src/HOL/Tools/SMT/smt_normalize.ML
author boehmes
Wed Nov 24 10:39:58 2010 +0100 (2010-11-24)
changeset 40681 872b08416fb4
parent 40663 e080c9e68752
child 40685 dcb27631cb45
permissions -rw-r--r--
be more precise: only treat constant 'distinct' applied to an explicit list as built-in
boehmes@36898
     1
(*  Title:      HOL/Tools/SMT/smt_normalize.ML
boehmes@36898
     2
    Author:     Sascha Boehme, TU Muenchen
boehmes@36898
     3
boehmes@36898
     4
Normalization steps on theorems required by SMT solvers:
boehmes@36898
     5
  * simplify trivial distincts (those with less than three elements),
boehmes@36898
     6
  * rewrite bool case expressions as if expressions,
boehmes@36898
     7
  * normalize numerals (e.g. replace negative numerals by negated positive
boehmes@36898
     8
    numerals),
boehmes@36898
     9
  * embed natural numbers into integers,
boehmes@36898
    10
  * add extra rules specifying types and constants which occur frequently,
boehmes@36898
    11
  * fully translate into object logic, add universal closure,
boehmes@39483
    12
  * monomorphize (create instances of schematic rules),
boehmes@36898
    13
  * lift lambda terms,
boehmes@36898
    14
  * make applications explicit for functions with varying number of arguments.
boehmes@39483
    15
  * add (hypothetical definitions for) missing datatype selectors,
boehmes@36898
    16
*)
boehmes@36898
    17
boehmes@36898
    18
signature SMT_NORMALIZE =
boehmes@36898
    19
sig
boehmes@40162
    20
  type extra_norm = bool -> (int * thm) list -> Proof.context ->
boehmes@40161
    21
    (int * thm) list * Proof.context
boehmes@40424
    22
  val normalize: extra_norm -> bool -> (int * thm) list -> Proof.context ->
boehmes@40161
    23
    (int * thm) list * Proof.context
boehmes@36899
    24
  val atomize_conv: Proof.context -> conv
boehmes@36898
    25
  val eta_expand_conv: (Proof.context -> conv) -> Proof.context -> conv
boehmes@36898
    26
end
boehmes@36898
    27
boehmes@36898
    28
structure SMT_Normalize: SMT_NORMALIZE =
boehmes@36898
    29
struct
boehmes@36898
    30
boehmes@40663
    31
structure U = SMT_Utils
boehmes@40663
    32
boehmes@36898
    33
infix 2 ??
boehmes@36898
    34
fun (test ?? f) x = if test x then f x else x
boehmes@36898
    35
boehmes@36898
    36
boehmes@36898
    37
boehmes@36898
    38
(* simplification of trivial distincts (distinct should have at least
boehmes@36898
    39
   three elements in the argument list) *)
boehmes@36898
    40
boehmes@36898
    41
local
boehmes@40681
    42
  fun is_trivial_distinct (Const (@{const_name distinct}, _) $ t) =
boehmes@40681
    43
        (case try HOLogic.dest_list t of
boehmes@40681
    44
          SOME [] => true
boehmes@40681
    45
        | SOME [_] => true
boehmes@40681
    46
        | _ => false)
boehmes@36898
    47
    | is_trivial_distinct _ = false
boehmes@36898
    48
boehmes@37786
    49
  val thms = map mk_meta_eq @{lemma
boehmes@40681
    50
    "distinct [] = True"
boehmes@40681
    51
    "distinct [x] = True"
boehmes@40681
    52
    "distinct [x, y] = (x ~= y)"
boehmes@40681
    53
    by simp_all}
boehmes@36898
    54
  fun distinct_conv _ =
boehmes@40663
    55
    U.if_true_conv is_trivial_distinct (Conv.rewrs_conv thms)
boehmes@36898
    56
in
boehmes@36898
    57
fun trivial_distinct ctxt =
boehmes@40161
    58
  map (apsnd ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??
boehmes@40161
    59
    Conv.fconv_rule (Conv.top_conv distinct_conv ctxt)))
boehmes@36898
    60
end
boehmes@36898
    61
boehmes@36898
    62
boehmes@36898
    63
boehmes@36898
    64
(* rewrite bool case expressions as if expressions *)
boehmes@36898
    65
boehmes@36898
    66
local
boehmes@36898
    67
  val is_bool_case = (fn
boehmes@36898
    68
      Const (@{const_name "bool.bool_case"}, _) $ _ $ _ $ _ => true
boehmes@36898
    69
    | _ => false)
boehmes@36898
    70
boehmes@40275
    71
  val thm = mk_meta_eq @{lemma
boehmes@40275
    72
    "(case P of True => x | False => y) = (if P then x else y)" by simp}
boehmes@40663
    73
  val unfold_conv = U.if_true_conv is_bool_case (Conv.rewr_conv thm)
boehmes@36898
    74
in
boehmes@36898
    75
fun rewrite_bool_cases ctxt =
boehmes@40161
    76
  map (apsnd ((Term.exists_subterm is_bool_case o Thm.prop_of) ??
boehmes@40161
    77
    Conv.fconv_rule (Conv.top_conv (K unfold_conv) ctxt)))
boehmes@36898
    78
end
boehmes@36898
    79
boehmes@36898
    80
boehmes@36898
    81
boehmes@36898
    82
(* normalization of numerals: rewriting of negative integer numerals into
boehmes@36898
    83
   positive numerals, Numeral0 into 0, Numeral1 into 1 *)
boehmes@36898
    84
boehmes@36898
    85
local
boehmes@36898
    86
  fun is_number_sort ctxt T =
boehmes@36898
    87
    Sign.of_sort (ProofContext.theory_of ctxt) (T, @{sort number_ring})
boehmes@36898
    88
boehmes@36898
    89
  fun is_strange_number ctxt (t as Const (@{const_name number_of}, _) $ _) =
boehmes@36898
    90
        (case try HOLogic.dest_number t of
boehmes@36898
    91
          SOME (T, i) => is_number_sort ctxt T andalso i < 2
boehmes@36898
    92
        | NONE => false)
boehmes@36898
    93
    | is_strange_number _ _ = false
boehmes@36898
    94
boehmes@36898
    95
  val pos_numeral_ss = HOL_ss
boehmes@36898
    96
    addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}]
boehmes@36898
    97
    addsimps [@{thm Int.number_of_Pls}, @{thm Int.numeral_1_eq_1}]
boehmes@36898
    98
    addsimps @{thms Int.pred_bin_simps}
boehmes@36898
    99
    addsimps @{thms Int.normalize_bin_simps}
boehmes@36898
   100
    addsimps @{lemma
boehmes@36898
   101
      "Int.Min = - Int.Bit1 Int.Pls"
boehmes@36898
   102
      "Int.Bit0 (- Int.Pls) = - Int.Pls"
boehmes@36898
   103
      "Int.Bit0 (- k) = - Int.Bit0 k"
boehmes@36898
   104
      "Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)"
boehmes@36898
   105
      by simp_all (simp add: pred_def)}
boehmes@36898
   106
boehmes@40663
   107
  fun pos_conv ctxt = U.if_conv (is_strange_number ctxt)
boehmes@36898
   108
    (Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss))
boehmes@36898
   109
    Conv.no_conv
boehmes@36898
   110
in
boehmes@36898
   111
fun normalize_numerals ctxt =
boehmes@40161
   112
  map (apsnd ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??
boehmes@40161
   113
    Conv.fconv_rule (Conv.top_sweep_conv pos_conv ctxt)))
boehmes@36898
   114
end
boehmes@36898
   115
boehmes@36898
   116
boehmes@36898
   117
boehmes@36898
   118
(* embedding of standard natural number operations into integer operations *)
boehmes@36898
   119
boehmes@36898
   120
local
boehmes@40161
   121
  val nat_embedding = map (pair ~1) @{lemma
boehmes@36898
   122
    "nat (int n) = n"
boehmes@36898
   123
    "i >= 0 --> int (nat i) = i"
boehmes@36898
   124
    "i < 0 --> int (nat i) = 0"
boehmes@36898
   125
    by simp_all}
boehmes@36898
   126
boehmes@36898
   127
  val nat_rewriting = @{lemma
boehmes@36898
   128
    "0 = nat 0"
boehmes@36898
   129
    "1 = nat 1"
boehmes@40279
   130
    "(number_of :: int => nat) = (%i. nat (number_of i))"
boehmes@36898
   131
    "int (nat 0) = 0"
boehmes@36898
   132
    "int (nat 1) = 1"
boehmes@40279
   133
    "op < = (%a b. int a < int b)"
boehmes@40279
   134
    "op <= = (%a b. int a <= int b)"
boehmes@40279
   135
    "Suc = (%a. nat (int a + 1))"
boehmes@40279
   136
    "op + = (%a b. nat (int a + int b))"
boehmes@40279
   137
    "op - = (%a b. nat (int a - int b))"
boehmes@40279
   138
    "op * = (%a b. nat (int a * int b))"
boehmes@40279
   139
    "op div = (%a b. nat (int a div int b))"
boehmes@40279
   140
    "op mod = (%a b. nat (int a mod int b))"
boehmes@40279
   141
    "min = (%a b. nat (min (int a) (int b)))"
boehmes@40279
   142
    "max = (%a b. nat (max (int a) (int b)))"
boehmes@36898
   143
    "int (nat (int a + int b)) = int a + int b"
boehmes@40279
   144
    "int (nat (int a + 1)) = int a + 1"  (* special rule due to Suc above *)
boehmes@36898
   145
    "int (nat (int a * int b)) = int a * int b"
boehmes@36898
   146
    "int (nat (int a div int b)) = int a div int b"
boehmes@36898
   147
    "int (nat (int a mod int b)) = int a mod int b"
boehmes@36898
   148
    "int (nat (min (int a) (int b))) = min (int a) (int b)"
boehmes@36898
   149
    "int (nat (max (int a) (int b))) = max (int a) (int b)"
boehmes@40279
   150
    by (auto intro!: ext simp add: nat_mult_distrib nat_div_distrib
boehmes@40279
   151
      nat_mod_distrib int_mult[symmetric] zdiv_int[symmetric]
boehmes@40279
   152
      zmod_int[symmetric])}
boehmes@36898
   153
boehmes@36898
   154
  fun on_positive num f x = 
boehmes@36898
   155
    (case try HOLogic.dest_number (Thm.term_of num) of
boehmes@36898
   156
      SOME (_, i) => if i >= 0 then SOME (f x) else NONE
boehmes@36898
   157
    | NONE => NONE)
boehmes@36898
   158
boehmes@36898
   159
  val cancel_int_nat_ss = HOL_ss
boehmes@36898
   160
    addsimps [@{thm Nat_Numeral.nat_number_of}]
boehmes@36898
   161
    addsimps [@{thm Nat_Numeral.int_nat_number_of}]
boehmes@36898
   162
    addsimps @{thms neg_simps}
boehmes@36898
   163
boehmes@40579
   164
  val int_eq = Thm.cterm_of @{theory} @{const "==" (int)}
boehmes@40579
   165
boehmes@36898
   166
  fun cancel_int_nat_simproc _ ss ct = 
boehmes@36898
   167
    let
boehmes@36898
   168
      val num = Thm.dest_arg (Thm.dest_arg ct)
boehmes@40579
   169
      val goal = Thm.mk_binop int_eq ct num
boehmes@36898
   170
      val simpset = Simplifier.inherit_context ss cancel_int_nat_ss
boehmes@36898
   171
      fun tac _ = Simplifier.simp_tac simpset 1
boehmes@36898
   172
    in on_positive num (Goal.prove_internal [] goal) tac end
boehmes@36898
   173
boehmes@36898
   174
  val nat_ss = HOL_ss
boehmes@36898
   175
    addsimps nat_rewriting
boehmes@40279
   176
    addsimprocs [
boehmes@40279
   177
      Simplifier.make_simproc {
boehmes@40279
   178
        name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}],
boehmes@40279
   179
        proc = cancel_int_nat_simproc, identifier = [] }]
boehmes@36898
   180
boehmes@36898
   181
  fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss)
boehmes@36898
   182
boehmes@36898
   183
  val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat}))
boehmes@40579
   184
  val uses_nat_int = Term.exists_subterm (member (op aconv)
boehmes@40579
   185
    [@{const of_nat (int)}, @{const nat}])
boehmes@36898
   186
in
boehmes@36898
   187
fun nat_as_int ctxt =
boehmes@40161
   188
  map (apsnd ((uses_nat_type o Thm.prop_of) ?? Conv.fconv_rule (conv ctxt))) #>
boehmes@40161
   189
  exists (uses_nat_int o Thm.prop_of o snd) ?? append nat_embedding
boehmes@36898
   190
end
boehmes@36898
   191
boehmes@36898
   192
boehmes@36898
   193
boehmes@36898
   194
(* further normalizations: beta/eta, universal closure, atomize *)
boehmes@36898
   195
boehmes@36898
   196
val eta_expand_eq = @{lemma "f == (%x. f x)" by (rule reflexive)}
boehmes@36898
   197
boehmes@36898
   198
fun eta_expand_conv cv ctxt =
boehmes@36898
   199
  Conv.rewr_conv eta_expand_eq then_conv Conv.abs_conv (cv o snd) ctxt
boehmes@36898
   200
boehmes@36898
   201
local
boehmes@36898
   202
  val eta_conv = eta_expand_conv
boehmes@36898
   203
boehmes@40279
   204
  fun args_conv cv ct =
boehmes@40279
   205
    (case Thm.term_of ct of
boehmes@40279
   206
      _ $ _ => Conv.combination_conv (args_conv cv) cv
boehmes@40279
   207
    | _ => Conv.all_conv) ct
boehmes@40279
   208
boehmes@40279
   209
  fun eta_args_conv cv 0 = args_conv o cv
boehmes@40279
   210
    | eta_args_conv cv i = eta_conv (eta_args_conv cv (i-1))
boehmes@40279
   211
wenzelm@36936
   212
  fun keep_conv ctxt = Conv.binder_conv (norm_conv o snd) ctxt
boehmes@36898
   213
  and eta_binder_conv ctxt = Conv.arg_conv (eta_conv norm_conv ctxt)
boehmes@36898
   214
  and keep_let_conv ctxt = Conv.combination_conv
boehmes@36898
   215
    (Conv.arg_conv (norm_conv ctxt)) (Conv.abs_conv (norm_conv o snd) ctxt)
boehmes@36898
   216
  and unfold_let_conv ctxt = Conv.combination_conv
boehmes@36898
   217
    (Conv.arg_conv (norm_conv ctxt)) (eta_conv norm_conv ctxt)
boehmes@36898
   218
  and unfold_conv thm ctxt = Conv.rewr_conv thm then_conv keep_conv ctxt
boehmes@36898
   219
  and unfold_ex1_conv ctxt = unfold_conv @{thm Ex1_def} ctxt
boehmes@37786
   220
  and unfold_ball_conv ctxt = unfold_conv (mk_meta_eq @{thm Ball_def}) ctxt
boehmes@37786
   221
  and unfold_bex_conv ctxt = unfold_conv (mk_meta_eq @{thm Bex_def}) ctxt
boehmes@36898
   222
  and norm_conv ctxt ct =
boehmes@36898
   223
    (case Thm.term_of ct of
boehmes@36898
   224
      Const (@{const_name All}, _) $ Abs _ => keep_conv
boehmes@36898
   225
    | Const (@{const_name All}, _) $ _ => eta_binder_conv
boehmes@36898
   226
    | Const (@{const_name All}, _) => eta_conv eta_binder_conv
boehmes@36898
   227
    | Const (@{const_name Ex}, _) $ Abs _ => keep_conv
boehmes@36898
   228
    | Const (@{const_name Ex}, _) $ _ => eta_binder_conv
boehmes@36898
   229
    | Const (@{const_name Ex}, _) => eta_conv eta_binder_conv
boehmes@36898
   230
    | Const (@{const_name Let}, _) $ _ $ Abs _ => keep_let_conv
boehmes@36898
   231
    | Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv
boehmes@36898
   232
    | Const (@{const_name Let}, _) $ _ => eta_conv unfold_let_conv
boehmes@36898
   233
    | Const (@{const_name Let}, _) => eta_conv (eta_conv unfold_let_conv)
boehmes@36898
   234
    | Const (@{const_name Ex1}, _) $ _ => unfold_ex1_conv
boehmes@36898
   235
    | Const (@{const_name Ex1}, _) => eta_conv unfold_ex1_conv 
boehmes@36898
   236
    | Const (@{const_name Ball}, _) $ _ $ _ => unfold_ball_conv
boehmes@36898
   237
    | Const (@{const_name Ball}, _) $ _ => eta_conv unfold_ball_conv
boehmes@36898
   238
    | Const (@{const_name Ball}, _) => eta_conv (eta_conv unfold_ball_conv)
boehmes@36898
   239
    | Const (@{const_name Bex}, _) $ _ $ _ => unfold_bex_conv
boehmes@36898
   240
    | Const (@{const_name Bex}, _) $ _ => eta_conv unfold_bex_conv
boehmes@36898
   241
    | Const (@{const_name Bex}, _) => eta_conv (eta_conv unfold_bex_conv)
boehmes@36898
   242
    | Abs _ => Conv.abs_conv (norm_conv o snd)
boehmes@40279
   243
    | _ =>
boehmes@40279
   244
        (case Term.strip_comb (Thm.term_of ct) of
boehmes@40279
   245
          (Const (c as (_, T)), ts) =>
boehmes@40279
   246
            if SMT_Builtin.is_builtin ctxt c
boehmes@40279
   247
            then eta_args_conv norm_conv
boehmes@40279
   248
              (length (Term.binder_types T) - length ts)
boehmes@40279
   249
            else args_conv o norm_conv
boehmes@40424
   250
        | _ => args_conv o norm_conv)) ctxt ct
boehmes@36898
   251
boehmes@40279
   252
  fun is_normed ctxt t =
boehmes@36898
   253
    (case t of
boehmes@40279
   254
      Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed ctxt u
boehmes@36898
   255
    | Const (@{const_name All}, _) $ _ => false
boehmes@36898
   256
    | Const (@{const_name All}, _) => false
boehmes@40279
   257
    | Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed ctxt u
boehmes@36898
   258
    | Const (@{const_name Ex}, _) $ _ => false
boehmes@36898
   259
    | Const (@{const_name Ex}, _) => false
boehmes@36898
   260
    | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
boehmes@40279
   261
        is_normed ctxt u1 andalso is_normed ctxt u2
boehmes@36898
   262
    | Const (@{const_name Let}, _) $ _ $ _ => false
boehmes@36898
   263
    | Const (@{const_name Let}, _) $ _ => false
boehmes@36898
   264
    | Const (@{const_name Let}, _) => false
boehmes@40279
   265
    | Const (@{const_name Ex1}, _) $ _ => false
boehmes@36898
   266
    | Const (@{const_name Ex1}, _) => false
boehmes@40279
   267
    | Const (@{const_name Ball}, _) $ _ $ _ => false
boehmes@40279
   268
    | Const (@{const_name Ball}, _) $ _ => false
boehmes@36898
   269
    | Const (@{const_name Ball}, _) => false
boehmes@40279
   270
    | Const (@{const_name Bex}, _) $ _ $ _ => false
boehmes@40279
   271
    | Const (@{const_name Bex}, _) $ _ => false
boehmes@36898
   272
    | Const (@{const_name Bex}, _) => false
boehmes@40279
   273
    | Abs (_, _, u) => is_normed ctxt u
boehmes@40279
   274
    | _ =>
boehmes@40279
   275
        (case Term.strip_comb t of
boehmes@40279
   276
          (Const (c as (_, T)), ts) =>
boehmes@40279
   277
            if SMT_Builtin.is_builtin ctxt c
boehmes@40279
   278
            then length (Term.binder_types T) = length ts andalso
boehmes@40279
   279
              forall (is_normed ctxt) ts
boehmes@40279
   280
            else forall (is_normed ctxt) ts
boehmes@40279
   281
        | (_, ts) => forall (is_normed ctxt) ts))
boehmes@36898
   282
in
boehmes@40279
   283
fun norm_binder_conv ctxt =
boehmes@40663
   284
  U.if_conv (is_normed ctxt) Conv.all_conv (norm_conv ctxt)
boehmes@36898
   285
end
boehmes@36898
   286
boehmes@36898
   287
fun norm_def ctxt thm =
boehmes@36898
   288
  (case Thm.prop_of thm of
boehmes@40579
   289
    @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
boehmes@36898
   290
      norm_def ctxt (thm RS @{thm fun_cong})
boehmes@36898
   291
  | Const (@{const_name "=="}, _) $ _ $ Abs _ =>
boehmes@36898
   292
      norm_def ctxt (thm RS @{thm meta_eq_to_obj_eq})
boehmes@36898
   293
  | _ => thm)
boehmes@36898
   294
boehmes@36898
   295
fun atomize_conv ctxt ct =
boehmes@36898
   296
  (case Thm.term_of ct of
boehmes@40579
   297
    @{const "==>"} $ _ $ _ =>
boehmes@36898
   298
      Conv.binop_conv (atomize_conv ctxt) then_conv
boehmes@36898
   299
      Conv.rewr_conv @{thm atomize_imp}
boehmes@36898
   300
  | Const (@{const_name "=="}, _) $ _ $ _ =>
boehmes@36898
   301
      Conv.binop_conv (atomize_conv ctxt) then_conv
boehmes@36898
   302
      Conv.rewr_conv @{thm atomize_eq}
boehmes@36898
   303
  | Const (@{const_name all}, _) $ Abs _ =>
wenzelm@36936
   304
      Conv.binder_conv (atomize_conv o snd) ctxt then_conv
boehmes@36898
   305
      Conv.rewr_conv @{thm atomize_all}
boehmes@36898
   306
  | _ => Conv.all_conv) ct
boehmes@36898
   307
boehmes@36898
   308
fun normalize_rule ctxt =
boehmes@36898
   309
  Conv.fconv_rule (
boehmes@36898
   310
    (* reduce lambda abstractions, except at known binders: *)
boehmes@36898
   311
    Thm.beta_conversion true then_conv
boehmes@36898
   312
    Thm.eta_conversion then_conv
boehmes@36898
   313
    norm_binder_conv ctxt) #>
boehmes@36898
   314
  norm_def ctxt #>
boehmes@36898
   315
  Drule.forall_intr_vars #>
boehmes@36898
   316
  Conv.fconv_rule (atomize_conv ctxt)
boehmes@36898
   317
boehmes@36898
   318
boehmes@36898
   319
boehmes@36898
   320
(* lift lambda terms into additional rules *)
boehmes@36898
   321
boehmes@36898
   322
local
boehmes@36898
   323
  fun used_vars cvs ct =
boehmes@36898
   324
    let
boehmes@36898
   325
      val lookup = AList.lookup (op aconv) (map (` Thm.term_of) cvs)
boehmes@36898
   326
      val add = (fn SOME ct => insert (op aconvc) ct | _ => I)
boehmes@36898
   327
    in Term.fold_aterms (add o lookup) (Thm.term_of ct) [] end
boehmes@36898
   328
boehmes@36898
   329
  fun apply cv thm = 
boehmes@36898
   330
    let val thm' = Thm.combination thm (Thm.reflexive cv)
boehmes@36898
   331
    in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end
boehmes@36898
   332
  fun apply_def cvs eq = Thm.symmetric (fold apply cvs eq)
boehmes@36898
   333
boehmes@36898
   334
  fun replace_lambda cvs ct (cx as (ctxt, defs)) =
boehmes@36898
   335
    let
boehmes@36898
   336
      val cvs' = used_vars cvs ct
boehmes@36898
   337
      val ct' = fold_rev Thm.cabs cvs' ct
boehmes@36898
   338
    in
boehmes@36898
   339
      (case Termtab.lookup defs (Thm.term_of ct') of
boehmes@36898
   340
        SOME eq => (apply_def cvs' eq, cx)
boehmes@36898
   341
      | NONE =>
boehmes@36898
   342
          let
boehmes@36898
   343
            val {T, ...} = Thm.rep_cterm ct' and n = Name.uu
boehmes@36898
   344
            val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
boehmes@40663
   345
            val cu = U.mk_cequals (U.certify ctxt (Free (n', T))) ct'
boehmes@36898
   346
            val (eq, ctxt'') = yield_singleton Assumption.add_assumes cu ctxt'
boehmes@36898
   347
            val defs' = Termtab.update (Thm.term_of ct', eq) defs
boehmes@36898
   348
          in (apply_def cvs' eq, (ctxt'', defs')) end)
boehmes@36898
   349
    end
boehmes@36898
   350
boehmes@36898
   351
  fun none ct cx = (Thm.reflexive ct, cx)
boehmes@36898
   352
  fun in_comb f g ct cx =
boehmes@36898
   353
    let val (cu1, cu2) = Thm.dest_comb ct
boehmes@36898
   354
    in cx |> f cu1 ||>> g cu2 |>> uncurry Thm.combination end
boehmes@36898
   355
  fun in_arg f = in_comb none f
boehmes@36898
   356
  fun in_abs f cvs ct (ctxt, defs) =
boehmes@36898
   357
    let
boehmes@36898
   358
      val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
boehmes@36898
   359
      val (cv, cu) = Thm.dest_abs (SOME n) ct
boehmes@36898
   360
    in  (ctxt', defs) |> f (cv :: cvs) cu |>> Thm.abstract_rule n cv end
boehmes@36898
   361
boehmes@36898
   362
  fun traverse cvs ct =
boehmes@36898
   363
    (case Thm.term_of ct of
boehmes@36898
   364
      Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs traverse cvs)
boehmes@36898
   365
    | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs traverse cvs)
boehmes@36898
   366
    | Const (@{const_name Let}, _) $ _ $ Abs _ =>
boehmes@36898
   367
        in_comb (in_arg (traverse cvs)) (in_abs traverse cvs)
boehmes@36898
   368
    | Abs _ => at_lambda cvs
boehmes@36898
   369
    | _ $ _ => in_comb (traverse cvs) (traverse cvs)
boehmes@36898
   370
    | _ => none) ct
boehmes@36898
   371
boehmes@36898
   372
  and at_lambda cvs ct =
boehmes@36898
   373
    in_abs traverse cvs ct #-> (fn thm =>
boehmes@36898
   374
    replace_lambda cvs (Thm.rhs_of thm) #>> Thm.transitive thm)
boehmes@36898
   375
boehmes@36898
   376
  fun has_free_lambdas t =
boehmes@36898
   377
    (case t of
boehmes@36898
   378
      Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u
boehmes@36898
   379
    | Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u
boehmes@36898
   380
    | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
boehmes@36898
   381
        has_free_lambdas u1 orelse has_free_lambdas u2
boehmes@36898
   382
    | Abs _ => true
boehmes@36898
   383
    | u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2
boehmes@36898
   384
    | _ => false)
boehmes@36898
   385
boehmes@36898
   386
  fun lift_lm f thm cx =
boehmes@36898
   387
    if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx)
boehmes@36898
   388
    else cx |> f (Thm.cprop_of thm) |>> (fn thm' => Thm.equal_elim thm' thm)
boehmes@36898
   389
in
boehmes@40161
   390
fun lift_lambdas irules ctxt =
boehmes@36898
   391
  let
boehmes@36898
   392
    val cx = (ctxt, Termtab.empty)
boehmes@40161
   393
    val (idxs, thms) = split_list irules
boehmes@36898
   394
    val (thms', (ctxt', defs)) = fold_map (lift_lm (traverse [])) thms cx
boehmes@36898
   395
    val eqs = Termtab.fold (cons o normalize_rule ctxt' o snd) defs []
boehmes@40161
   396
  in (map (pair ~1) eqs @ (idxs ~~ thms'), ctxt') end
boehmes@36898
   397
end
boehmes@36898
   398
boehmes@36898
   399
boehmes@36898
   400
boehmes@36898
   401
(* make application explicit for functions with varying number of arguments *)
boehmes@36898
   402
boehmes@36898
   403
local
boehmes@36898
   404
  val const = prefix "c" and free = prefix "f"
boehmes@36898
   405
  fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e
boehmes@36898
   406
  fun add t i = Symtab.map_default (t, (false, i)) (min i)
boehmes@36898
   407
  fun traverse t =
boehmes@36898
   408
    (case Term.strip_comb t of
boehmes@36898
   409
      (Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts 
boehmes@36898
   410
    | (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts
boehmes@36898
   411
    | (Abs (_, _, u), ts) => fold traverse (u :: ts)
boehmes@36898
   412
    | (_, ts) => fold traverse ts)
boehmes@40161
   413
  fun prune tab = Symtab.fold (fn (n, (true, i)) =>
boehmes@40161
   414
    Symtab.update (n, i) | _ => I) tab Symtab.empty
boehmes@36898
   415
boehmes@36898
   416
  fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
boehmes@36898
   417
  fun nary_conv conv1 conv2 ct =
boehmes@36898
   418
    (Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct
boehmes@36898
   419
  fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) =>
boehmes@36898
   420
    let val n = fst (Term.dest_Free (Thm.term_of cv))
boehmes@36898
   421
    in conv (Symtab.update (free n, 0) tb) cx end)
boehmes@37153
   422
  val fun_app_rule = @{lemma "f x == fun_app f x" by (simp add: fun_app_def)}
boehmes@36898
   423
in
boehmes@40161
   424
fun explicit_application ctxt irules =
boehmes@36898
   425
  let
boehmes@36898
   426
    fun sub_conv tb ctxt ct =
boehmes@36898
   427
      (case Term.strip_comb (Thm.term_of ct) of
boehmes@36898
   428
        (Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt
boehmes@36898
   429
      | (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt
boehmes@36898
   430
      | (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt)
boehmes@36898
   431
      | (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct
boehmes@36898
   432
    and app_conv tb n i ctxt =
boehmes@36898
   433
      (case Symtab.lookup tb n of
boehmes@36898
   434
        NONE => nary_conv Conv.all_conv (sub_conv tb ctxt)
boehmes@37153
   435
      | SOME j => fun_app_conv tb ctxt (i - j))
boehmes@37153
   436
    and fun_app_conv tb ctxt i ct = (
boehmes@36898
   437
      if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt)
boehmes@36898
   438
      else
boehmes@37153
   439
        Conv.rewr_conv fun_app_rule then_conv
boehmes@37153
   440
        binop_conv (fun_app_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct
boehmes@36898
   441
boehmes@36898
   442
    fun needs_exp_app tab = Term.exists_subterm (fn
boehmes@36898
   443
        Bound _ $ _ => true
boehmes@36898
   444
      | Const (n, _) => Symtab.defined tab (const n)
boehmes@36898
   445
      | Free (n, _) => Symtab.defined tab (free n)
boehmes@36898
   446
      | _ => false)
boehmes@36898
   447
boehmes@36898
   448
    fun rewrite tab ctxt thm =
boehmes@36898
   449
      if not (needs_exp_app tab (Thm.prop_of thm)) then thm
boehmes@36898
   450
      else Conv.fconv_rule (sub_conv tab ctxt) thm
boehmes@36898
   451
boehmes@40161
   452
    val tab = prune (fold (traverse o Thm.prop_of o snd) irules Symtab.empty)
boehmes@40161
   453
  in map (apsnd (rewrite tab ctxt)) irules end
boehmes@36898
   454
end
boehmes@36898
   455
boehmes@36898
   456
boehmes@36898
   457
boehmes@39483
   458
(* add missing datatype selectors via hypothetical definitions *)
boehmes@39483
   459
boehmes@39483
   460
local
boehmes@39483
   461
  val add = (fn Type (n, _) => Symtab.update (n, ()) | _ => I)
boehmes@39483
   462
boehmes@39483
   463
  fun collect t =
boehmes@39483
   464
    (case Term.strip_comb t of
boehmes@39483
   465
      (Abs (_, T, t), _) => add T #> collect t
boehmes@39483
   466
    | (Const (_, T), ts) => collects T ts
boehmes@39483
   467
    | (Free (_, T), ts) => collects T ts
boehmes@39483
   468
    | _ => I)
boehmes@39483
   469
  and collects T ts =
boehmes@39483
   470
    let val ((Ts, Us), U) = Term.strip_type T |> apfst (chop (length ts))
boehmes@39483
   471
    in fold add Ts #> add (Us ---> U) #> fold collect ts end
boehmes@39483
   472
boehmes@39483
   473
  fun add_constructors thy n =
boehmes@39483
   474
    (case Datatype.get_info thy n of
boehmes@39483
   475
      NONE => I
boehmes@39483
   476
    | SOME {descr, ...} => fold (fn (_, (_, _, cs)) => fold (fn (n, ds) =>
boehmes@39483
   477
        fold (insert (op =) o pair n) (1 upto length ds)) cs) descr)
boehmes@39483
   478
boehmes@39483
   479
  fun add_selector (c as (n, i)) ctxt =
boehmes@39483
   480
    (case Datatype_Selectors.lookup_selector ctxt c of
boehmes@39483
   481
      SOME _ => ctxt
boehmes@39483
   482
    | NONE =>
boehmes@39483
   483
        let
boehmes@39483
   484
          val T = Sign.the_const_type (ProofContext.theory_of ctxt) n
boehmes@39483
   485
          val U = Term.body_type T --> nth (Term.binder_types T) (i-1)
boehmes@39483
   486
        in
boehmes@39483
   487
          ctxt
boehmes@39483
   488
          |> yield_singleton Variable.variant_fixes Name.uu
boehmes@39483
   489
          |>> pair ((n, T), i) o rpair U
boehmes@39483
   490
          |-> Context.proof_map o Datatype_Selectors.add_selector
boehmes@39483
   491
        end)
boehmes@39483
   492
in
boehmes@39483
   493
boehmes@40161
   494
fun datatype_selectors irules ctxt =
boehmes@39483
   495
  let
boehmes@40161
   496
    val ns = Symtab.keys (fold (collect o Thm.prop_of o snd) irules Symtab.empty)
boehmes@39483
   497
    val cs = fold (add_constructors (ProofContext.theory_of ctxt)) ns []
boehmes@40161
   498
  in (irules, fold add_selector cs ctxt) end
boehmes@39483
   499
    (* FIXME: also generate hypothetical definitions for the selectors *)
boehmes@39483
   500
boehmes@39483
   501
end
boehmes@39483
   502
boehmes@39483
   503
boehmes@39483
   504
boehmes@36898
   505
(* combined normalization *)
boehmes@36898
   506
boehmes@40162
   507
type extra_norm = bool -> (int * thm) list -> Proof.context ->
boehmes@40161
   508
  (int * thm) list * Proof.context
boehmes@36898
   509
boehmes@40161
   510
fun with_context f irules ctxt = (f ctxt irules, ctxt)
boehmes@36898
   511
boehmes@40424
   512
fun normalize extra_norm with_datatypes irules ctxt =
boehmes@40278
   513
  let
boehmes@40278
   514
    fun norm f ctxt' (i, thm) =
boehmes@40424
   515
      if Config.get ctxt' SMT_Config.drop_bad_facts then
boehmes@40278
   516
        (case try (f ctxt') thm of
boehmes@40278
   517
          SOME thm' => SOME (i, thm')
boehmes@40424
   518
        | NONE => (SMT_Config.verbose_msg ctxt' (prefix ("Warning: " ^
boehmes@40278
   519
            "dropping assumption: ") o Display.string_of_thm ctxt') thm; NONE))
boehmes@40424
   520
      else SOME (i, f ctxt' thm)
boehmes@40278
   521
  in
boehmes@40278
   522
    irules
boehmes@40278
   523
    |> trivial_distinct ctxt
boehmes@40278
   524
    |> rewrite_bool_cases ctxt
boehmes@40278
   525
    |> normalize_numerals ctxt
boehmes@40278
   526
    |> nat_as_int ctxt
boehmes@40278
   527
    |> rpair ctxt
boehmes@40278
   528
    |-> extra_norm with_datatypes
boehmes@40278
   529
    |-> with_context (map_filter o norm normalize_rule)
boehmes@40278
   530
    |-> SMT_Monomorph.monomorph
boehmes@40278
   531
    |-> lift_lambdas
boehmes@40278
   532
    |-> with_context explicit_application
boehmes@40278
   533
    |-> (if with_datatypes then datatype_selectors else pair)
boehmes@40278
   534
  end
boehmes@36898
   535
boehmes@36898
   536
end