src/HOL/Tools/SMT/smt_normalize.ML
author boehmes
Fri Oct 29 18:17:05 2010 +0200 (2010-10-29)
changeset 40275 eed48b11abdb
parent 40274 6486c610a549
child 40278 0fc78bb54f18
permissions -rw-r--r--
tuned
     1 (*  Title:      HOL/Tools/SMT/smt_normalize.ML
     2     Author:     Sascha Boehme, TU Muenchen
     3 
     4 Normalization steps on theorems required by SMT solvers:
     5   * simplify trivial distincts (those with less than three elements),
     6   * rewrite bool case expressions as if expressions,
     7   * normalize numerals (e.g. replace negative numerals by negated positive
     8     numerals),
     9   * embed natural numbers into integers,
    10   * add extra rules specifying types and constants which occur frequently,
    11   * fully translate into object logic, add universal closure,
    12   * monomorphize (create instances of schematic rules),
    13   * lift lambda terms,
    14   * make applications explicit for functions with varying number of arguments.
    15   * add (hypothetical definitions for) missing datatype selectors,
    16 *)
    17 
    18 signature SMT_NORMALIZE =
    19 sig
    20   type extra_norm = bool -> (int * thm) list -> Proof.context ->
    21     (int * thm) list * Proof.context
    22   val normalize: extra_norm -> bool -> (int * thm) list -> Proof.context ->
    23     (int * thm) list * Proof.context
    24   val atomize_conv: Proof.context -> conv
    25   val eta_expand_conv: (Proof.context -> conv) -> Proof.context -> conv
    26 end
    27 
    28 structure SMT_Normalize: SMT_NORMALIZE =
    29 struct
    30 
    31 infix 2 ??
    32 fun (test ?? f) x = if test x then f x else x
    33 
    34 fun if_conv c cv1 cv2 ct = (if c (Thm.term_of ct) then cv1 else cv2) ct
    35 fun if_true_conv c cv = if_conv c cv Conv.all_conv
    36 
    37 
    38 
    39 (* simplification of trivial distincts (distinct should have at least
    40    three elements in the argument list) *)
    41 
    42 local
    43   fun is_trivial_distinct (Const (@{const_name SMT.distinct}, _) $ t) =
    44        (length (HOLogic.dest_list t) <= 2
    45         handle TERM _ => error ("SMT: constant " ^
    46           quote @{const_name SMT.distinct} ^ " must be applied to " ^
    47           "an explicit list."))
    48     | is_trivial_distinct _ = false
    49 
    50   val thms = map mk_meta_eq @{lemma
    51     "SMT.distinct [] = True"
    52     "SMT.distinct [x] = True"
    53     "SMT.distinct [x, y] = (x ~= y)"
    54     by (simp_all add: distinct_def)}
    55   fun distinct_conv _ =
    56     if_true_conv is_trivial_distinct (Conv.rewrs_conv thms)
    57 in
    58 fun trivial_distinct ctxt =
    59   map (apsnd ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??
    60     Conv.fconv_rule (Conv.top_conv distinct_conv ctxt)))
    61 end
    62 
    63 
    64 
    65 (* rewrite bool case expressions as if expressions *)
    66 
    67 local
    68   val is_bool_case = (fn
    69       Const (@{const_name "bool.bool_case"}, _) $ _ $ _ $ _ => true
    70     | _ => false)
    71 
    72   val thm = mk_meta_eq @{lemma
    73     "(case P of True => x | False => y) = (if P then x else y)" by simp}
    74   val unfold_conv = if_true_conv is_bool_case (Conv.rewr_conv thm)
    75 in
    76 fun rewrite_bool_cases ctxt =
    77   map (apsnd ((Term.exists_subterm is_bool_case o Thm.prop_of) ??
    78     Conv.fconv_rule (Conv.top_conv (K unfold_conv) ctxt)))
    79 end
    80 
    81 
    82 
    83 (* normalization of numerals: rewriting of negative integer numerals into
    84    positive numerals, Numeral0 into 0, Numeral1 into 1 *)
    85 
    86 local
    87   fun is_number_sort ctxt T =
    88     Sign.of_sort (ProofContext.theory_of ctxt) (T, @{sort number_ring})
    89 
    90   fun is_strange_number ctxt (t as Const (@{const_name number_of}, _) $ _) =
    91         (case try HOLogic.dest_number t of
    92           SOME (T, i) => is_number_sort ctxt T andalso i < 2
    93         | NONE => false)
    94     | is_strange_number _ _ = false
    95 
    96   val pos_numeral_ss = HOL_ss
    97     addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}]
    98     addsimps [@{thm Int.number_of_Pls}, @{thm Int.numeral_1_eq_1}]
    99     addsimps @{thms Int.pred_bin_simps}
   100     addsimps @{thms Int.normalize_bin_simps}
   101     addsimps @{lemma
   102       "Int.Min = - Int.Bit1 Int.Pls"
   103       "Int.Bit0 (- Int.Pls) = - Int.Pls"
   104       "Int.Bit0 (- k) = - Int.Bit0 k"
   105       "Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)"
   106       by simp_all (simp add: pred_def)}
   107 
   108   fun pos_conv ctxt = if_conv (is_strange_number ctxt)
   109     (Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss))
   110     Conv.no_conv
   111 in
   112 fun normalize_numerals ctxt =
   113   map (apsnd ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??
   114     Conv.fconv_rule (Conv.top_sweep_conv pos_conv ctxt)))
   115 end
   116 
   117 
   118 
   119 (* embedding of standard natural number operations into integer operations *)
   120 
   121 local
   122   val nat_embedding = map (pair ~1) @{lemma
   123     "nat (int n) = n"
   124     "i >= 0 --> int (nat i) = i"
   125     "i < 0 --> int (nat i) = 0"
   126     by simp_all}
   127 
   128   val nat_rewriting = @{lemma
   129     "0 = nat 0"
   130     "1 = nat 1"
   131     "number_of i = nat (number_of i)"
   132     "int (nat 0) = 0"
   133     "int (nat 1) = 1"
   134     "a < b = (int a < int b)"
   135     "a <= b = (int a <= int b)"
   136     "Suc a = nat (int a + 1)"
   137     "a + b = nat (int a + int b)"
   138     "a - b = nat (int a - int b)"
   139     "a * b = nat (int a * int b)"
   140     "a div b = nat (int a div int b)"
   141     "a mod b = nat (int a mod int b)"
   142     "min a b = nat (min (int a) (int b))"
   143     "max a b = nat (max (int a) (int b))"
   144     "int (nat (int a + int b)) = int a + int b"
   145     "int (nat (int a * int b)) = int a * int b"
   146     "int (nat (int a div int b)) = int a div int b"
   147     "int (nat (int a mod int b)) = int a mod int b"
   148     "int (nat (min (int a) (int b))) = min (int a) (int b)"
   149     "int (nat (max (int a) (int b))) = max (int a) (int b)"
   150     by (simp_all add: nat_mult_distrib nat_div_distrib nat_mod_distrib
   151       int_mult[symmetric] zdiv_int[symmetric] zmod_int[symmetric])}
   152 
   153   fun on_positive num f x = 
   154     (case try HOLogic.dest_number (Thm.term_of num) of
   155       SOME (_, i) => if i >= 0 then SOME (f x) else NONE
   156     | NONE => NONE)
   157 
   158   val cancel_int_nat_ss = HOL_ss
   159     addsimps [@{thm Nat_Numeral.nat_number_of}]
   160     addsimps [@{thm Nat_Numeral.int_nat_number_of}]
   161     addsimps @{thms neg_simps}
   162 
   163   fun cancel_int_nat_simproc _ ss ct = 
   164     let
   165       val num = Thm.dest_arg (Thm.dest_arg ct)
   166       val goal = Thm.mk_binop @{cterm "op == :: int => _"} ct num
   167       val simpset = Simplifier.inherit_context ss cancel_int_nat_ss
   168       fun tac _ = Simplifier.simp_tac simpset 1
   169     in on_positive num (Goal.prove_internal [] goal) tac end
   170 
   171   val nat_ss = HOL_ss
   172     addsimps nat_rewriting
   173     addsimprocs [Simplifier.make_simproc {
   174       name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}],
   175       proc = cancel_int_nat_simproc, identifier = [] }]
   176 
   177   fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss)
   178 
   179   val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat}))
   180   val uses_nat_int =
   181     Term.exists_subterm (member (op aconv) [@{term int}, @{term nat}])
   182 in
   183 fun nat_as_int ctxt =
   184   map (apsnd ((uses_nat_type o Thm.prop_of) ?? Conv.fconv_rule (conv ctxt))) #>
   185   exists (uses_nat_int o Thm.prop_of o snd) ?? append nat_embedding
   186 end
   187 
   188 
   189 
   190 (* further normalizations: beta/eta, universal closure, atomize *)
   191 
   192 val eta_expand_eq = @{lemma "f == (%x. f x)" by (rule reflexive)}
   193 
   194 fun eta_expand_conv cv ctxt =
   195   Conv.rewr_conv eta_expand_eq then_conv Conv.abs_conv (cv o snd) ctxt
   196 
   197 local
   198   val eta_conv = eta_expand_conv
   199 
   200   fun keep_conv ctxt = Conv.binder_conv (norm_conv o snd) ctxt
   201   and eta_binder_conv ctxt = Conv.arg_conv (eta_conv norm_conv ctxt)
   202   and keep_let_conv ctxt = Conv.combination_conv
   203     (Conv.arg_conv (norm_conv ctxt)) (Conv.abs_conv (norm_conv o snd) ctxt)
   204   and unfold_let_conv ctxt = Conv.combination_conv
   205     (Conv.arg_conv (norm_conv ctxt)) (eta_conv norm_conv ctxt)
   206   and unfold_conv thm ctxt = Conv.rewr_conv thm then_conv keep_conv ctxt
   207   and unfold_ex1_conv ctxt = unfold_conv @{thm Ex1_def} ctxt
   208   and unfold_ball_conv ctxt = unfold_conv (mk_meta_eq @{thm Ball_def}) ctxt
   209   and unfold_bex_conv ctxt = unfold_conv (mk_meta_eq @{thm Bex_def}) ctxt
   210   and norm_conv ctxt ct =
   211     (case Thm.term_of ct of
   212       Const (@{const_name All}, _) $ Abs _ => keep_conv
   213     | Const (@{const_name All}, _) $ _ => eta_binder_conv
   214     | Const (@{const_name All}, _) => eta_conv eta_binder_conv
   215     | Const (@{const_name Ex}, _) $ Abs _ => keep_conv
   216     | Const (@{const_name Ex}, _) $ _ => eta_binder_conv
   217     | Const (@{const_name Ex}, _) => eta_conv eta_binder_conv
   218     | Const (@{const_name Let}, _) $ _ $ Abs _ => keep_let_conv
   219     | Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv
   220     | Const (@{const_name Let}, _) $ _ => eta_conv unfold_let_conv
   221     | Const (@{const_name Let}, _) => eta_conv (eta_conv unfold_let_conv)
   222     | Const (@{const_name Ex1}, _) $ _ => unfold_ex1_conv
   223     | Const (@{const_name Ex1}, _) => eta_conv unfold_ex1_conv 
   224     | Const (@{const_name Ball}, _) $ _ $ _ => unfold_ball_conv
   225     | Const (@{const_name Ball}, _) $ _ => eta_conv unfold_ball_conv
   226     | Const (@{const_name Ball}, _) => eta_conv (eta_conv unfold_ball_conv)
   227     | Const (@{const_name Bex}, _) $ _ $ _ => unfold_bex_conv
   228     | Const (@{const_name Bex}, _) $ _ => eta_conv unfold_bex_conv
   229     | Const (@{const_name Bex}, _) => eta_conv (eta_conv unfold_bex_conv)
   230     | Abs _ => Conv.abs_conv (norm_conv o snd)
   231     | _ $ _ => Conv.comb_conv o norm_conv
   232     | _ => K Conv.all_conv) ctxt ct
   233 
   234   fun is_normed t =
   235     (case t of
   236       Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed u
   237     | Const (@{const_name All}, _) $ _ => false
   238     | Const (@{const_name All}, _) => false
   239     | Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed u
   240     | Const (@{const_name Ex}, _) $ _ => false
   241     | Const (@{const_name Ex}, _) => false
   242     | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
   243         is_normed u1 andalso is_normed u2
   244     | Const (@{const_name Let}, _) $ _ $ _ => false
   245     | Const (@{const_name Let}, _) $ _ => false
   246     | Const (@{const_name Let}, _) => false
   247     | Const (@{const_name Ex1}, _) => false
   248     | Const (@{const_name Ball}, _) => false
   249     | Const (@{const_name Bex}, _) => false
   250     | Abs (_, _, u) => is_normed u
   251     | u1 $ u2 => is_normed u1 andalso is_normed u2
   252     | _ => true)
   253 in
   254 fun norm_binder_conv ctxt = if_conv is_normed Conv.all_conv (norm_conv ctxt)
   255 end
   256 
   257 fun norm_def ctxt thm =
   258   (case Thm.prop_of thm of
   259     @{term Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
   260       norm_def ctxt (thm RS @{thm fun_cong})
   261   | Const (@{const_name "=="}, _) $ _ $ Abs _ =>
   262       norm_def ctxt (thm RS @{thm meta_eq_to_obj_eq})
   263   | _ => thm)
   264 
   265 fun atomize_conv ctxt ct =
   266   (case Thm.term_of ct of
   267     @{term "op ==>"} $ _ $ _ =>
   268       Conv.binop_conv (atomize_conv ctxt) then_conv
   269       Conv.rewr_conv @{thm atomize_imp}
   270   | Const (@{const_name "=="}, _) $ _ $ _ =>
   271       Conv.binop_conv (atomize_conv ctxt) then_conv
   272       Conv.rewr_conv @{thm atomize_eq}
   273   | Const (@{const_name all}, _) $ Abs _ =>
   274       Conv.binder_conv (atomize_conv o snd) ctxt then_conv
   275       Conv.rewr_conv @{thm atomize_all}
   276   | _ => Conv.all_conv) ct
   277 
   278 fun normalize_rule ctxt =
   279   Conv.fconv_rule (
   280     (* reduce lambda abstractions, except at known binders: *)
   281     Thm.beta_conversion true then_conv
   282     Thm.eta_conversion then_conv
   283     norm_binder_conv ctxt) #>
   284   norm_def ctxt #>
   285   Drule.forall_intr_vars #>
   286   Conv.fconv_rule (atomize_conv ctxt)
   287 
   288 
   289 
   290 (* lift lambda terms into additional rules *)
   291 
   292 local
   293   val meta_eq = @{cpat "op =="}
   294   val meta_eqT = hd (Thm.dest_ctyp (Thm.ctyp_of_term meta_eq))
   295   fun inst_meta cT = Thm.instantiate_cterm ([(meta_eqT, cT)], []) meta_eq
   296   fun mk_meta_eq ct cu = Thm.mk_binop (inst_meta (Thm.ctyp_of_term ct)) ct cu
   297 
   298   fun cert ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
   299 
   300   fun used_vars cvs ct =
   301     let
   302       val lookup = AList.lookup (op aconv) (map (` Thm.term_of) cvs)
   303       val add = (fn SOME ct => insert (op aconvc) ct | _ => I)
   304     in Term.fold_aterms (add o lookup) (Thm.term_of ct) [] end
   305 
   306   fun apply cv thm = 
   307     let val thm' = Thm.combination thm (Thm.reflexive cv)
   308     in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end
   309   fun apply_def cvs eq = Thm.symmetric (fold apply cvs eq)
   310 
   311   fun replace_lambda cvs ct (cx as (ctxt, defs)) =
   312     let
   313       val cvs' = used_vars cvs ct
   314       val ct' = fold_rev Thm.cabs cvs' ct
   315     in
   316       (case Termtab.lookup defs (Thm.term_of ct') of
   317         SOME eq => (apply_def cvs' eq, cx)
   318       | NONE =>
   319           let
   320             val {T, ...} = Thm.rep_cterm ct' and n = Name.uu
   321             val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
   322             val cu = mk_meta_eq (cert ctxt (Free (n', T))) ct'
   323             val (eq, ctxt'') = yield_singleton Assumption.add_assumes cu ctxt'
   324             val defs' = Termtab.update (Thm.term_of ct', eq) defs
   325           in (apply_def cvs' eq, (ctxt'', defs')) end)
   326     end
   327 
   328   fun none ct cx = (Thm.reflexive ct, cx)
   329   fun in_comb f g ct cx =
   330     let val (cu1, cu2) = Thm.dest_comb ct
   331     in cx |> f cu1 ||>> g cu2 |>> uncurry Thm.combination end
   332   fun in_arg f = in_comb none f
   333   fun in_abs f cvs ct (ctxt, defs) =
   334     let
   335       val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
   336       val (cv, cu) = Thm.dest_abs (SOME n) ct
   337     in  (ctxt', defs) |> f (cv :: cvs) cu |>> Thm.abstract_rule n cv end
   338 
   339   fun traverse cvs ct =
   340     (case Thm.term_of ct of
   341       Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs traverse cvs)
   342     | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs traverse cvs)
   343     | Const (@{const_name Let}, _) $ _ $ Abs _ =>
   344         in_comb (in_arg (traverse cvs)) (in_abs traverse cvs)
   345     | Abs _ => at_lambda cvs
   346     | _ $ _ => in_comb (traverse cvs) (traverse cvs)
   347     | _ => none) ct
   348 
   349   and at_lambda cvs ct =
   350     in_abs traverse cvs ct #-> (fn thm =>
   351     replace_lambda cvs (Thm.rhs_of thm) #>> Thm.transitive thm)
   352 
   353   fun has_free_lambdas t =
   354     (case t of
   355       Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u
   356     | Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u
   357     | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
   358         has_free_lambdas u1 orelse has_free_lambdas u2
   359     | Abs _ => true
   360     | u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2
   361     | _ => false)
   362 
   363   fun lift_lm f thm cx =
   364     if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx)
   365     else cx |> f (Thm.cprop_of thm) |>> (fn thm' => Thm.equal_elim thm' thm)
   366 in
   367 fun lift_lambdas irules ctxt =
   368   let
   369     val cx = (ctxt, Termtab.empty)
   370     val (idxs, thms) = split_list irules
   371     val (thms', (ctxt', defs)) = fold_map (lift_lm (traverse [])) thms cx
   372     val eqs = Termtab.fold (cons o normalize_rule ctxt' o snd) defs []
   373   in (map (pair ~1) eqs @ (idxs ~~ thms'), ctxt') end
   374 end
   375 
   376 
   377 
   378 (* make application explicit for functions with varying number of arguments *)
   379 
   380 local
   381   val const = prefix "c" and free = prefix "f"
   382   fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e
   383   fun add t i = Symtab.map_default (t, (false, i)) (min i)
   384   fun traverse t =
   385     (case Term.strip_comb t of
   386       (Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts 
   387     | (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts
   388     | (Abs (_, _, u), ts) => fold traverse (u :: ts)
   389     | (_, ts) => fold traverse ts)
   390   fun prune tab = Symtab.fold (fn (n, (true, i)) =>
   391     Symtab.update (n, i) | _ => I) tab Symtab.empty
   392 
   393   fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
   394   fun nary_conv conv1 conv2 ct =
   395     (Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct
   396   fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) =>
   397     let val n = fst (Term.dest_Free (Thm.term_of cv))
   398     in conv (Symtab.update (free n, 0) tb) cx end)
   399   val fun_app_rule = @{lemma "f x == fun_app f x" by (simp add: fun_app_def)}
   400 in
   401 fun explicit_application ctxt irules =
   402   let
   403     fun sub_conv tb ctxt ct =
   404       (case Term.strip_comb (Thm.term_of ct) of
   405         (Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt
   406       | (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt
   407       | (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt)
   408       | (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct
   409     and app_conv tb n i ctxt =
   410       (case Symtab.lookup tb n of
   411         NONE => nary_conv Conv.all_conv (sub_conv tb ctxt)
   412       | SOME j => fun_app_conv tb ctxt (i - j))
   413     and fun_app_conv tb ctxt i ct = (
   414       if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt)
   415       else
   416         Conv.rewr_conv fun_app_rule then_conv
   417         binop_conv (fun_app_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct
   418 
   419     fun needs_exp_app tab = Term.exists_subterm (fn
   420         Bound _ $ _ => true
   421       | Const (n, _) => Symtab.defined tab (const n)
   422       | Free (n, _) => Symtab.defined tab (free n)
   423       | _ => false)
   424 
   425     fun rewrite tab ctxt thm =
   426       if not (needs_exp_app tab (Thm.prop_of thm)) then thm
   427       else Conv.fconv_rule (sub_conv tab ctxt) thm
   428 
   429     val tab = prune (fold (traverse o Thm.prop_of o snd) irules Symtab.empty)
   430   in map (apsnd (rewrite tab ctxt)) irules end
   431 end
   432 
   433 
   434 
   435 (* add missing datatype selectors via hypothetical definitions *)
   436 
   437 local
   438   val add = (fn Type (n, _) => Symtab.update (n, ()) | _ => I)
   439 
   440   fun collect t =
   441     (case Term.strip_comb t of
   442       (Abs (_, T, t), _) => add T #> collect t
   443     | (Const (_, T), ts) => collects T ts
   444     | (Free (_, T), ts) => collects T ts
   445     | _ => I)
   446   and collects T ts =
   447     let val ((Ts, Us), U) = Term.strip_type T |> apfst (chop (length ts))
   448     in fold add Ts #> add (Us ---> U) #> fold collect ts end
   449 
   450   fun add_constructors thy n =
   451     (case Datatype.get_info thy n of
   452       NONE => I
   453     | SOME {descr, ...} => fold (fn (_, (_, _, cs)) => fold (fn (n, ds) =>
   454         fold (insert (op =) o pair n) (1 upto length ds)) cs) descr)
   455 
   456   fun add_selector (c as (n, i)) ctxt =
   457     (case Datatype_Selectors.lookup_selector ctxt c of
   458       SOME _ => ctxt
   459     | NONE =>
   460         let
   461           val T = Sign.the_const_type (ProofContext.theory_of ctxt) n
   462           val U = Term.body_type T --> nth (Term.binder_types T) (i-1)
   463         in
   464           ctxt
   465           |> yield_singleton Variable.variant_fixes Name.uu
   466           |>> pair ((n, T), i) o rpair U
   467           |-> Context.proof_map o Datatype_Selectors.add_selector
   468         end)
   469 in
   470 
   471 fun datatype_selectors irules ctxt =
   472   let
   473     val ns = Symtab.keys (fold (collect o Thm.prop_of o snd) irules Symtab.empty)
   474     val cs = fold (add_constructors (ProofContext.theory_of ctxt)) ns []
   475   in (irules, fold add_selector cs ctxt) end
   476     (* FIXME: also generate hypothetical definitions for the selectors *)
   477 
   478 end
   479 
   480 
   481 
   482 (* combined normalization *)
   483 
   484 type extra_norm = bool -> (int * thm) list -> Proof.context ->
   485   (int * thm) list * Proof.context
   486 
   487 fun with_context f irules ctxt = (f ctxt irules, ctxt)
   488 
   489 fun normalize extra_norm with_datatypes irules ctxt =
   490   irules
   491   |> trivial_distinct ctxt
   492   |> rewrite_bool_cases ctxt
   493   |> normalize_numerals ctxt
   494   |> nat_as_int ctxt
   495   |> rpair ctxt
   496   |-> extra_norm with_datatypes
   497   |-> with_context (fn cx => map (apsnd (normalize_rule cx)))
   498   |-> SMT_Monomorph.monomorph
   499   |-> lift_lambdas
   500   |-> with_context explicit_application
   501   |-> (if with_datatypes then datatype_selectors else pair)
   502 
   503 end