex1}, @{thm Ex1_def_raw}), |
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(@{const_name Ball}, @{thm Ball_def_raw}), |
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(@{const_name Bex}, @{thm Bex_def_raw})] |
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local |
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fun special_quant (Const (n, _)) = AList.lookup (op =) special_quant_table n |
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| special_quant _ = NONE |
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fun special_quant_conv _ ct = |
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(case special_quant (Thm.term_of ct) of |
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SOME thm => Conv.rewr_conv thm |
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| NONE => Conv.all_conv) ct |
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in |
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fun unfold_special_quants_conv ctxt = |
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SMT_Util.if_exists_conv (is_some o special_quant) (Conv.top_conv special_quant_conv ctxt) |
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val setup_unfolded_quants = fold (SMT_Builtin.add_builtin_fun_ext'' o fst) special_quant_table |
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end |
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(** trigger inference **) |
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local |
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(*** check trigger syntax ***) |
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fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true |
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| dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false |
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| dest_trigger _ = NONE |
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fun eq_list [] = false |
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| eq_list (b :: bs) = forall (equal b) bs |
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fun proper_trigger t = |
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t |
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|> these o try SMT_Util.dest_symb_list |
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|> map (map_filter dest_trigger o these o try SMT_Util.dest_symb_list) |
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|> (fn [] => false | bss => forall eq_list bss) |
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fun proper_quant inside f t = |
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(case t of |
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Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u |
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| Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u |
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| @{const trigger} $ p $ u => |
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(if inside then f p else false) andalso proper_quant false f u |
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| Abs (_, _, u) => proper_quant false f u |
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| u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2 |
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| _ => true) |
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fun check_trigger_error ctxt t = |
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error ("SMT triggers must only occur under quantifier and multipatterns " ^ |
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"must have the same kind: " ^ Syntax.string_of_term ctxt t) |
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133 |
|
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fun check_trigger_conv ctxt ct = |
58061 | 135 |
if proper_quant false proper_trigger (SMT_Util.term_of ct) then Conv.all_conv ct |
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else check_trigger_error ctxt (Thm.term_of ct) |
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137 |
|
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138 |
|
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(*** infer simple triggers ***) |
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140 |
|
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fun dest_cond_eq ct = |
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(case Thm.term_of ct of |
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Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct |
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| @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct) |
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| _ => raise CTERM ("no equation", [ct])) |
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|
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fun get_constrs thy (Type (n, _)) = these (BNF_LFP_Compat.get_constrs thy n) |
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| get_constrs _ _ = [] |
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|
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fun is_constr thy (n, T) = |
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let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U) |
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in can (the o find_first match o get_constrs thy o Term.body_type) T end |
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153 |
|
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fun is_constr_pat thy t = |
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(case Term.strip_comb t of |
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(Free _, []) => true |
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| (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts |
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158 |
| _ => false) |
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159 |
|
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fun is_simp_lhs ctxt t = |
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(case Term.strip_comb t of |
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(Const c, ts as _ :: _) => |
58061 | 163 |
not (SMT_Builtin.is_builtin_fun_ext ctxt c ts) andalso |
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forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts |
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| _ => false) |
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166 |
|
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fun has_all_vars vs t = |
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subset (op aconv) (vs, map Free (Term.add_frees t [])) |
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169 |
|
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fun minimal_pats vs ct = |
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if has_all_vars vs (Thm.term_of ct) then |
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(case Thm.term_of ct of |
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_ $ _ => |
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(case apply2 (minimal_pats vs) (Thm.dest_comb ct) of |
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([], []) => [[ct]] |
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| (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss') |
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| _ => []) |
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else [] |
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179 |
|
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fun proper_mpat _ _ _ [] = false |
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| proper_mpat thy gen u cts = |
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let |
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val tps = (op ~~) (`gen (map Thm.term_of cts)) |
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fun some_match u = tps |> exists (fn (t', t) => |
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Pattern.matches thy (t', u) andalso not (t aconv u)) |
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in not (Term.exists_subterm some_match u) end |
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187 |
|
58061 | 188 |
val pat = SMT_Util.mk_const_pat @{theory} @{const_name pat} SMT_Util.destT1 |
189 |
fun mk_pat ct = Thm.apply (SMT_Util.instT' ct pat) ct |
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|
57230 | 191 |
fun mk_clist T = |
59632 | 192 |
apply2 (Thm.cterm_of @{context}) (SMT_Util.symb_cons_const T, SMT_Util.symb_nil_const T) |
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fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil |
57230 | 194 |
val mk_pat_list = mk_list (mk_clist @{typ pattern}) |
195 |
val mk_mpat_list = mk_list (mk_clist @{typ "pattern symb_list"}) |
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fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss |
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|
57230 | 198 |
val trigger_eq = mk_meta_eq @{lemma "p = trigger t p" by (simp add: trigger_def)} |
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199 |
|
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fun insert_trigger_conv [] ct = Conv.all_conv ct |
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201 |
| insert_trigger_conv ctss ct = |
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let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct |
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|
203 |
in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end |
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204 |
|
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fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct = |
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let |
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val (lhs, rhs) = dest_cond_eq ct |
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208 |
|
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val vs = map Thm.term_of cvs |
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210 |
val thy = Proof_Context.theory_of ctxt |
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211 |
|
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212 |
fun get_mpats ct = |
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213 |
if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct |
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214 |
else [] |
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val gen = Variable.export_terms ctxt outer_ctxt |
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val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs)) |
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217 |
|
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in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end |
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219 |
|
57230 | 220 |
fun has_trigger (@{const trigger} $ _ $ _) = true |
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221 |
| has_trigger _ = false |
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222 |
|
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223 |
fun try_trigger_conv cv ct = |
58061 | 224 |
if SMT_Util.under_quant has_trigger (SMT_Util.term_of ct) then Conv.all_conv ct |
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225 |
else Conv.try_conv cv ct |
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226 |
|
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227 |
fun infer_trigger_conv ctxt = |
58061 | 228 |
if Config.get ctxt SMT_Config.infer_triggers then |
229 |
try_trigger_conv (SMT_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt) |
|
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230 |
else Conv.all_conv |
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|
231 |
in |
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232 |
|
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|
233 |
fun trigger_conv ctxt = |
58061 | 234 |
SMT_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt) |
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235 |
|
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236 |
val setup_trigger = |
58061 | 237 |
fold SMT_Builtin.add_builtin_fun_ext'' |
57230 | 238 |
[@{const_name pat}, @{const_name nopat}, @{const_name trigger}] |
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239 |
|
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240 |
end |
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241 |
|
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242 |
|
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|
243 |
(** combined general normalizations **) |
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244 |
|
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245 |
fun gen_normalize1_conv ctxt = |
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246 |
atomize_conv ctxt then_conv |
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247 |
unfold_special_quants_conv ctxt then_conv |
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248 |
Thm.beta_conversion true then_conv |
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249 |
trigger_conv ctxt |
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250 |
|
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251 |
fun gen_normalize1 ctxt = |
56107 | 252 |
instantiate_elim #> |
253 |
norm_def #> |
|
254 |
Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #> |
|
255 |
Drule.forall_intr_vars #> |
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256 |
Conv.fconv_rule (gen_normalize1_conv ctxt) #> |
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257 |
(* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *) |
56107 | 258 |
Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]} |
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259 |
|
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fun gen_norm1_safe ctxt (i, thm) = |
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(case try (gen_normalize1 ctxt) thm of |
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SOME thm' => SOME (i, thm') |
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| NONE => (drop_fact_warning ctxt thm; NONE)) |
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|
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fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms |
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|
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|
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(* unfolding of definitions and theory-specific rewritings *) |
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|
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fun expand_head_conv cv ct = |
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(case Thm.term_of ct of |
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_ $ _ => |
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Conv.fun_conv (expand_head_conv cv) then_conv |
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Conv.try_conv (Thm.beta_conversion false) |
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| _ => cv) ct |
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|
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|
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(** rewrite bool case expressions as if expressions **) |
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|
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val case_bool_entry = (@{const_name "bool.case_bool"}, @{thm case_bool_if}) |
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|
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local |
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fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true |
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| is_case_bool _ = false |
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|
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fun unfold_conv _ = |
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SMT_Util.if_true_conv (is_case_bool o Term.head_of) |
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(expand_head_conv (Conv.rewr_conv @{thm case_bool_if})) |
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in |
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|
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fun rewrite_case_bool_conv ctxt = |
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SMT_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt) |
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|
58061 | 294 |
val setup_case_bool = SMT_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"} |
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|
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296 |
end |
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|
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|
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(** unfold abs, min and max **) |
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|
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val abs_min_max_table = [ |
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(@{const_name min}, @{thm min_def_raw}), |
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(@{const_name max}, @{thm max_def_raw}), |
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(@{const_name abs}, @{thm abs_if_raw})] |
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|
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local |
56100 | 307 |
fun abs_min_max ctxt (Const (n, Type (@{type_name fun}, [T, _]))) = |
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(case AList.lookup (op =) abs_min_max_table n of |
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NONE => NONE |
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| SOME thm => if SMT_Builtin.is_builtin_typ_ext ctxt T then SOME thm else NONE) |
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| abs_min_max _ _ = NONE |
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|
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fun unfold_amm_conv ctxt ct = |
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(case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of |
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SOME thm => expand_head_conv (Conv.rewr_conv thm) |
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|
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| NONE => Conv.all_conv) ct |
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in |
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|
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|
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|
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fun unfold_abs_min_max_conv ctxt = |
58061 | 320 |
SMT_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt) |
57230 | 321 |
|
58061 | 322 |
val setup_abs_min_max = fold (SMT_Builtin.add_builtin_fun_ext'' o fst) abs_min_max_table |
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|
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324 |
end |
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|
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|
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|
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|
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|
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(** normalize numerals **) |
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|
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|
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local |
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|
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(* |
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|
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rewrite Numeral1 into 1 |
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rewrite - 0 into 0 |
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|
333 |
*) |
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|
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|
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|
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fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) = |
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|
336 |
true |
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|
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| is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) = |
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true |
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| is_irregular_number _ = false |
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|
58061 | 341 |
fun is_strange_number ctxt t = is_irregular_number t andalso SMT_Builtin.is_builtin_num ctxt t |
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|
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|
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|
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val proper_num_ss = |
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simpset_of (put_simpset HOL_ss @{context} addsimps @{thms Num.numeral_One minus_zero}) |
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|
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|
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|
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fun norm_num_conv ctxt = |
58061 | 347 |
SMT_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt)) |
56090 | 348 |
Conv.no_conv |
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in |
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|
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|
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|
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fun normalize_numerals_conv ctxt = |
58061 | 352 |
SMT_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt) |
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|
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|
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|
354 |
end |
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|
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|
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|
356 |
|
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|
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(** combined unfoldings and rewritings **) |
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|
358 |
|
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|
359 |
fun unfold_conv ctxt = |
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|
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rewrite_case_bool_conv ctxt then_conv |
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|
361 |
unfold_abs_min_max_conv ctxt then_conv |
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|
362 |
Thm.beta_conversion true |
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|
363 |
|
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|
364 |
fun unfold_polymorph ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt))) |
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|
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fun unfold_monomorph ctxt = map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt))) |
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366 |
|
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|
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|
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|
368 |
(* overall normalization *) |
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|
369 |
|
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|
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fun burrow_ids f ithms = |
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|
371 |
let |
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|
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val (is, thms) = split_list ithms |
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|
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val (thms', extra_thms) = f thms |
56106 | 374 |
in (is ~~ thms') @ map (pair ~1) extra_thms end |
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|
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|
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type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list |
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|
377 |
|
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|
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structure Extra_Norms = Generic_Data |
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|
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( |
58061 | 380 |
type T = extra_norm SMT_Util.dict |
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|
381 |
val empty = [] |
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|
382 |
val extend = I |
58061 | 383 |
fun merge data = SMT_Util.dict_merge fst data |
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|
384 |
) |
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|
385 |
|
58061 | 386 |
fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT_Util.dict_update (cs, norm)) |
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|
387 |
|
624faeda77b5
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changeset
|
388 |
fun apply_extra_norms ctxt ithms = |
624faeda77b5
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|
389 |
let |
58061 | 390 |
val cs = SMT_Config.solver_class_of ctxt |
391 |
val es = SMT_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs |
|
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624faeda77b5
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|
392 |
in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end |
624faeda77b5
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changeset
|
393 |
|
624faeda77b5
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|
394 |
local |
624faeda77b5
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|
395 |
val ignored = member (op =) [@{const_name All}, @{const_name Ex}, |
624faeda77b5
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parents:
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|
396 |
@{const_name Let}, @{const_name If}, @{const_name HOL.eq}] |
624faeda77b5
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parents:
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changeset
|
397 |
|
624faeda77b5
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changeset
|
398 |
val schematic_consts_of = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
399 |
let |
57230 | 400 |
fun collect (@{const trigger} $ p $ t) = collect_trigger p #> collect t |
56078
624faeda77b5
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parents:
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changeset
|
401 |
| collect (t $ u) = collect t #> collect u |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
402 |
| collect (Abs (_, _, t)) = collect t |
57230 | 403 |
| collect (t as Const (n, _)) = |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
404 |
if not (ignored n) then Monomorph.add_schematic_consts_of t else I |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
405 |
| collect _ = I |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
406 |
and collect_trigger t = |
58061 | 407 |
let val dest = these o try SMT_Util.dest_symb_list |
56078
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moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
408 |
in fold (fold collect_pat o dest) (dest t) end |
57230 | 409 |
and collect_pat (Const (@{const_name pat}, _) $ t) = collect t |
410 |
| collect_pat (Const (@{const_name nopat}, _) $ t) = collect t |
|
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moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
411 |
| collect_pat _ = I |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
412 |
in (fn t => collect t Symtab.empty) end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
413 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
414 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
415 |
fun monomorph ctxt xthms = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
416 |
let val (xs, thms) = split_list xthms |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
417 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
418 |
map (pair 1) thms |
624faeda77b5
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parents:
diff
changeset
|
419 |
|> Monomorph.monomorph schematic_consts_of ctxt |
624faeda77b5
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parents:
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changeset
|
420 |
|> maps (uncurry (map o pair)) o map2 pair xs o map (map snd) |
624faeda77b5
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changeset
|
421 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
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changeset
|
422 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
423 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
424 |
|
56106 | 425 |
fun normalize ctxt wthms = |
426 |
wthms |
|
427 |
|> map_index I |
|
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
428 |
|> gen_normalize ctxt |
57696
fb71c6f100f8
do not embed 'nat' into 'int's in 'smt2' method -- this is highly inefficient and decreases the Sledgehammer success rate significantly
blanchet
parents:
57230
diff
changeset
|
429 |
|> unfold_polymorph ctxt |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
430 |
|> monomorph ctxt |
57696
fb71c6f100f8
do not embed 'nat' into 'int's in 'smt2' method -- this is highly inefficient and decreases the Sledgehammer success rate significantly
blanchet
parents:
57230
diff
changeset
|
431 |
|> unfold_monomorph ctxt |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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parents:
diff
changeset
|
432 |
|> apply_extra_norms ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
433 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
434 |
val _ = Theory.setup (Context.theory_map ( |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
435 |
setup_atomize #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
436 |
setup_unfolded_quants #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
437 |
setup_trigger #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
438 |
setup_case_bool #> |
57696
fb71c6f100f8
do not embed 'nat' into 'int's in 'smt2' method -- this is highly inefficient and decreases the Sledgehammer success rate significantly
blanchet
parents:
57230
diff
changeset
|
439 |
setup_abs_min_max)) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
440 |
|
57229 | 441 |
end; |