src/HOL/Library/SMT/smt_normalize.ML

+(*  Title:      HOL/Library/SMT/smt_normalize.ML
+    Author:     Sascha Boehme, TU Muenchen
+
+Normalization steps on theorems required by SMT solvers.
+*)
+
+signature SMT_NORMALIZE =
+sig
+  val drop_fact_warning: Proof.context -> thm -> unit
+  val atomize_conv: Proof.context -> conv
+  type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+  val add_extra_norm: SMT_Utils.class * extra_norm -> Context.generic ->
+    Context.generic
+  val normalize: (int * (int option * thm)) list -> Proof.context ->
+    (int * thm) list * Proof.context
+  val setup: theory -> theory
+end
+
+structure SMT_Normalize: SMT_NORMALIZE =
+struct
+
+fun drop_fact_warning ctxt =
+  SMT_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o
+    Display.string_of_thm ctxt)
+
+
+(* general theorem normalizations *)
+
+(** instantiate elimination rules **)
+ 
+local
+  val (cpfalse, cfalse) =
+    `SMT_Utils.mk_cprop (Thm.cterm_of @{theory} @{const False})
+
+  fun inst f ct thm =
+    let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm))
+    in Thm.instantiate ([], [(cv, ct)]) thm end
+in
+
+fun instantiate_elim thm =
+  (case Thm.concl_of thm of
+    @{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm
+  | Var _ => inst I cpfalse thm
+  | _ => thm)
+
+end
+
+
+(** normalize definitions **)
+
+fun norm_def thm =
+  (case Thm.prop_of thm of
+    @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
+      norm_def (thm RS @{thm fun_cong})
+  | Const (@{const_name Pure.eq}, _) $ _ $ Abs _ =>
+      norm_def (thm RS @{thm meta_eq_to_obj_eq})
+  | _ => thm)
+
+
+(** atomization **)
+
+fun atomize_conv ctxt ct =
+  (case Thm.term_of ct of
+    @{const Pure.imp} $ _ $ _ =>
+      Conv.binop_conv (atomize_conv ctxt) then_conv
+      Conv.rewr_conv @{thm atomize_imp}
+  | Const (@{const_name Pure.eq}, _) $ _ $ _ =>
+      Conv.binop_conv (atomize_conv ctxt) then_conv
+      Conv.rewr_conv @{thm atomize_eq}
+  | Const (@{const_name Pure.all}, _) $ Abs _ =>
+      Conv.binder_conv (atomize_conv o snd) ctxt then_conv
+      Conv.rewr_conv @{thm atomize_all}
+  | _ => Conv.all_conv) ct
+
+val setup_atomize =
+  fold SMT_Builtin.add_builtin_fun_ext'' [@{const_name Pure.imp},
+    @{const_name Pure.eq}, @{const_name Pure.all}, @{const_name Trueprop}]
+
+
+(** unfold special quantifiers **)
+
+local
+  val ex1_def = mk_meta_eq @{lemma
+    "Ex1 = (%P. EX x. P x & (ALL y. P y --> y = x))"
+    by (rule ext) (simp only: Ex1_def)}
+
+  val ball_def = mk_meta_eq @{lemma "Ball = (%A P. ALL x. x : A --> P x)"
+    by (rule ext)+ (rule Ball_def)}
+
+  val bex_def = mk_meta_eq @{lemma "Bex = (%A P. EX x. x : A & P x)"
+    by (rule ext)+ (rule Bex_def)}
+
+  val special_quants = [(@{const_name Ex1}, ex1_def),
+    (@{const_name Ball}, ball_def), (@{const_name Bex}, bex_def)]
+  
+  fun special_quant (Const (n, _)) = AList.lookup (op =) special_quants n
+    | special_quant _ = NONE
+
+  fun special_quant_conv _ ct =
+    (case special_quant (Thm.term_of ct) of
+      SOME thm => Conv.rewr_conv thm
+    | NONE => Conv.all_conv) ct
+in
+
+fun unfold_special_quants_conv ctxt =
+  SMT_Utils.if_exists_conv (is_some o special_quant)
+    (Conv.top_conv special_quant_conv ctxt)
+
+val setup_unfolded_quants =
+  fold (SMT_Builtin.add_builtin_fun_ext'' o fst) special_quants
+
+end
+
+
+(** trigger inference **)
+
+local
+  (*** check trigger syntax ***)
+
+  fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true
+    | dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false
+    | dest_trigger _ = NONE
+
+  fun eq_list [] = false
+    | eq_list (b :: bs) = forall (equal b) bs
+
+  fun proper_trigger t =
+    t
+    |> these o try HOLogic.dest_list
+    |> map (map_filter dest_trigger o these o try HOLogic.dest_list)
+    |> (fn [] => false | bss => forall eq_list bss)
+
+  fun proper_quant inside f t =
+    (case t of
+      Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u
+    | Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u
+    | @{const trigger} $ p $ u =>
+        (if inside then f p else false) andalso proper_quant false f u
+    | Abs (_, _, u) => proper_quant false f u
+    | u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2
+    | _ => true)
+
+  fun check_trigger_error ctxt t =
+    error ("SMT triggers must only occur under quantifier and multipatterns " ^
+      "must have the same kind: " ^ Syntax.string_of_term ctxt t)
+
+  fun check_trigger_conv ctxt ct =
+    if proper_quant false proper_trigger (SMT_Utils.term_of ct) then
+      Conv.all_conv ct
+    else check_trigger_error ctxt (Thm.term_of ct)
+
+
+  (*** infer simple triggers ***)
+
+  fun dest_cond_eq ct =
+    (case Thm.term_of ct of
+      Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct
+    | @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct)
+    | _ => raise CTERM ("no equation", [ct]))
+
+  fun get_constrs thy (Type (n, _)) = these (Datatype_Data.get_constrs thy n)
+    | get_constrs _ _ = []
+
+  fun is_constr thy (n, T) =
+    let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U)
+    in can (the o find_first match o get_constrs thy o Term.body_type) T end
+
+  fun is_constr_pat thy t =
+    (case Term.strip_comb t of
+      (Free _, []) => true
+    | (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts
+    | _ => false)
+
+  fun is_simp_lhs ctxt t =
+    (case Term.strip_comb t of
+      (Const c, ts as _ :: _) =>
+        not (SMT_Builtin.is_builtin_fun_ext ctxt c ts) andalso
+        forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts
+    | _ => false)
+
+  fun has_all_vars vs t =
+    subset (op aconv) (vs, map Free (Term.add_frees t []))
+
+  fun minimal_pats vs ct =
+    if has_all_vars vs (Thm.term_of ct) then
+      (case Thm.term_of ct of
+        _ $ _ =>
+          (case pairself (minimal_pats vs) (Thm.dest_comb ct) of
+            ([], []) => [[ct]]
+          | (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss')
+      | _ => [])
+    else []
+
+  fun proper_mpat _ _ _ [] = false
+    | proper_mpat thy gen u cts =
+        let
+          val tps = (op ~~) (`gen (map Thm.term_of cts))
+          fun some_match u = tps |> exists (fn (t', t) =>
+            Pattern.matches thy (t', u) andalso not (t aconv u))
+        in not (Term.exists_subterm some_match u) end
+
+  val pat =
+    SMT_Utils.mk_const_pat @{theory} @{const_name SMT.pat} SMT_Utils.destT1
+  fun mk_pat ct = Thm.apply (SMT_Utils.instT' ct pat) ct
+
+  fun mk_clist T = pairself (Thm.cterm_of @{theory})
+    (HOLogic.cons_const T, HOLogic.nil_const T)
+  fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil
+  val mk_pat_list = mk_list (mk_clist @{typ SMT.pattern})
+  val mk_mpat_list = mk_list (mk_clist @{typ "SMT.pattern list"})  
+  fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss
+
+  val trigger_eq =
+    mk_meta_eq @{lemma "p = SMT.trigger t p" by (simp add: trigger_def)}
+
+  fun insert_trigger_conv [] ct = Conv.all_conv ct
+    | insert_trigger_conv ctss ct =
+        let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct
+        in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end
+
+  fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct =
+    let
+      val (lhs, rhs) = dest_cond_eq ct
+
+      val vs = map Thm.term_of cvs
+      val thy = Proof_Context.theory_of ctxt
+
+      fun get_mpats ct =
+        if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct
+        else []
+      val gen = Variable.export_terms ctxt outer_ctxt
+      val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs))
+
+    in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end
+
+  fun has_trigger (@{const SMT.trigger} $ _ $ _) = true
+    | has_trigger _ = false
+
+  fun try_trigger_conv cv ct =
+    if SMT_Utils.under_quant has_trigger (SMT_Utils.term_of ct) then
+      Conv.all_conv ct
+    else Conv.try_conv cv ct
+
+  fun infer_trigger_conv ctxt =
+    if Config.get ctxt SMT_Config.infer_triggers then
+      try_trigger_conv
+        (SMT_Utils.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt)
+    else Conv.all_conv
+in
+
+fun trigger_conv ctxt =
+  SMT_Utils.prop_conv
+    (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt)
+
+val setup_trigger =
+  fold SMT_Builtin.add_builtin_fun_ext''
+    [@{const_name SMT.pat}, @{const_name SMT.nopat}, @{const_name SMT.trigger}]
+
+end
+
+
+(** adding quantifier weights **)
+
+local
+  (*** check weight syntax ***)
+
+  val has_no_weight =
+    not o Term.exists_subterm (fn @{const SMT.weight} => true | _ => false)
+
+  fun is_weight (@{const SMT.weight} $ w $ t) =
+        (case try HOLogic.dest_number w of
+          SOME (_, i) => i >= 0 andalso has_no_weight t
+        | _ => false)
+    | is_weight t = has_no_weight t
+
+  fun proper_trigger (@{const SMT.trigger} $ _ $ t) = is_weight t
+    | proper_trigger t = is_weight t 
+
+  fun check_weight_error ctxt t =
+    error ("SMT weight must be a non-negative number and must only occur " ^
+      "under the top-most quantifier and an optional trigger: " ^
+      Syntax.string_of_term ctxt t)
+
+  fun check_weight_conv ctxt ct =
+    if SMT_Utils.under_quant proper_trigger (SMT_Utils.term_of ct) then
+      Conv.all_conv ct
+    else check_weight_error ctxt (Thm.term_of ct)
+
+
+  (*** insertion of weights ***)
+
+  fun under_trigger_conv cv ct =
+    (case Thm.term_of ct of
+      @{const SMT.trigger} $ _ $ _ => Conv.arg_conv cv
+    | _ => cv) ct
+
+  val weight_eq =
+    mk_meta_eq @{lemma "p = SMT.weight i p" by (simp add: weight_def)}
+  fun mk_weight_eq w =
+    let val cv = Thm.dest_arg1 (Thm.rhs_of weight_eq)
+    in
+      Thm.instantiate ([], [(cv, Numeral.mk_cnumber @{ctyp int} w)]) weight_eq
+    end
+
+  fun add_weight_conv NONE _ = Conv.all_conv
+    | add_weight_conv (SOME weight) ctxt =
+        let val cv = Conv.rewr_conv (mk_weight_eq weight)
+        in SMT_Utils.under_quant_conv (K (under_trigger_conv cv)) ctxt end
+in
+
+fun weight_conv weight ctxt = 
+  SMT_Utils.prop_conv
+    (check_weight_conv ctxt then_conv add_weight_conv weight ctxt)
+
+val setup_weight = SMT_Builtin.add_builtin_fun_ext'' @{const_name SMT.weight}
+
+end
+
+
+(** combined general normalizations **)
+
+fun gen_normalize1_conv ctxt weight =
+  atomize_conv ctxt then_conv
+  unfold_special_quants_conv ctxt then_conv
+  Thm.beta_conversion true then_conv
+  trigger_conv ctxt then_conv
+  weight_conv weight ctxt
+
+fun gen_normalize1 ctxt weight thm =
+  thm
+  |> instantiate_elim
+  |> norm_def
+  |> Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion)
+  |> Drule.forall_intr_vars
+  |> Conv.fconv_rule (gen_normalize1_conv ctxt weight)
+
+fun gen_norm1_safe ctxt (i, (weight, thm)) =
+  (case try (gen_normalize1 ctxt weight) thm of
+    SOME thm' => SOME (i, thm')
+  | NONE => (drop_fact_warning ctxt thm; NONE))
+
+fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms
+
+
+
+(* unfolding of definitions and theory-specific rewritings *)
+
+fun expand_head_conv cv ct =
+  (case Thm.term_of ct of
+    _ $ _ =>
+      Conv.fun_conv (expand_head_conv cv) then_conv
+      Conv.try_conv (Thm.beta_conversion false)
+  | _ => cv) ct
+
+
+(** rewrite bool case expressions as if expressions **)
+
+local
+  fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true
+    | is_case_bool _ = false
+
+  val thm = mk_meta_eq @{lemma
+    "case_bool = (%x y P. if P then x else y)" by (rule ext)+ simp}
+
+  fun unfold_conv _ =
+    SMT_Utils.if_true_conv (is_case_bool o Term.head_of)
+      (expand_head_conv (Conv.rewr_conv thm))
+in
+
+fun rewrite_case_bool_conv ctxt =
+  SMT_Utils.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt)
+
+val setup_case_bool =
+  SMT_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"}
+
+end
+
+
+(** unfold abs, min and max **)
+
+local
+  val abs_def = mk_meta_eq @{lemma
+    "abs = (%a::'a::abs_if. if a < 0 then - a else a)"
+    by (rule ext) (rule abs_if)}
+
+  val min_def = mk_meta_eq @{lemma "min = (%a b. if a <= b then a else b)"
+    by (rule ext)+ (rule min_def)}
+
+  val max_def = mk_meta_eq  @{lemma "max = (%a b. if a <= b then b else a)"
+    by (rule ext)+ (rule max_def)}
+
+  val defs = [(@{const_name min}, min_def), (@{const_name max}, max_def),
+    (@{const_name abs}, abs_def)]
+
+  fun is_builtinT ctxt T =
+    SMT_Builtin.is_builtin_typ_ext ctxt (Term.domain_type T)
+
+  fun abs_min_max ctxt (Const (n, T)) =
+        (case AList.lookup (op =) defs n of
+          NONE => NONE
+        | SOME thm => if is_builtinT ctxt T then SOME thm else NONE)
+    | abs_min_max _ _ = NONE
+
+  fun unfold_amm_conv ctxt ct =
+    (case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of
+      SOME thm => expand_head_conv (Conv.rewr_conv thm)
+    | NONE => Conv.all_conv) ct
+in
+
+fun unfold_abs_min_max_conv ctxt =
+  SMT_Utils.if_exists_conv (is_some o abs_min_max ctxt)
+    (Conv.top_conv unfold_amm_conv ctxt)
+  
+val setup_abs_min_max = fold (SMT_Builtin.add_builtin_fun_ext'' o fst) defs
+
+end
+
+
+(** embedding of standard natural number operations into integer operations **)
+
+local
+  val nat_embedding = @{lemma
+    "ALL n. nat (int n) = n"
+    "ALL i. i >= 0 --> int (nat i) = i"
+    "ALL i. i < 0 --> int (nat i) = 0"
+    by simp_all}
+
+  val simple_nat_ops = [
+    @{const less (nat)}, @{const less_eq (nat)},
+    @{const Suc}, @{const plus (nat)}, @{const minus (nat)}]
+
+  val mult_nat_ops =
+    [@{const times (nat)}, @{const div (nat)}, @{const mod (nat)}]
+
+  val nat_ops = simple_nat_ops @ mult_nat_ops
+
+  val nat_consts = nat_ops @ [@{const numeral (nat)},
+    @{const zero_class.zero (nat)}, @{const one_class.one (nat)}]
+
+  val nat_int_coercions = [@{const of_nat (int)}, @{const nat}]
+
+  val builtin_nat_ops = nat_int_coercions @ simple_nat_ops
+
+  val is_nat_const = member (op aconv) nat_consts
+
+  fun is_nat_const' @{const of_nat (int)} = true
+    | is_nat_const' t = is_nat_const t
+
+  val expands = map mk_meta_eq @{lemma
+    "0 = nat 0"
+    "1 = nat 1"
+    "(numeral :: num => nat) = (%i. nat (numeral i))"
+    "op < = (%a b. int a < int b)"
+    "op <= = (%a b. int a <= int b)"
+    "Suc = (%a. nat (int a + 1))"
+    "op + = (%a b. nat (int a + int b))"
+    "op - = (%a b. nat (int a - int b))"
+    "op * = (%a b. nat (int a * int b))"
+    "op div = (%a b. nat (int a div int b))"
+    "op mod = (%a b. nat (int a mod int b))"
+    by (fastforce simp add: nat_mult_distrib nat_div_distrib nat_mod_distrib)+}
+
+  val ints = map mk_meta_eq @{lemma
+    "int 0 = 0"
+    "int 1 = 1"
+    "int (Suc n) = int n + 1"
+    "int (n + m) = int n + int m"
+    "int (n - m) = int (nat (int n - int m))"
+    "int (n * m) = int n * int m"
+    "int (n div m) = int n div int m"
+    "int (n mod m) = int n mod int m"
+    by (auto simp add: int_mult zdiv_int zmod_int)}
+
+  val int_if = mk_meta_eq @{lemma
+    "int (if P then n else m) = (if P then int n else int m)"
+    by simp}
+
+  fun mk_number_eq ctxt i lhs =
+    let
+      val eq = SMT_Utils.mk_cequals lhs (Numeral.mk_cnumber @{ctyp int} i)
+      val tac =
+        Simplifier.simp_tac (put_simpset HOL_ss ctxt addsimps [@{thm Int.int_numeral}]) 1
+    in Goal.norm_result ctxt (Goal.prove_internal ctxt [] eq (K tac)) end
+
+  fun ite_conv cv1 cv2 =
+    Conv.combination_conv (Conv.combination_conv (Conv.arg_conv cv1) cv2) cv2
+
+  fun int_conv ctxt ct =
+    (case Thm.term_of ct of
+      @{const of_nat (int)} $ (n as (@{const numeral (nat)} $ _)) =>
+        Conv.rewr_conv (mk_number_eq ctxt (snd (HOLogic.dest_number n)) ct)
+    | @{const of_nat (int)} $ _ =>
+        (Conv.rewrs_conv ints then_conv Conv.sub_conv ints_conv ctxt) else_conv
+        (Conv.rewr_conv int_if then_conv
+          ite_conv (nat_conv ctxt) (int_conv ctxt)) else_conv
+        Conv.sub_conv (Conv.top_sweep_conv nat_conv) ctxt
+    | _ => Conv.no_conv) ct
+
+  and ints_conv ctxt = Conv.top_sweep_conv int_conv ctxt
+
+  and expand_conv ctxt =
+    SMT_Utils.if_conv (is_nat_const o Term.head_of)
+      (expand_head_conv (Conv.rewrs_conv expands) then_conv ints_conv ctxt)
+      (int_conv ctxt)
+
+  and nat_conv ctxt = SMT_Utils.if_exists_conv is_nat_const'
+    (Conv.top_sweep_conv expand_conv ctxt)
+
+  val uses_nat_int = Term.exists_subterm (member (op aconv) nat_int_coercions)
+in
+
+val nat_as_int_conv = nat_conv
+
+fun add_nat_embedding thms =
+  if exists (uses_nat_int o Thm.prop_of) thms then (thms, nat_embedding)
+  else (thms, [])
+
+val setup_nat_as_int =
+  SMT_Builtin.add_builtin_typ_ext (@{typ nat}, K true) #>
+  fold (SMT_Builtin.add_builtin_fun_ext' o Term.dest_Const) builtin_nat_ops
+
+end
+
+
+(** normalize numerals **)
+
+local
+  (*
+    rewrite Numeral1 into 1
+    rewrite - 0 into 0
+  *)
+
+  fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) =
+        true
+    | is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) =
+        true
+    | is_irregular_number _ =
+        false;
+
+  fun is_strange_number ctxt t = is_irregular_number t andalso SMT_Builtin.is_builtin_num ctxt t;
+
+  val proper_num_ss =
+    simpset_of (put_simpset HOL_ss @{context}
+      addsimps @{thms Num.numeral_One minus_zero})
+
+  fun norm_num_conv ctxt =
+    SMT_Utils.if_conv (is_strange_number ctxt)
+      (Simplifier.rewrite (put_simpset proper_num_ss ctxt)) Conv.no_conv
+in
+
+fun normalize_numerals_conv ctxt =
+  SMT_Utils.if_exists_conv (is_strange_number ctxt)
+    (Conv.top_sweep_conv norm_num_conv ctxt)
+
+end
+
+
+(** combined unfoldings and rewritings **)
+
+fun unfold_conv ctxt =
+  rewrite_case_bool_conv ctxt then_conv
+  unfold_abs_min_max_conv ctxt then_conv
+  nat_as_int_conv ctxt then_conv
+  Thm.beta_conversion true
+
+fun unfold1 ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt)))
+
+fun burrow_ids f ithms =
+  let
+    val (is, thms) = split_list ithms
+    val (thms', extra_thms) = f thms
+  in (is ~~ thms') @ map (pair ~1) extra_thms end
+
+fun unfold2 ctxt ithms =
+  ithms
+  |> map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt)))
+  |> burrow_ids add_nat_embedding
+
+
+
+(* overall normalization *)
+
+type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+
+structure Extra_Norms = Generic_Data
+(
+  type T = extra_norm SMT_Utils.dict
+  val empty = []
+  val extend = I
+  fun merge data = SMT_Utils.dict_merge fst data
+)
+
+fun add_extra_norm (cs, norm) =
+  Extra_Norms.map (SMT_Utils.dict_update (cs, norm))
+
+fun apply_extra_norms ctxt ithms =
+  let
+    val cs = SMT_Config.solver_class_of ctxt
+    val es = SMT_Utils.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs
+  in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end
+
+local
+  val ignored = member (op =) [@{const_name All}, @{const_name Ex},
+    @{const_name Let}, @{const_name If}, @{const_name HOL.eq}]
+
+  val schematic_consts_of =
+    let
+      fun collect (@{const SMT.trigger} $ p $ t) =
+            collect_trigger p #> collect t
+        | collect (t $ u) = collect t #> collect u
+        | collect (Abs (_, _, t)) = collect t
+        | collect (t as Const (n, _)) = 
+            if not (ignored n) then Monomorph.add_schematic_consts_of t else I
+        | collect _ = I
+      and collect_trigger t =
+        let val dest = these o try HOLogic.dest_list 
+        in fold (fold collect_pat o dest) (dest t) end
+      and collect_pat (Const (@{const_name SMT.pat}, _) $ t) = collect t
+        | collect_pat (Const (@{const_name SMT.nopat}, _) $ t) = collect t
+        | collect_pat _ = I
+    in (fn t => collect t Symtab.empty) end
+in
+
+fun monomorph ctxt xthms =
+  let val (xs, thms) = split_list xthms
+  in
+    map (pair 1) thms
+    |> Monomorph.monomorph schematic_consts_of ctxt
+    |> maps (uncurry (map o pair)) o map2 pair xs o map (map snd)
+  end
+
+end
+
+fun normalize iwthms ctxt =
+  iwthms
+  |> gen_normalize ctxt
+  |> unfold1 ctxt
+  |> monomorph ctxt
+  |> unfold2 ctxt
+  |> apply_extra_norms ctxt
+  |> rpair ctxt
+
+val setup = Context.theory_map (
+  setup_atomize #>
+  setup_unfolded_quants #>
+  setup_trigger #>
+  setup_weight #>
+  setup_case_bool #>
+  setup_abs_min_max #>
+  setup_nat_as_int)
+
+end