author | blanchet |
Fri, 16 May 2014 19:13:50 +0200 | |
changeset 56981 | 3ef45ce002b5 |
parent 56245 | 84fc7dfa3cd4 |
child 57165 | 7b1bf424ec5f |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT2/smt2_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 SMT2_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: SMT2_Util.class * extra_norm -> Context.generic -> Context.generic |
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val normalize: Proof.context -> (int option * thm) list -> (int * thm) list |
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end |
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structure SMT2_Normalize: SMT2_NORMALIZE = |
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struct |
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fun drop_fact_warning ctxt = |
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SMT2_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) = `SMT2_Util.mk_cprop (Thm.cterm_of @{theory} @{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 SMT2_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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SMT2_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 (SMT2_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 HOLogic.dest_list |
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|> map (map_filter dest_trigger o these o try HOLogic.dest_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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129 |
|
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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 = |
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if proper_quant false proper_trigger (SMT2_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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146 |
|
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fun get_constrs thy (Type (n, _)) = these (Datatype.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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|
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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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| _ => 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 _ :: _) => |
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not (SMT2_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 pairself (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 |
|
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val pat = SMT2_Util.mk_const_pat @{theory} @{const_name SMT2.pat} SMT2_Util.destT1 |
189 |
fun mk_pat ct = Thm.apply (SMT2_Util.instT' ct pat) ct |
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|
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fun mk_clist T = pairself (Thm.cterm_of @{theory}) (HOLogic.cons_const T, HOLogic.nil_const T) |
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fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil |
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val mk_pat_list = mk_list (mk_clist @{typ SMT2.pattern}) |
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val mk_mpat_list = mk_list (mk_clist @{typ "SMT2.pattern list"}) |
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fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss |
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196 |
|
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val trigger_eq = mk_meta_eq @{lemma "p = SMT2.trigger t p" by (simp add: trigger_def)} |
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198 |
|
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fun insert_trigger_conv [] ct = Conv.all_conv ct |
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| insert_trigger_conv ctss ct = |
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201 |
let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct |
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in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end |
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203 |
|
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fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct = |
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205 |
let |
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val (lhs, rhs) = dest_cond_eq ct |
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207 |
|
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val vs = map Thm.term_of cvs |
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val thy = Proof_Context.theory_of ctxt |
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210 |
|
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fun get_mpats ct = |
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212 |
if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct |
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213 |
else [] |
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val gen = Variable.export_terms ctxt outer_ctxt |
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215 |
val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs)) |
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216 |
|
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in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end |
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218 |
|
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fun has_trigger (@{const SMT2.trigger} $ _ $ _) = true |
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220 |
| has_trigger _ = false |
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221 |
|
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222 |
fun try_trigger_conv cv ct = |
56090 | 223 |
if SMT2_Util.under_quant has_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct |
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224 |
else Conv.try_conv cv ct |
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225 |
|
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226 |
fun infer_trigger_conv ctxt = |
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227 |
if Config.get ctxt SMT2_Config.infer_triggers then |
56090 | 228 |
try_trigger_conv (SMT2_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt) |
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229 |
else Conv.all_conv |
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230 |
in |
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231 |
|
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232 |
fun trigger_conv ctxt = |
56090 | 233 |
SMT2_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt) |
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234 |
|
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235 |
val setup_trigger = |
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236 |
fold SMT2_Builtin.add_builtin_fun_ext'' |
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237 |
[@{const_name SMT2.pat}, @{const_name SMT2.nopat}, @{const_name SMT2.trigger}] |
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238 |
|
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239 |
end |
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240 |
|
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241 |
|
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242 |
(** adding quantifier weights **) |
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243 |
|
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local |
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(*** check weight syntax ***) |
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|
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val has_no_weight = |
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not o Term.exists_subterm (fn @{const SMT2.weight} => true | _ => false) |
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|
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fun is_weight (@{const SMT2.weight} $ w $ t) = |
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(case try HOLogic.dest_number w of |
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SOME (_, i) => i >= 0 andalso has_no_weight t |
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| _ => false) |
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| is_weight t = has_no_weight t |
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|
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fun proper_trigger (@{const SMT2.trigger} $ _ $ t) = is_weight t |
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| proper_trigger t = is_weight t |
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|
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fun check_weight_error ctxt t = |
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error ("SMT weight must be a non-negative number and must only occur " ^ |
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"under the top-most quantifier and an optional trigger: " ^ |
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Syntax.string_of_term ctxt t) |
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|
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fun check_weight_conv ctxt ct = |
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if SMT2_Util.under_quant proper_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct |
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else check_weight_error ctxt (Thm.term_of ct) |
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|
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|
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(*** insertion of weights ***) |
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|
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fun under_trigger_conv cv ct = |
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(case Thm.term_of ct of |
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@{const SMT2.trigger} $ _ $ _ => Conv.arg_conv cv |
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| _ => cv) ct |
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|
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val weight_eq = mk_meta_eq @{lemma "p = SMT2.weight i p" by (simp add: weight_def)} |
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fun mk_weight_eq w = |
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let val cv = Thm.dest_arg1 (Thm.rhs_of weight_eq) |
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in Thm.instantiate ([], [(cv, Numeral.mk_cnumber @{ctyp int} w)]) weight_eq end |
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|
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fun add_weight_conv NONE _ = Conv.all_conv |
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| add_weight_conv (SOME weight) ctxt = |
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let val cv = Conv.rewr_conv (mk_weight_eq weight) |
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in SMT2_Util.under_quant_conv (K (under_trigger_conv cv)) ctxt end |
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in |
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|
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fun weight_conv weight ctxt = |
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SMT2_Util.prop_conv (check_weight_conv ctxt then_conv add_weight_conv weight ctxt) |
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|
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val setup_weight = SMT2_Builtin.add_builtin_fun_ext'' @{const_name SMT2.weight} |
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|
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end |
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|
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|
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(** combined general normalizations **) |
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|
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fun gen_normalize1_conv ctxt weight = |
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atomize_conv ctxt then_conv |
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unfold_special_quants_conv ctxt then_conv |
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Thm.beta_conversion true then_conv |
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trigger_conv ctxt then_conv |
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weight_conv weight ctxt |
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|
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fun gen_normalize1 ctxt weight = |
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instantiate_elim #> |
|
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norm_def #> |
|
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Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #> |
|
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Drule.forall_intr_vars #> |
|
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Conv.fconv_rule (gen_normalize1_conv ctxt weight) #> |
|
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(* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *) |
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Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]} |
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|
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fun gen_norm1_safe ctxt (i, (weight, thm)) = |
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(case try (gen_normalize1 ctxt weight) 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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|
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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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SMT2_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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SMT2_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt) |
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|
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val setup_case_bool = SMT2_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"} |
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|
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350 |
end |
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|
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352 |
|
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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 |
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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 SMT2_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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moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
370 |
| NONE => Conv.all_conv) ct |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
371 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
372 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
373 |
fun unfold_abs_min_max_conv ctxt = |
56090 | 374 |
SMT2_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
375 |
|
56981
3ef45ce002b5
honor original format of conjecture or hypotheses in Z3-to-Isar proofs
blanchet
parents:
56245
diff
changeset
|
376 |
val setup_abs_min_max = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) abs_min_max_table |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
377 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
378 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
379 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
380 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
381 |
(** embedding of standard natural number operations into integer operations **) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
382 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
383 |
local |
56107 | 384 |
val nat_embedding = @{thms nat_int' int_nat_nneg int_nat_neg} |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
385 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
386 |
val simple_nat_ops = [ |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
387 |
@{const less (nat)}, @{const less_eq (nat)}, |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
388 |
@{const Suc}, @{const plus (nat)}, @{const minus (nat)}] |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
389 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
390 |
val mult_nat_ops = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
391 |
[@{const times (nat)}, @{const div (nat)}, @{const mod (nat)}] |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
392 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
393 |
val nat_ops = simple_nat_ops @ mult_nat_ops |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
394 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
395 |
val nat_consts = nat_ops @ [@{const numeral (nat)}, |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
396 |
@{const zero_class.zero (nat)}, @{const one_class.one (nat)}] |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
397 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
398 |
val nat_int_coercions = [@{const of_nat (int)}, @{const nat}] |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
399 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
400 |
val builtin_nat_ops = nat_int_coercions @ simple_nat_ops |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
401 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
402 |
val is_nat_const = member (op aconv) nat_consts |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
403 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
404 |
fun is_nat_const' @{const of_nat (int)} = true |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
405 |
| is_nat_const' t = is_nat_const t |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
406 |
|
56103
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
407 |
val expands = map mk_meta_eq @{thms nat_zero_as_int nat_one_as_int nat_numeral_as_int |
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
408 |
nat_less_as_int nat_leq_as_int Suc_as_int nat_plus_as_int nat_minus_as_int nat_times_as_int |
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
409 |
nat_div_as_int nat_mod_as_int} |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
410 |
|
56103
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
411 |
val ints = map mk_meta_eq @{thms int_0 int_1 int_Suc int_plus int_minus int_mult zdiv_int |
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
412 |
zmod_int} |
6689512f3710
move lemmas to theory file, towards textual proof reconstruction
blanchet
parents:
56100
diff
changeset
|
413 |
val int_if = mk_meta_eq @{lemma "int (if P then n else m) = (if P then int n else int m)" by simp} |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
414 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
415 |
fun mk_number_eq ctxt i lhs = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
416 |
let |
56090 | 417 |
val eq = SMT2_Util.mk_cequals lhs (Numeral.mk_cnumber @{ctyp int} i) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
418 |
val ctxt' = put_simpset HOL_ss ctxt addsimps @{thms Int.int_numeral} |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
419 |
val tac = HEADGOAL (Simplifier.simp_tac ctxt') |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
420 |
in Goal.norm_result ctxt (Goal.prove_internal ctxt [] eq (K tac)) end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
421 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
422 |
fun ite_conv cv1 cv2 = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
423 |
Conv.combination_conv (Conv.combination_conv (Conv.arg_conv cv1) cv2) cv2 |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
424 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
425 |
fun int_conv ctxt ct = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
426 |
(case Thm.term_of ct of |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
427 |
@{const of_nat (int)} $ (n as (@{const numeral (nat)} $ _)) => |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
428 |
Conv.rewr_conv (mk_number_eq ctxt (snd (HOLogic.dest_number n)) ct) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
429 |
| @{const of_nat (int)} $ _ => |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
430 |
(Conv.rewrs_conv ints then_conv Conv.sub_conv ints_conv ctxt) else_conv |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
431 |
(Conv.rewr_conv int_if then_conv |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
432 |
ite_conv (nat_conv ctxt) (int_conv ctxt)) else_conv |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
433 |
Conv.sub_conv (Conv.top_sweep_conv nat_conv) ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
434 |
| _ => Conv.no_conv) ct |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
435 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
436 |
and ints_conv ctxt = Conv.top_sweep_conv int_conv ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
437 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
438 |
and expand_conv ctxt = |
56090 | 439 |
SMT2_Util.if_conv (is_nat_const o Term.head_of) |
440 |
(expand_head_conv (Conv.rewrs_conv expands) then_conv ints_conv ctxt) (int_conv ctxt) |
|
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
441 |
|
56090 | 442 |
and nat_conv ctxt = SMT2_Util.if_exists_conv is_nat_const' (Conv.top_sweep_conv expand_conv ctxt) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
443 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
444 |
val uses_nat_int = Term.exists_subterm (member (op aconv) nat_int_coercions) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
445 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
446 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
447 |
val nat_as_int_conv = nat_conv |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
448 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
449 |
fun add_nat_embedding thms = |
56100 | 450 |
if exists (uses_nat_int o Thm.prop_of) thms then (thms, nat_embedding) else (thms, []) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
451 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
452 |
val setup_nat_as_int = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
453 |
SMT2_Builtin.add_builtin_typ_ext (@{typ nat}, K true) #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
454 |
fold (SMT2_Builtin.add_builtin_fun_ext' o Term.dest_Const) builtin_nat_ops |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
455 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
456 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
457 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
458 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
459 |
(** normalize numerals **) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
460 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
461 |
local |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
462 |
(* |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
463 |
rewrite Numeral1 into 1 |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
464 |
rewrite - 0 into 0 |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
465 |
*) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
466 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
467 |
fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
468 |
true |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
469 |
| is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
470 |
true |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
471 |
| is_irregular_number _ = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
472 |
false; |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
473 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
474 |
fun is_strange_number ctxt t = is_irregular_number t andalso SMT2_Builtin.is_builtin_num ctxt t; |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
475 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
476 |
val proper_num_ss = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
477 |
simpset_of (put_simpset HOL_ss @{context} |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
478 |
addsimps @{thms Num.numeral_One minus_zero}) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
479 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
480 |
fun norm_num_conv ctxt = |
56090 | 481 |
SMT2_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt)) |
482 |
Conv.no_conv |
|
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
483 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
484 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
485 |
fun normalize_numerals_conv ctxt = |
56090 | 486 |
SMT2_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt) |
56078
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
487 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
488 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
489 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
490 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
blanchet
parents:
diff
changeset
|
491 |
(** combined unfoldings and rewritings **) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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624faeda77b5
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fun unfold_conv ctxt = |
624faeda77b5
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494 |
rewrite_case_bool_conv ctxt then_conv |
624faeda77b5
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unfold_abs_min_max_conv ctxt then_conv |
624faeda77b5
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nat_as_int_conv ctxt then_conv |
624faeda77b5
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Thm.beta_conversion true |
624faeda77b5
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624faeda77b5
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fun unfold1 ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt))) |
624faeda77b5
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624faeda77b5
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fun burrow_ids f ithms = |
624faeda77b5
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let |
624faeda77b5
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val (is, thms) = split_list ithms |
624faeda77b5
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val (thms', extra_thms) = f thms |
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in (is ~~ thms') @ map (pair ~1) extra_thms end |
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624faeda77b5
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624faeda77b5
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fun unfold2 ctxt ithms = |
624faeda77b5
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ithms |
624faeda77b5
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|> map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt))) |
624faeda77b5
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|> burrow_ids add_nat_embedding |
624faeda77b5
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511 |
|
624faeda77b5
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624faeda77b5
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624faeda77b5
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(* overall normalization *) |
624faeda77b5
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|
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type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list |
624faeda77b5
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structure Extra_Norms = Generic_Data |
624faeda77b5
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( |
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type T = extra_norm SMT2_Util.dict |
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val empty = [] |
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val extend = I |
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fun merge data = SMT2_Util.dict_merge fst data |
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624faeda77b5
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) |
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|
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fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT2_Util.dict_update (cs, norm)) |
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624faeda77b5
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|
624faeda77b5
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fun apply_extra_norms ctxt ithms = |
624faeda77b5
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let |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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val cs = SMT2_Config.solver_class_of ctxt |
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val es = SMT2_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs |
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624faeda77b5
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in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end |
624faeda77b5
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|
624faeda77b5
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local |
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val ignored = member (op =) [@{const_name All}, @{const_name Ex}, |
624faeda77b5
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@{const_name Let}, @{const_name If}, @{const_name HOL.eq}] |
624faeda77b5
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|
624faeda77b5
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538 |
val schematic_consts_of = |
624faeda77b5
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539 |
let |
624faeda77b5
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fun collect (@{const SMT2.trigger} $ p $ t) = |
624faeda77b5
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|
541 |
collect_trigger p #> collect t |
624faeda77b5
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542 |
| collect (t $ u) = collect t #> collect u |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
543 |
| collect (Abs (_, _, t)) = collect t |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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544 |
| collect (t as Const (n, _)) = |
624faeda77b5
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545 |
if not (ignored n) then Monomorph.add_schematic_consts_of t else I |
624faeda77b5
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546 |
| collect _ = I |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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547 |
and collect_trigger t = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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548 |
let val dest = these o try HOLogic.dest_list |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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549 |
in fold (fold collect_pat o dest) (dest t) end |
624faeda77b5
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550 |
and collect_pat (Const (@{const_name SMT2.pat}, _) $ t) = collect t |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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551 |
| collect_pat (Const (@{const_name SMT2.nopat}, _) $ t) = collect t |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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552 |
| collect_pat _ = I |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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553 |
in (fn t => collect t Symtab.empty) end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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554 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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555 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
556 |
fun monomorph ctxt xthms = |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
557 |
let val (xs, thms) = split_list xthms |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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558 |
in |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
559 |
map (pair 1) thms |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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560 |
|> Monomorph.monomorph schematic_consts_of ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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561 |
|> maps (uncurry (map o pair)) o map2 pair xs o map (map snd) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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562 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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563 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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564 |
end |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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565 |
|
56106 | 566 |
fun normalize ctxt wthms = |
567 |
wthms |
|
568 |
|> map_index I |
|
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624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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569 |
|> gen_normalize ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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570 |
|> unfold1 ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
571 |
|> monomorph ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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572 |
|> unfold2 ctxt |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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573 |
|> apply_extra_norms ctxt |
624faeda77b5
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|
574 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
575 |
val _ = Theory.setup (Context.theory_map ( |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
576 |
setup_atomize #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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changeset
|
577 |
setup_unfolded_quants #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
578 |
setup_trigger #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
579 |
setup_weight #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
580 |
setup_case_bool #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
581 |
setup_abs_min_max #> |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
582 |
setup_nat_as_int)) |
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
583 |
|
624faeda77b5
moved 'SMT2' (SMT-LIB-2-based SMT module) into Isabelle
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|
584 |
end |