(*  Title:      HOL/Tools/SMT/smt_normalize.ML

    Author:     Sascha Boehme, TU Muenchen

Normalization steps on theorems required by SMT solvers:

  * simplify trivial distincts (those with less than three elements),

  * rewrite bool case expressions as if expressions,

  * normalize numerals (e.g. replace negative numerals by negated positive

    numerals),

  * embed natural numbers into integers,

  * add extra rules specifying types and constants which occur frequently,

  * fully translate into object logic, add universal closure,

  * monomorphize (create instances of schematic rules),

  * lift lambda terms,

  * make applications explicit for functions with varying number of arguments.

  * add (hypothetical definitions for) missing datatype selectors,

*)

signature SMT_NORMALIZE =

sig

  type extra_norm = bool -> (int * thm) list -> Proof.context ->

    (int * thm) list * Proof.context

  val normalize: extra_norm -> bool -> (int * thm) list -> Proof.context ->

    (int * thm) list * Proof.context

  val atomize_conv: Proof.context -> conv

  val eta_expand_conv: (Proof.context -> conv) -> Proof.context -> conv

  val setup: theory -> theory

end

structure SMT_Normalize: SMT_NORMALIZE =

struct

structure U = SMT_Utils

structure B = SMT_Builtin

infix 2 ??

fun (test ?? f) x = if test x then f x else x

(* instantiate elimination rules *)

local

  val (cpfalse, cfalse) = `U.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

(* simplification of trivial distincts (distinct should have at least

   three elements in the argument list) *)

local

  fun is_trivial_distinct (Const (@{const_name distinct}, _) $ t) =

        (case try HOLogic.dest_list t of

          SOME [] => true

        | SOME [_] => true

        | _ => false)

    | is_trivial_distinct _ = false

  val thms = map mk_meta_eq @{lemma

    "distinct [] = True"

    "distinct [x] = True"

    "distinct [x, y] = (x ~= y)"

    by simp_all}

  fun distinct_conv _ =

    U.if_true_conv is_trivial_distinct (Conv.rewrs_conv thms)

in

fun trivial_distinct ctxt =

  map (apsnd ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??

    Conv.fconv_rule (Conv.top_conv distinct_conv ctxt)))

end

(* rewrite bool case expressions as if expressions *)

local

  val is_bool_case = (fn

      Const (@{const_name "bool.bool_case"}, _) $ _ $ _ $ _ => true

    | _ => false)

  val thm = mk_meta_eq @{lemma

    "(case P of True => x | False => y) = (if P then x else y)" by simp}

  val unfold_conv = U.if_true_conv is_bool_case (Conv.rewr_conv thm)

in

fun rewrite_bool_cases ctxt =

  map (apsnd ((Term.exists_subterm is_bool_case o Thm.prop_of) ??

    Conv.fconv_rule (Conv.top_conv (K unfold_conv) ctxt)))

val setup_bool_case = B.add_builtin_fun_ext'' @{const_name "bool.bool_case"}

end

(* normalization of numerals: rewriting of negative integer numerals into

   positive numerals, Numeral0 into 0, Numeral1 into 1 *)

local

  fun is_number_sort ctxt T =

    Sign.of_sort (ProofContext.theory_of ctxt) (T, @{sort number_ring})

  fun is_strange_number ctxt (t as Const (@{const_name number_of}, _) $ _) =

        (case try HOLogic.dest_number t of

          SOME (T, i) => is_number_sort ctxt T andalso i < 2

        | NONE => false)

    | is_strange_number _ _ = false

  val pos_numeral_ss = HOL_ss

    addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}]

    addsimps [@{thm Int.number_of_Pls}, @{thm Int.numeral_1_eq_1}]

    addsimps @{thms Int.pred_bin_simps}

    addsimps @{thms Int.normalize_bin_simps}

    addsimps @{lemma

      "Int.Min = - Int.Bit1 Int.Pls"

      "Int.Bit0 (- Int.Pls) = - Int.Pls"

      "Int.Bit0 (- k) = - Int.Bit0 k"

      "Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)"

      by simp_all (simp add: pred_def)}

  fun pos_conv ctxt = U.if_conv (is_strange_number ctxt)

    (Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss))

    Conv.no_conv

in

fun normalize_numerals ctxt =

  map (apsnd ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??

    Conv.fconv_rule (Conv.top_sweep_conv pos_conv ctxt)))

end

(* embedding of standard natural number operations into integer operations *)

local

  val nat_embedding = map (pair ~1) @{lemma

    "nat (int n) = n"

    "i >= 0 --> int (nat i) = i"

    "i < 0 --> int (nat i) = 0"

    by simp_all}

  val nat_rewriting = @{lemma

    "0 = nat 0"

    "1 = nat 1"

    "(number_of :: int => nat) = (%i. nat (number_of i))"

    "int (nat 0) = 0"

    "int (nat 1) = 1"

    "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))"

    "min = (%a b. nat (min (int a) (int b)))"

    "max = (%a b. nat (max (int a) (int b)))"

    "int (nat (int a + int b)) = int a + int b"

    "int (nat (int a + 1)) = int a + 1"  (* special rule due to Suc above *)

    "int (nat (int a * int b)) = int a * int b"

    "int (nat (int a div int b)) = int a div int b"

    "int (nat (int a mod int b)) = int a mod int b"

    "int (nat (min (int a) (int b))) = min (int a) (int b)"

    "int (nat (max (int a) (int b))) = max (int a) (int b)"

    by (auto intro!: ext simp add: nat_mult_distrib nat_div_distrib

      nat_mod_distrib int_mult[symmetric] zdiv_int[symmetric]

      zmod_int[symmetric])}

  fun on_positive num f x = 

    (case try HOLogic.dest_number (Thm.term_of num) of

      SOME (_, i) => if i >= 0 then SOME (f x) else NONE

    | NONE => NONE)

  val cancel_int_nat_ss = HOL_ss

    addsimps [@{thm Nat_Numeral.nat_number_of}]

    addsimps [@{thm Nat_Numeral.int_nat_number_of}]

    addsimps @{thms neg_simps}

  val int_eq = Thm.cterm_of @{theory} @{const "==" (int)}

  fun cancel_int_nat_simproc _ ss ct = 

    let

      val num = Thm.dest_arg (Thm.dest_arg ct)

      val goal = Thm.mk_binop int_eq ct num

      val simpset = Simplifier.inherit_context ss cancel_int_nat_ss

      fun tac _ = Simplifier.simp_tac simpset 1

    in on_positive num (Goal.prove_internal [] goal) tac end

  val nat_ss = HOL_ss

    addsimps nat_rewriting

    addsimprocs [

      Simplifier.make_simproc {

        name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}],

        proc = cancel_int_nat_simproc, identifier = [] }]

  fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss)

  val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat}))

  val uses_nat_int = Term.exists_subterm (member (op aconv)

    [@{const of_nat (int)}, @{const nat}])

  val nat_ops = [

    @{const less (nat)}, @{const less_eq (nat)},

    @{const Suc}, @{const plus (nat)}, @{const minus (nat)},

    @{const times (nat)}, @{const div (nat)}, @{const mod (nat)}]

  val nat_ops' = @{const of_nat (int)} :: @{const nat} :: nat_ops

in

fun nat_as_int ctxt =

  map (apsnd ((uses_nat_type o Thm.prop_of) ?? Conv.fconv_rule (conv ctxt))) #>

  exists (uses_nat_int o Thm.prop_of o snd) ?? append nat_embedding

val setup_nat_as_int =

  B.add_builtin_typ_ext (@{typ nat}, K true) #>

  fold (B.add_builtin_fun_ext' o Term.dest_Const) nat_ops'

end

(* further normalizations: beta/eta, universal closure, atomize *)

val eta_expand_eq = @{lemma "f == (%x. f x)" by (rule reflexive)}

fun eta_expand_conv cv ctxt =

  Conv.rewr_conv eta_expand_eq then_conv Conv.abs_conv (cv o snd) ctxt

local

  val eta_conv = eta_expand_conv

  fun args_conv cv ct =

    (case Thm.term_of ct of

      _ $ _ => Conv.combination_conv (args_conv cv) cv

    | _ => Conv.all_conv) ct

  fun eta_args_conv cv 0 = args_conv o cv

    | eta_args_conv cv i = eta_conv (eta_args_conv cv (i-1))

  fun keep_conv ctxt = Conv.binder_conv (norm_conv o snd) ctxt

  and eta_binder_conv ctxt = Conv.arg_conv (eta_conv norm_conv ctxt)

  and keep_let_conv ctxt = Conv.combination_conv

    (Conv.arg_conv (norm_conv ctxt)) (Conv.abs_conv (norm_conv o snd) ctxt)

  and unfold_let_conv ctxt = Conv.combination_conv

    (Conv.arg_conv (norm_conv ctxt)) (eta_conv norm_conv ctxt)

  and unfold_conv thm ctxt = Conv.rewr_conv thm then_conv keep_conv ctxt

  and unfold_ex1_conv ctxt = unfold_conv @{thm Ex1_def} ctxt

  and unfold_ball_conv ctxt = unfold_conv (mk_meta_eq @{thm Ball_def}) ctxt

  and unfold_bex_conv ctxt = unfold_conv (mk_meta_eq @{thm Bex_def}) ctxt

  and norm_conv ctxt ct =

    (case Thm.term_of ct of

      Const (@{const_name All}, _) $ Abs _ => keep_conv

    | Const (@{const_name All}, _) $ _ => eta_binder_conv

    | Const (@{const_name All}, _) => eta_conv eta_binder_conv

    | Const (@{const_name Ex}, _) $ Abs _ => keep_conv

    | Const (@{const_name Ex}, _) $ _ => eta_binder_conv

    | Const (@{const_name Ex}, _) => eta_conv eta_binder_conv

    | Const (@{const_name Let}, _) $ _ $ Abs _ => keep_let_conv

    | Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv

    | Const (@{const_name Let}, _) $ _ => eta_conv unfold_let_conv

    | Const (@{const_name Let}, _) => eta_conv (eta_conv unfold_let_conv)

    | Const (@{const_name Ex1}, _) $ _ => unfold_ex1_conv

    | Const (@{const_name Ex1}, _) => eta_conv unfold_ex1_conv 

    | Const (@{const_name Ball}, _) $ _ $ _ => unfold_ball_conv

    | Const (@{const_name Ball}, _) $ _ => eta_conv unfold_ball_conv

    | Const (@{const_name Ball}, _) => eta_conv (eta_conv unfold_ball_conv)

    | Const (@{const_name Bex}, _) $ _ $ _ => unfold_bex_conv

    | Const (@{const_name Bex}, _) $ _ => eta_conv unfold_bex_conv

    | Const (@{const_name Bex}, _) => eta_conv (eta_conv unfold_bex_conv)

    | Abs _ => Conv.abs_conv (norm_conv o snd)

    | _ =>

        (case Term.strip_comb (Thm.term_of ct) of

          (Const (c as (_, T)), ts) =>

            if SMT_Builtin.is_builtin_fun ctxt c ts

            then eta_args_conv norm_conv

              (length (Term.binder_types T) - length ts)

            else args_conv o norm_conv

        | _ => args_conv o norm_conv)) ctxt ct

  fun is_normed ctxt t =

    (case t of

      Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed ctxt u

    | Const (@{const_name All}, _) $ _ => false

    | Const (@{const_name All}, _) => false

    | Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed ctxt u

    | Const (@{const_name Ex}, _) $ _ => false

    | Const (@{const_name Ex}, _) => false

    | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>

        is_normed ctxt u1 andalso is_normed ctxt u2

    | Const (@{const_name Let}, _) $ _ $ _ => false

    | Const (@{const_name Let}, _) $ _ => false

    | Const (@{const_name Let}, _) => false

    | Const (@{const_name Ex1}, _) $ _ => false

    | Const (@{const_name Ex1}, _) => false

    | Const (@{const_name Ball}, _) $ _ $ _ => false

    | Const (@{const_name Ball}, _) $ _ => false

    | Const (@{const_name Ball}, _) => false

    | Const (@{const_name Bex}, _) $ _ $ _ => false

    | Const (@{const_name Bex}, _) $ _ => false

    | Const (@{const_name Bex}, _) => false

    | Abs (_, _, u) => is_normed ctxt u

    | _ =>

        (case Term.strip_comb t of

          (Const (c as (_, T)), ts) =>

            if SMT_Builtin.is_builtin_fun ctxt c ts

            then length (Term.binder_types T) = length ts andalso

              forall (is_normed ctxt) ts

            else forall (is_normed ctxt) ts

        | (_, ts) => forall (is_normed ctxt) ts))

in

fun norm_binder_conv ctxt =

  U.if_conv (is_normed ctxt) Conv.all_conv (norm_conv ctxt)

val setup_unfolded_quants =

  fold B.add_builtin_fun_ext'' [@{const_name Ball}, @{const_name Bex},

    @{const_name Ex1}]

end

fun norm_def ctxt thm =

  (case Thm.prop_of thm of

    @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>

      norm_def ctxt (thm RS @{thm fun_cong})

  | Const (@{const_name "=="}, _) $ _ $ Abs _ =>

      norm_def ctxt (thm RS @{thm meta_eq_to_obj_eq})

  | _ => thm)

fun atomize_conv ctxt ct =

  (case Thm.term_of ct of

    @{const "==>"} $ _ $ _ =>

      Conv.binop_conv (atomize_conv ctxt) then_conv

      Conv.rewr_conv @{thm atomize_imp}

  | Const (@{const_name "=="}, _) $ _ $ _ =>

      Conv.binop_conv (atomize_conv ctxt) then_conv

      Conv.rewr_conv @{thm atomize_eq}

  | Const (@{const_name 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 B.add_builtin_fun_ext'' [@{const_name "==>"}, @{const_name "=="},

    @{const_name all}, @{const_name Trueprop}]

fun normalize_rule ctxt =

  Conv.fconv_rule (

    (* reduce lambda abstractions, except at known binders: *)

    Thm.beta_conversion true then_conv

    Thm.eta_conversion then_conv

    norm_binder_conv ctxt) #>

  norm_def ctxt #>

  Drule.forall_intr_vars #>

  Conv.fconv_rule (atomize_conv ctxt)

(* lift lambda terms into additional rules *)

local

  fun used_vars cvs ct =

    let

      val lookup = AList.lookup (op aconv) (map (` Thm.term_of) cvs)

      val add = (fn SOME ct => insert (op aconvc) ct | _ => I)

    in Term.fold_aterms (add o lookup) (Thm.term_of ct) [] end

  fun apply cv thm = 

    let val thm' = Thm.combination thm (Thm.reflexive cv)

    in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end

  fun apply_def cvs eq = Thm.symmetric (fold apply cvs eq)

  fun replace_lambda cvs ct (cx as (ctxt, defs)) =

    let

      val cvs' = used_vars cvs ct

      val ct' = fold_rev Thm.cabs cvs' ct

    in

      (case Termtab.lookup defs (Thm.term_of ct') of

        SOME eq => (apply_def cvs' eq, cx)

      | NONE =>

          let

            val {T, ...} = Thm.rep_cterm ct' and n = Name.uu

            val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt

            val cu = U.mk_cequals (U.certify ctxt (Free (n', T))) ct'

            val (eq, ctxt'') = yield_singleton Assumption.add_assumes cu ctxt'

            val defs' = Termtab.update (Thm.term_of ct', eq) defs

          in (apply_def cvs' eq, (ctxt'', defs')) end)

    end

  fun none ct cx = (Thm.reflexive ct, cx)

  fun in_comb f g ct cx =

    let val (cu1, cu2) = Thm.dest_comb ct

    in cx |> f cu1 ||>> g cu2 |>> uncurry Thm.combination end

  fun in_arg f = in_comb none f

  fun in_abs f cvs ct (ctxt, defs) =

    let

      val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt

      val (cv, cu) = Thm.dest_abs (SOME n) ct

    in  (ctxt', defs) |> f (cv :: cvs) cu |>> Thm.abstract_rule n cv end

  fun traverse cvs ct =

    (case Thm.term_of ct of

      Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs traverse cvs)

    | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs traverse cvs)

    | Const (@{const_name Let}, _) $ _ $ Abs _ =>

        in_comb (in_arg (traverse cvs)) (in_abs traverse cvs)

    | Abs _ => at_lambda cvs

    | _ $ _ => in_comb (traverse cvs) (traverse cvs)

    | _ => none) ct

  and at_lambda cvs ct =

    in_abs traverse cvs ct #-> (fn thm =>

    replace_lambda cvs (Thm.rhs_of thm) #>> Thm.transitive thm)

  fun has_free_lambdas t =

    (case t of

      Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u

    | Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u

    | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>

        has_free_lambdas u1 orelse has_free_lambdas u2

    | Abs _ => true

    | u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2

    | _ => false)

  fun lift_lm f thm cx =

    if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx)

    else cx |> f (Thm.cprop_of thm) |>> (fn thm' => Thm.equal_elim thm' thm)

in

fun lift_lambdas irules ctxt =

  let

    val cx = (ctxt, Termtab.empty)

    val (idxs, thms) = split_list irules

    val (thms', (ctxt', defs)) = fold_map (lift_lm (traverse [])) thms cx

    val eqs = Termtab.fold (cons o normalize_rule ctxt' o snd) defs []

  in (map (pair ~1) eqs @ (idxs ~~ thms'), ctxt') end

end

(* make application explicit for functions with varying number of arguments *)

local

  val const = prefix "c" and free = prefix "f"

  fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e

  fun add t i = Symtab.map_default (t, (false, i)) (min i)

  fun traverse t =

    (case Term.strip_comb t of

      (Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts 

    | (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts

    | (Abs (_, _, u), ts) => fold traverse (u :: ts)

    | (_, ts) => fold traverse ts)

  fun prune tab = Symtab.fold (fn (n, (true, i)) =>

    Symtab.update (n, i) | _ => I) tab Symtab.empty

  fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2

  fun nary_conv conv1 conv2 ct =

    (Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct

  fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) =>

    let val n = fst (Term.dest_Free (Thm.term_of cv))

    in conv (Symtab.update (free n, 0) tb) cx end)

  val fun_app_rule = @{lemma "f x == fun_app f x" by (simp add: fun_app_def)}

in

fun explicit_application ctxt irules =

  let

    fun sub_conv tb ctxt ct =

      (case Term.strip_comb (Thm.term_of ct) of

        (Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt

      | (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt

      | (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt)

      | (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct

    and app_conv tb n i ctxt =

      (case Symtab.lookup tb n of

        NONE => nary_conv Conv.all_conv (sub_conv tb ctxt)

      | SOME j => fun_app_conv tb ctxt (i - j))

    and fun_app_conv tb ctxt i ct = (

      if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt)

      else

        Conv.rewr_conv fun_app_rule then_conv

        binop_conv (fun_app_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct

    fun needs_exp_app tab = Term.exists_subterm (fn

        Bound _ $ _ => true

      | Const (n, _) => Symtab.defined tab (const n)

      | Free (n, _) => Symtab.defined tab (free n)

      | _ => false)

    fun rewrite tab ctxt thm =

      if not (needs_exp_app tab (Thm.prop_of thm)) then thm

      else Conv.fconv_rule (sub_conv tab ctxt) thm

    val tab = prune (fold (traverse o Thm.prop_of o snd) irules Symtab.empty)

  in map (apsnd (rewrite tab ctxt)) irules end

end

(* add missing datatype selectors via hypothetical definitions *)

local

  val add = (fn Type (n, _) => Symtab.update (n, ()) | _ => I)

  fun collect t =

    (case Term.strip_comb t of

      (Abs (_, T, t), _) => add T #> collect t

    | (Const (_, T), ts) => collects T ts

    | (Free (_, T), ts) => collects T ts

    | _ => I)

  and collects T ts =

    let val ((Ts, Us), U) = Term.strip_type T |> apfst (chop (length ts))

    in fold add Ts #> add (Us ---> U) #> fold collect ts end

  fun add_constructors thy n =

    (case Datatype.get_info thy n of

      NONE => I

    | SOME {descr, ...} => fold (fn (_, (_, _, cs)) => fold (fn (n, ds) =>

        fold (insert (op =) o pair n) (1 upto length ds)) cs) descr)

  fun add_selector (c as (n, i)) ctxt =

    (case Datatype_Selectors.lookup_selector ctxt c of

      SOME _ => ctxt

    | NONE =>

        let

          val T = Sign.the_const_type (ProofContext.theory_of ctxt) n

          val U = Term.body_type T --> nth (Term.binder_types T) (i-1)

        in

          ctxt

          |> yield_singleton Variable.variant_fixes Name.uu

          |>> pair ((n, T), i) o rpair U

          |-> Context.proof_map o Datatype_Selectors.add_selector

        end)

in

fun datatype_selectors irules ctxt =

  let

    val ns = Symtab.keys (fold (collect o Thm.prop_of o snd) irules Symtab.empty)

    val cs = fold (add_constructors (ProofContext.theory_of ctxt)) ns []

  in (irules, fold add_selector cs ctxt) end

    (* FIXME: also generate hypothetical definitions for the selectors *)

end

(* combined normalization *)

type extra_norm = bool -> (int * thm) list -> Proof.context ->

  (int * thm) list * Proof.context

fun with_context f irules ctxt = (f ctxt irules, ctxt)

fun normalize extra_norm with_datatypes irules ctxt =

  let

    fun norm f ctxt' (i, thm) =

      if Config.get ctxt' SMT_Config.drop_bad_facts then

        (case try (f ctxt') thm of

          SOME thm' => SOME (i, thm')

        | NONE => (SMT_Config.verbose_msg ctxt' (prefix ("Warning: " ^

            "dropping assumption: ") o Display.string_of_thm ctxt') thm; NONE))

      else SOME (i, f ctxt' thm)

  in

    irules

    |> map (apsnd instantiate_elim)

    |> trivial_distinct ctxt

    |> rewrite_bool_cases ctxt

    |> normalize_numerals ctxt

    |> nat_as_int ctxt

    |> rpair ctxt

    |-> extra_norm with_datatypes

    |-> with_context (map_filter o norm normalize_rule)

    |-> SMT_Monomorph.monomorph

    |-> lift_lambdas

    |-> with_context explicit_application

    |-> (if with_datatypes then datatype_selectors else pair)

  end

(* setup *)

val setup =

  setup_bool_case #>

  setup_nat_as_int #>

  setup_unfolded_quants #>

  setup_atomize

end