src/HOL/Tools/Nitpick/nitpick_preproc.ML
author blanchet
Tue Dec 07 11:56:53 2010 +0100 (2010-12-07)
changeset 41052 3db267a01c1d
parent 41001 11715564e2ad
child 41791 01d722707a36
permissions -rw-r--r--
remove the "fin_fun" optimization in Nitpick -- it was always a hack and didn't help much
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(*  Title:      HOL/Tools/Nitpick/nitpick_preproc.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009, 2010
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Nitpick's HOL preprocessor.
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*)
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signature NITPICK_PREPROC =
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sig
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  type hol_context = Nitpick_HOL.hol_context
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  val preprocess_formulas :
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    hol_context -> term list -> term
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    -> term list * term list * bool * bool * bool
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end;
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structure Nitpick_Preproc : NITPICK_PREPROC =
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struct
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open Nitpick_Util
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open Nitpick_HOL
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open Nitpick_Mono
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fun is_positive_existential polar quant_s =
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  (polar = Pos andalso quant_s = @{const_name Ex}) orelse
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  (polar = Neg andalso quant_s <> @{const_name Ex})
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val is_descr =
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  member (op =) [@{const_name The}, @{const_name Eps}, @{const_name safe_The}]
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(** Binary coding of integers **)
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(* If a formula contains a numeral whose absolute value is more than this
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   threshold, the unary coding is likely not to work well and we prefer the
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   binary coding. *)
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val binary_int_threshold = 3
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val may_use_binary_ints =
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  let
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    fun aux def (Const (@{const_name "=="}, _) $ t1 $ t2) =
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        aux def t1 andalso aux false t2
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      | aux def (@{const "==>"} $ t1 $ t2) = aux false t1 andalso aux def t2
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      | aux def (Const (@{const_name HOL.eq}, _) $ t1 $ t2) =
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        aux def t1 andalso aux false t2
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      | aux def (@{const HOL.implies} $ t1 $ t2) = aux false t1 andalso aux def t2
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      | aux def (t1 $ t2) = aux def t1 andalso aux def t2
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      | aux def (t as Const (s, _)) =
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        (not def orelse t <> @{const Suc}) andalso
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        not (member (op =) [@{const_name Abs_Frac}, @{const_name Rep_Frac},
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                            @{const_name nat_gcd}, @{const_name nat_lcm},
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                            @{const_name Frac}, @{const_name norm_frac}] s)
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      | aux def (Abs (_, _, t')) = aux def t'
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      | aux _ _ = true
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  in aux end
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val should_use_binary_ints =
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  let
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    fun aux (t1 $ t2) = aux t1 orelse aux t2
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      | aux (Const (s, T)) =
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        ((s = @{const_name times} orelse s = @{const_name div}) andalso
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         is_integer_type (body_type T)) orelse
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        (String.isPrefix numeral_prefix s andalso
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         let val n = the (Int.fromString (unprefix numeral_prefix s)) in
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           n < ~ binary_int_threshold orelse n > binary_int_threshold
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         end)
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      | aux (Abs (_, _, t')) = aux t'
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      | aux _ = false
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  in aux end
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(** Uncurrying **)
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fun add_to_uncurry_table ctxt t =
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  let
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    val thy = ProofContext.theory_of ctxt
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    fun aux (t1 $ t2) args table =
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        let val table = aux t2 [] table in aux t1 (t2 :: args) table end
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      | aux (Abs (_, _, t')) _ table = aux t' [] table
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      | aux (t as Const (x as (s, _))) args table =
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        if is_built_in_const thy [(NONE, true)] x orelse
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           is_constr_like ctxt x orelse
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           is_sel s orelse s = @{const_name Sigma} then
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          table
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        else
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          Termtab.map_default (t, 65536) (Integer.min (length args)) table
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      | aux _ _ table = table
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  in aux t [] end
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fun uncurry_prefix_for k j =
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  uncurry_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
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fun uncurry_term table t =
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  let
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    fun aux (t1 $ t2) args = aux t1 (aux t2 [] :: args)
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      | aux (Abs (s, T, t')) args = s_betapplys [] (Abs (s, T, aux t' []), args)
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      | aux (t as Const (s, T)) args =
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        (case Termtab.lookup table t of
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           SOME n =>
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           if n >= 2 then
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             let
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               val arg_Ts = strip_n_binders n T |> fst
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               val j =
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                 if is_iterator_type (hd arg_Ts) then
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                   1
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                 else case find_index (not_equal bool_T) arg_Ts of
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                   ~1 => n
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                 | j => j
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               val ((before_args, tuple_args), after_args) =
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                 args |> chop n |>> chop j
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               val ((before_arg_Ts, tuple_arg_Ts), rest_T) =
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                 T |> strip_n_binders n |>> chop j
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               val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
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             in
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               if n - j < 2 then
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                 s_betapplys [] (t, args)
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               else
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                 s_betapplys []
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                     (Const (uncurry_prefix_for (n - j) j ^ s,
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                             before_arg_Ts ---> tuple_T --> rest_T),
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                      before_args @ [mk_flat_tuple tuple_T tuple_args] @
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                      after_args)
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             end
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           else
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             s_betapplys [] (t, args)
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         | NONE => s_betapplys [] (t, args))
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      | aux t args = s_betapplys [] (t, args)
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  in aux t [] end
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(** Boxing **)
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fun box_fun_and_pair_in_term (hol_ctxt as {ctxt, thy, stds, ...}) def orig_t =
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  let
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    fun box_relational_operator_type (Type (@{type_name fun}, Ts)) =
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        Type (@{type_name fun}, map box_relational_operator_type Ts)
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      | box_relational_operator_type (Type (@{type_name prod}, Ts)) =
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        Type (@{type_name prod}, map (box_type hol_ctxt InPair) Ts)
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      | box_relational_operator_type T = T
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    fun add_boxed_types_for_var (z as (_, T)) (T', t') =
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      case t' of
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        Var z' => z' = z ? insert (op =) T'
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      | Const (@{const_name Pair}, _) $ t1 $ t2 =>
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        (case T' of
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           Type (_, [T1, T2]) =>
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           fold (add_boxed_types_for_var z) [(T1, t1), (T2, t2)]
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         | _ => raise TYPE ("Nitpick_Preproc.box_fun_and_pair_in_term.\
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                            \add_boxed_types_for_var", [T'], []))
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      | _ => exists_subterm (curry (op =) (Var z)) t' ? insert (op =) T
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    fun box_var_in_def new_Ts old_Ts t (z as (_, T)) =
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      case t of
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        @{const Trueprop} $ t1 => box_var_in_def new_Ts old_Ts t1 z
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      | Const (s0, _) $ t1 $ _ =>
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        if s0 = @{const_name "=="} orelse s0 = @{const_name HOL.eq} then
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          let
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            val (t', args) = strip_comb t1
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            val T' = fastype_of1 (new_Ts, do_term new_Ts old_Ts Neut t')
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          in
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            case fold (add_boxed_types_for_var z)
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                      (fst (strip_n_binders (length args) T') ~~ args) [] of
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              [T''] => T''
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            | _ => T
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          end
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        else
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          T
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      | _ => T
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    and do_quantifier new_Ts old_Ts polar quant_s quant_T abs_s abs_T t =
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      let
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        val abs_T' =
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          if polar = Neut orelse is_positive_existential polar quant_s then
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            box_type hol_ctxt InFunLHS abs_T
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          else
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            abs_T
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        val body_T = body_type quant_T
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      in
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        Const (quant_s, (abs_T' --> body_T) --> body_T)
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        $ Abs (abs_s, abs_T',
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               t |> do_term (abs_T' :: new_Ts) (abs_T :: old_Ts) polar)
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      end
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    and do_equals new_Ts old_Ts s0 T0 t1 t2 =
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      let
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        val (t1, t2) = pairself (do_term new_Ts old_Ts Neut) (t1, t2)
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        val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)
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        val T = if def then T1
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                else [T1, T2] |> sort (int_ord o pairself size_of_typ) |> hd
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      in
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        list_comb (Const (s0, T --> T --> body_type T0),
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                   map2 (coerce_term hol_ctxt new_Ts T) [T1, T2] [t1, t2])
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      end
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    and do_descr s T =
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      let val T1 = box_type hol_ctxt InFunLHS (range_type T) in
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        Const (s, (T1 --> bool_T) --> T1)
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      end
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    and do_term new_Ts old_Ts polar t =
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      case t of
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        Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
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        do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
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      | Const (s0 as @{const_name "=="}, T0) $ t1 $ t2 =>
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        do_equals new_Ts old_Ts s0 T0 t1 t2
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      | @{const "==>"} $ t1 $ t2 =>
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        @{const "==>"} $ do_term new_Ts old_Ts (flip_polarity polar) t1
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        $ do_term new_Ts old_Ts polar t2
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      | @{const Pure.conjunction} $ t1 $ t2 =>
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        @{const Pure.conjunction} $ do_term new_Ts old_Ts polar t1
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        $ do_term new_Ts old_Ts polar t2
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      | @{const Trueprop} $ t1 =>
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        @{const Trueprop} $ do_term new_Ts old_Ts polar t1
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      | @{const Not} $ t1 =>
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        @{const Not} $ do_term new_Ts old_Ts (flip_polarity polar) t1
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      | Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
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        do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
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      | Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
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        do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
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      | Const (s0 as @{const_name HOL.eq}, T0) $ t1 $ t2 =>
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        do_equals new_Ts old_Ts s0 T0 t1 t2
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      | @{const HOL.conj} $ t1 $ t2 =>
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        @{const HOL.conj} $ do_term new_Ts old_Ts polar t1
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        $ do_term new_Ts old_Ts polar t2
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      | @{const HOL.disj} $ t1 $ t2 =>
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        @{const HOL.disj} $ do_term new_Ts old_Ts polar t1
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        $ do_term new_Ts old_Ts polar t2
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      | @{const HOL.implies} $ t1 $ t2 =>
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        @{const HOL.implies} $ do_term new_Ts old_Ts (flip_polarity polar) t1
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        $ do_term new_Ts old_Ts polar t2
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      | Const (x as (s, T)) =>
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        if is_descr s then
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          do_descr s T
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        else
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          Const (s, if s = @{const_name converse} orelse
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                       s = @{const_name trancl} then
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                      box_relational_operator_type T
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                    else if String.isPrefix quot_normal_prefix s then
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                      let val T' = box_type hol_ctxt InFunLHS (domain_type T) in
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                        T' --> T'
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                      end
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                    else if is_built_in_const thy stds x orelse
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                            s = @{const_name Sigma} then
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                      T
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                    else if is_constr_like ctxt x then
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                      box_type hol_ctxt InConstr T
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                    else if is_sel s orelse is_rep_fun ctxt x then
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                      box_type hol_ctxt InSel T
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                    else
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                      box_type hol_ctxt InExpr T)
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      | t1 $ Abs (s, T, t2') =>
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        let
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          val t1 = do_term new_Ts old_Ts Neut t1
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          val T1 = fastype_of1 (new_Ts, t1)
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          val (s1, Ts1) = dest_Type T1
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          val T' = hd (snd (dest_Type (hd Ts1)))
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          val t2 = Abs (s, T', do_term (T' :: new_Ts) (T :: old_Ts) Neut t2')
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          val T2 = fastype_of1 (new_Ts, t2)
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          val t2 = coerce_term hol_ctxt new_Ts (hd Ts1) T2 t2
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        in
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          s_betapply new_Ts (if s1 = @{type_name fun} then
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                               t1
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                             else
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                               select_nth_constr_arg ctxt stds
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                                   (@{const_name FunBox},
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                                    Type (@{type_name fun}, Ts1) --> T1) t1 0
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                                   (Type (@{type_name fun}, Ts1)), t2)
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        end
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      | t1 $ t2 =>
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        let
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          val t1 = do_term new_Ts old_Ts Neut t1
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          val T1 = fastype_of1 (new_Ts, t1)
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          val (s1, Ts1) = dest_Type T1
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          val t2 = do_term new_Ts old_Ts Neut t2
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          val T2 = fastype_of1 (new_Ts, t2)
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          val t2 = coerce_term hol_ctxt new_Ts (hd Ts1) T2 t2
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        in
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          s_betapply new_Ts (if s1 = @{type_name fun} then
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                               t1
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                             else
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                               select_nth_constr_arg ctxt stds
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                                   (@{const_name FunBox},
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                                    Type (@{type_name fun}, Ts1) --> T1) t1 0
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                                   (Type (@{type_name fun}, Ts1)), t2)
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        end
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      | Free (s, T) => Free (s, box_type hol_ctxt InExpr T)
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      | Var (z as (x, T)) =>
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        Var (x, if def then box_var_in_def new_Ts old_Ts orig_t z
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                else box_type hol_ctxt InExpr T)
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      | Bound _ => t
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      | Abs (s, T, t') =>
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        Abs (s, T, do_term (T :: new_Ts) (T :: old_Ts) Neut t')
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  in do_term [] [] Pos orig_t end
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(** Destruction of constructors **)
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val val_var_prefix = nitpick_prefix ^ "v"
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fun fresh_value_var Ts k n j t =
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  Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
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fun has_heavy_bounds_or_vars Ts t =
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  let
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    fun aux [] = false
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      | aux [T] = is_fun_type T orelse is_pair_type T
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      | aux _ = true
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  in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
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fun pull_out_constr_comb ({ctxt, stds, ...} : hol_context) Ts relax k level t
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                         args seen =
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  let val t_comb = list_comb (t, args) in
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   301
    case t of
blanchet@35070
   302
      Const x =>
blanchet@37256
   303
      if not relax andalso is_constr ctxt stds x andalso
blanchet@35070
   304
         not (is_fun_type (fastype_of1 (Ts, t_comb))) andalso
blanchet@35280
   305
         has_heavy_bounds_or_vars Ts t_comb andalso
blanchet@35070
   306
         not (loose_bvar (t_comb, level)) then
blanchet@35070
   307
        let
blanchet@35070
   308
          val (j, seen) = case find_index (curry (op =) t_comb) seen of
blanchet@35070
   309
                            ~1 => (0, t_comb :: seen)
blanchet@35070
   310
                          | j => (j, seen)
blanchet@35070
   311
        in (fresh_value_var Ts k (length seen) j t_comb, seen) end
blanchet@35070
   312
      else
blanchet@35070
   313
        (t_comb, seen)
blanchet@35070
   314
    | _ => (t_comb, seen)
blanchet@35070
   315
  end
blanchet@35070
   316
blanchet@35070
   317
fun equations_for_pulled_out_constrs mk_eq Ts k seen =
blanchet@35070
   318
  let val n = length seen in
blanchet@35070
   319
    map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
blanchet@35070
   320
         (index_seq 0 n) seen
blanchet@35070
   321
  end
blanchet@35070
   322
blanchet@35220
   323
fun pull_out_universal_constrs hol_ctxt def t =
blanchet@35070
   324
  let
blanchet@35070
   325
    val k = maxidx_of_term t + 1
blanchet@35070
   326
    fun do_term Ts def t args seen =
blanchet@35070
   327
      case t of
blanchet@35070
   328
        (t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
blanchet@35070
   329
        do_eq_or_imp Ts true def t0 t1 t2 seen
blanchet@35070
   330
      | (t0 as @{const "==>"}) $ t1 $ t2 =>
blanchet@35070
   331
        if def then (t, []) else do_eq_or_imp Ts false def t0 t1 t2 seen
haftmann@38864
   332
      | (t0 as Const (@{const_name HOL.eq}, _)) $ t1 $ t2 =>
blanchet@35070
   333
        do_eq_or_imp Ts true def t0 t1 t2 seen
haftmann@38786
   334
      | (t0 as @{const HOL.implies}) $ t1 $ t2 =>
blanchet@35070
   335
        do_eq_or_imp Ts false def t0 t1 t2 seen
blanchet@35070
   336
      | Abs (s, T, t') =>
blanchet@35070
   337
        let val (t', seen) = do_term (T :: Ts) def t' [] seen in
blanchet@35070
   338
          (list_comb (Abs (s, T, t'), args), seen)
blanchet@35070
   339
        end
blanchet@35070
   340
      | t1 $ t2 =>
blanchet@35070
   341
        let val (t2, seen) = do_term Ts def t2 [] seen in
blanchet@35070
   342
          do_term Ts def t1 (t2 :: args) seen
blanchet@35070
   343
        end
blanchet@35220
   344
      | _ => pull_out_constr_comb hol_ctxt Ts def k 0 t args seen
blanchet@35070
   345
    and do_eq_or_imp Ts eq def t0 t1 t2 seen =
blanchet@35070
   346
      let
blanchet@35070
   347
        val (t2, seen) = if eq andalso def then (t2, seen)
blanchet@35070
   348
                         else do_term Ts false t2 [] seen
blanchet@35070
   349
        val (t1, seen) = do_term Ts false t1 [] seen
blanchet@35070
   350
      in (t0 $ t1 $ t2, seen) end
blanchet@35070
   351
    val (concl, seen) = do_term [] def t [] []
blanchet@35070
   352
  in
blanchet@35070
   353
    Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
blanchet@35070
   354
                                                         seen, concl)
blanchet@35070
   355
  end
blanchet@35070
   356
blanchet@35070
   357
fun mk_exists v t =
blanchet@35070
   358
  HOLogic.exists_const (fastype_of v) $ lambda v (incr_boundvars 1 t)
blanchet@35070
   359
blanchet@35220
   360
fun pull_out_existential_constrs hol_ctxt t =
blanchet@35070
   361
  let
blanchet@35070
   362
    val k = maxidx_of_term t + 1
blanchet@35070
   363
    fun aux Ts num_exists t args seen =
blanchet@35070
   364
      case t of
blanchet@35070
   365
        (t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1) =>
blanchet@35070
   366
        let
blanchet@35070
   367
          val (t1, seen') = aux (T1 :: Ts) (num_exists + 1) t1 [] []
blanchet@35070
   368
          val n = length seen'
blanchet@35070
   369
          fun vars () = map2 (fresh_value_var Ts k n) (index_seq 0 n) seen'
blanchet@35070
   370
        in
blanchet@35070
   371
          (equations_for_pulled_out_constrs HOLogic.mk_eq Ts k seen'
blanchet@35070
   372
           |> List.foldl s_conj t1 |> fold mk_exists (vars ())
blanchet@35070
   373
           |> curry3 Abs s1 T1 |> curry (op $) t0, seen)
blanchet@35070
   374
        end
blanchet@35070
   375
      | t1 $ t2 =>
blanchet@35070
   376
        let val (t2, seen) = aux Ts num_exists t2 [] seen in
blanchet@35070
   377
          aux Ts num_exists t1 (t2 :: args) seen
blanchet@35070
   378
        end
blanchet@35070
   379
      | Abs (s, T, t') =>
blanchet@35070
   380
        let
blanchet@35070
   381
          val (t', seen) = aux (T :: Ts) 0 t' [] (map (incr_boundvars 1) seen)
blanchet@35070
   382
        in (list_comb (Abs (s, T, t'), args), map (incr_boundvars ~1) seen) end
blanchet@35070
   383
      | _ =>
blanchet@35070
   384
        if num_exists > 0 then
blanchet@35220
   385
          pull_out_constr_comb hol_ctxt Ts false k num_exists t args seen
blanchet@35070
   386
        else
blanchet@35070
   387
          (list_comb (t, args), seen)
blanchet@35070
   388
  in aux [] 0 t [] [] |> fst end
blanchet@35070
   389
blanchet@37256
   390
fun destroy_pulled_out_constrs (hol_ctxt as {ctxt, stds, ...}) axiom t =
blanchet@35070
   391
  let
blanchet@35070
   392
    val num_occs_of_var =
blanchet@35070
   393
      fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
blanchet@35070
   394
                    | _ => I) t (K 0)
blanchet@35070
   395
    fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
blanchet@35070
   396
        aux_eq careful true t0 t1 t2
blanchet@35070
   397
      | aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
blanchet@35070
   398
        t0 $ aux false t1 $ aux careful t2
haftmann@38864
   399
      | aux careful ((t0 as Const (@{const_name HOL.eq}, _)) $ t1 $ t2) =
blanchet@35070
   400
        aux_eq careful true t0 t1 t2
haftmann@38786
   401
      | aux careful ((t0 as @{const HOL.implies}) $ t1 $ t2) =
blanchet@35070
   402
        t0 $ aux false t1 $ aux careful t2
blanchet@35070
   403
      | aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
blanchet@35070
   404
      | aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
blanchet@35070
   405
      | aux _ t = t
blanchet@35070
   406
    and aux_eq careful pass1 t0 t1 t2 =
blanchet@35070
   407
      ((if careful then
blanchet@35070
   408
          raise SAME ()
blanchet@35070
   409
        else if axiom andalso is_Var t2 andalso
blanchet@35070
   410
                num_occs_of_var (dest_Var t2) = 1 then
blanchet@35070
   411
          @{const True}
blanchet@35070
   412
        else case strip_comb t2 of
blanchet@35070
   413
          (* The first case is not as general as it could be. *)
blanchet@35070
   414
          (Const (@{const_name PairBox}, _),
blanchet@35070
   415
                  [Const (@{const_name fst}, _) $ Var z1,
blanchet@35070
   416
                   Const (@{const_name snd}, _) $ Var z2]) =>
blanchet@35070
   417
          if z1 = z2 andalso num_occs_of_var z1 = 2 then @{const True}
blanchet@35070
   418
          else raise SAME ()
blanchet@35070
   419
        | (Const (x as (s, T)), args) =>
blanchet@35386
   420
          let
blanchet@35386
   421
            val (arg_Ts, dataT) = strip_type T
blanchet@35386
   422
            val n = length arg_Ts
blanchet@35386
   423
          in
blanchet@35386
   424
            if length args = n andalso
blanchet@37256
   425
               (is_constr ctxt stds x orelse s = @{const_name Pair} orelse
blanchet@35386
   426
                x = (@{const_name Suc}, nat_T --> nat_T)) andalso
blanchet@35070
   427
               (not careful orelse not (is_Var t1) orelse
blanchet@35070
   428
                String.isPrefix val_var_prefix (fst (fst (dest_Var t1)))) then
blanchet@37476
   429
                s_let "l" (n + 1) dataT bool_T
blanchet@37476
   430
                      (fn t1 => discriminate_value hol_ctxt x t1 ::
blanchet@37476
   431
                                map3 (sel_eq x t1) (index_seq 0 n) arg_Ts args
blanchet@37476
   432
                                |> foldr1 s_conj) t1
blanchet@35070
   433
            else
blanchet@35070
   434
              raise SAME ()
blanchet@35070
   435
          end
blanchet@35070
   436
        | _ => raise SAME ())
blanchet@35070
   437
       |> body_type (type_of t0) = prop_T ? HOLogic.mk_Trueprop)
blanchet@35070
   438
      handle SAME () => if pass1 then aux_eq careful false t0 t2 t1
blanchet@35070
   439
                        else t0 $ aux false t2 $ aux false t1
blanchet@35070
   440
    and sel_eq x t n nth_T nth_t =
blanchet@35220
   441
      HOLogic.eq_const nth_T $ nth_t
blanchet@37256
   442
                             $ select_nth_constr_arg ctxt stds x t n nth_T
blanchet@35070
   443
      |> aux false
blanchet@35070
   444
  in aux axiom t end
blanchet@35070
   445
blanchet@35070
   446
(** Destruction of universal and existential equalities **)
blanchet@35070
   447
blanchet@35070
   448
fun curry_assms (@{const "==>"} $ (@{const Trueprop}
haftmann@38795
   449
                                   $ (@{const HOL.conj} $ t1 $ t2)) $ t3) =
blanchet@35070
   450
    curry_assms (Logic.list_implies ([t1, t2] |> map HOLogic.mk_Trueprop, t3))
blanchet@35070
   451
  | curry_assms (@{const "==>"} $ t1 $ t2) =
blanchet@35070
   452
    @{const "==>"} $ curry_assms t1 $ curry_assms t2
blanchet@35070
   453
  | curry_assms t = t
blanchet@35070
   454
blanchet@35070
   455
val destroy_universal_equalities =
blanchet@35070
   456
  let
blanchet@35070
   457
    fun aux prems zs t =
blanchet@35070
   458
      case t of
blanchet@35070
   459
        @{const "==>"} $ t1 $ t2 => aux_implies prems zs t1 t2
blanchet@35070
   460
      | _ => Logic.list_implies (rev prems, t)
blanchet@35070
   461
    and aux_implies prems zs t1 t2 =
blanchet@35070
   462
      case t1 of
blanchet@35070
   463
        Const (@{const_name "=="}, _) $ Var z $ t' => aux_eq prems zs z t' t1 t2
haftmann@38864
   464
      | @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ Var z $ t') =>
blanchet@35070
   465
        aux_eq prems zs z t' t1 t2
haftmann@38864
   466
      | @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ t' $ Var z) =>
blanchet@35070
   467
        aux_eq prems zs z t' t1 t2
blanchet@35070
   468
      | _ => aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@35070
   469
    and aux_eq prems zs z t' t1 t2 =
blanchet@35070
   470
      if not (member (op =) zs z) andalso
blanchet@35070
   471
         not (exists_subterm (curry (op =) (Var z)) t') then
blanchet@35070
   472
        aux prems zs (subst_free [(Var z, t')] t2)
blanchet@35070
   473
      else
blanchet@35070
   474
        aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@35070
   475
  in aux [] [] end
blanchet@35070
   476
blanchet@37256
   477
fun find_bound_assign ctxt stds j =
blanchet@35220
   478
  let
blanchet@35220
   479
    fun do_term _ [] = NONE
blanchet@35220
   480
      | do_term seen (t :: ts) =
blanchet@35220
   481
        let
blanchet@35220
   482
          fun do_eq pass1 t1 t2 =
blanchet@35220
   483
            (if loose_bvar1 (t2, j) then
blanchet@35220
   484
               if pass1 then do_eq false t2 t1 else raise SAME ()
blanchet@35220
   485
             else case t1 of
blanchet@35220
   486
               Bound j' => if j' = j then SOME (t2, ts @ seen) else raise SAME ()
blanchet@35665
   487
             | Const (s, Type (@{type_name fun}, [T1, T2])) $ Bound j' =>
blanchet@35220
   488
               if j' = j andalso
blanchet@35220
   489
                  s = nth_sel_name_for_constr_name @{const_name FunBox} 0 then
blanchet@37256
   490
                 SOME (construct_value ctxt stds
blanchet@37256
   491
                                       (@{const_name FunBox}, T2 --> T1) [t2],
blanchet@37256
   492
                       ts @ seen)
blanchet@35220
   493
               else
blanchet@35220
   494
                 raise SAME ()
blanchet@35220
   495
             | _ => raise SAME ())
blanchet@35220
   496
            handle SAME () => do_term (t :: seen) ts
blanchet@35220
   497
        in
blanchet@35220
   498
          case t of
haftmann@38864
   499
            Const (@{const_name HOL.eq}, _) $ t1 $ t2 => do_eq true t1 t2
blanchet@35220
   500
          | _ => do_term (t :: seen) ts
blanchet@35220
   501
        end
blanchet@35220
   502
  in do_term end
blanchet@35070
   503
blanchet@35070
   504
fun subst_one_bound j arg t =
blanchet@35070
   505
  let
blanchet@35070
   506
    fun aux (Bound i, lev) =
blanchet@35070
   507
        if i < lev then raise SAME ()
blanchet@35070
   508
        else if i = lev then incr_boundvars (lev - j) arg
blanchet@35070
   509
        else Bound (i - 1)
blanchet@35070
   510
      | aux (Abs (a, T, body), lev) = Abs (a, T, aux (body, lev + 1))
blanchet@35070
   511
      | aux (f $ t, lev) =
blanchet@35070
   512
        (aux (f, lev) $ (aux (t, lev) handle SAME () => t)
blanchet@35070
   513
         handle SAME () => f $ aux (t, lev))
blanchet@35070
   514
      | aux _ = raise SAME ()
blanchet@35070
   515
  in aux (t, j) handle SAME () => t end
blanchet@35070
   516
blanchet@37256
   517
fun destroy_existential_equalities ({ctxt, stds, ...} : hol_context) =
blanchet@35070
   518
  let
blanchet@35070
   519
    fun kill [] [] ts = foldr1 s_conj ts
blanchet@35070
   520
      | kill (s :: ss) (T :: Ts) ts =
blanchet@37256
   521
        (case find_bound_assign ctxt stds (length ss) [] ts of
blanchet@35070
   522
           SOME (_, []) => @{const True}
blanchet@35070
   523
         | SOME (arg_t, ts) =>
blanchet@35070
   524
           kill ss Ts (map (subst_one_bound (length ss)
blanchet@35070
   525
                                (incr_bv (~1, length ss + 1, arg_t))) ts)
blanchet@35070
   526
         | NONE =>
blanchet@35070
   527
           Const (@{const_name Ex}, (T --> bool_T) --> bool_T)
blanchet@35070
   528
           $ Abs (s, T, kill ss Ts ts))
wenzelm@40722
   529
      | kill _ _ _ = raise ListPair.UnequalLengths
blanchet@35280
   530
    fun gather ss Ts (Const (@{const_name Ex}, _) $ Abs (s1, T1, t1)) =
blanchet@35070
   531
        gather (ss @ [s1]) (Ts @ [T1]) t1
blanchet@35070
   532
      | gather [] [] (Abs (s, T, t1)) = Abs (s, T, gather [] [] t1)
blanchet@35070
   533
      | gather [] [] (t1 $ t2) = gather [] [] t1 $ gather [] [] t2
blanchet@35070
   534
      | gather [] [] t = t
blanchet@35070
   535
      | gather ss Ts t = kill ss Ts (conjuncts_of (gather [] [] t))
blanchet@35070
   536
  in gather [] [] end
blanchet@35070
   537
blanchet@35070
   538
(** Skolemization **)
blanchet@35070
   539
blanchet@35070
   540
fun skolem_prefix_for k j =
blanchet@35070
   541
  skolem_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
blanchet@35070
   542
blanchet@35070
   543
fun skolemize_term_and_more (hol_ctxt as {thy, def_table, skolems, ...})
blanchet@35070
   544
                            skolem_depth =
blanchet@35070
   545
  let
blanchet@35070
   546
    val incrs = map (Integer.add 1)
blanchet@37928
   547
    fun aux ss Ts js skolemizable polar t =
blanchet@35070
   548
      let
blanchet@35070
   549
        fun do_quantifier quant_s quant_T abs_s abs_T t =
blanchet@37928
   550
          (if not (loose_bvar1 (t, 0)) then
blanchet@37928
   551
             aux ss Ts js skolemizable polar (incr_boundvars ~1 t)
blanchet@37928
   552
           else if is_positive_existential polar quant_s then
blanchet@37928
   553
             let
blanchet@37928
   554
               val j = length (!skolems) + 1
blanchet@37928
   555
               val (js', (ss', Ts')) =
blanchet@37928
   556
                 js ~~ (ss ~~ Ts)
blanchet@37928
   557
                 |> filter (fn (j, _) => loose_bvar1 (t, j + 1))
blanchet@37928
   558
                 |> ListPair.unzip ||> ListPair.unzip
blanchet@37928
   559
             in
blanchet@37928
   560
               if skolemizable andalso length js' <= skolem_depth then
blanchet@37928
   561
                 let
blanchet@37928
   562
                   val sko_s = skolem_prefix_for (length js') j ^ abs_s
blanchet@37928
   563
                   val _ = Unsynchronized.change skolems (cons (sko_s, ss'))
blanchet@37928
   564
                   val sko_t = list_comb (Const (sko_s, rev Ts' ---> abs_T),
blanchet@37928
   565
                                          map Bound (rev js'))
blanchet@37928
   566
                   val abs_t = Abs (abs_s, abs_T,
blanchet@37928
   567
                                    aux ss Ts (incrs js) skolemizable polar t)
blanchet@37928
   568
                 in
blanchet@37928
   569
                   if null js' then
blanchet@37928
   570
                     s_betapply Ts (abs_t, sko_t)
blanchet@35070
   571
                   else
blanchet@37928
   572
                     Const (@{const_name Let}, abs_T --> quant_T) $ sko_t
blanchet@37928
   573
                     $ abs_t
blanchet@37928
   574
                 end
blanchet@37928
   575
               else
blanchet@37928
   576
                 raise SAME ()
blanchet@37928
   577
             end
blanchet@37928
   578
           else
blanchet@37928
   579
             raise SAME ())
blanchet@37928
   580
          handle SAME () =>
blanchet@37928
   581
                 Const (quant_s, quant_T)
blanchet@37928
   582
                 $ Abs (abs_s, abs_T,
blanchet@38166
   583
                        aux (abs_s :: ss) (abs_T :: Ts) (0 :: incrs js)
blanchet@38166
   584
                            (skolemizable andalso
blanchet@38166
   585
                             not (is_higher_order_type abs_T)) polar t)
blanchet@35070
   586
      in
blanchet@35070
   587
        case t of
blanchet@35070
   588
          Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
blanchet@35070
   589
          do_quantifier s0 T0 s1 T1 t1
blanchet@35070
   590
        | @{const "==>"} $ t1 $ t2 =>
blanchet@37928
   591
          @{const "==>"} $ aux ss Ts js skolemizable (flip_polarity polar) t1
blanchet@37928
   592
          $ aux ss Ts js skolemizable polar t2
blanchet@35070
   593
        | @{const Pure.conjunction} $ t1 $ t2 =>
blanchet@37928
   594
          @{const Pure.conjunction} $ aux ss Ts js skolemizable polar t1
blanchet@37928
   595
          $ aux ss Ts js skolemizable polar t2
blanchet@35070
   596
        | @{const Trueprop} $ t1 =>
blanchet@37928
   597
          @{const Trueprop} $ aux ss Ts js skolemizable polar t1
blanchet@35070
   598
        | @{const Not} $ t1 =>
blanchet@37928
   599
          @{const Not} $ aux ss Ts js skolemizable (flip_polarity polar) t1
blanchet@35070
   600
        | Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
blanchet@35070
   601
          do_quantifier s0 T0 s1 T1 t1
blanchet@35070
   602
        | Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
blanchet@35070
   603
          do_quantifier s0 T0 s1 T1 t1
haftmann@38795
   604
        | @{const HOL.conj} $ t1 $ t2 =>
blanchet@37928
   605
          s_conj (pairself (aux ss Ts js skolemizable polar) (t1, t2))
haftmann@38795
   606
        | @{const HOL.disj} $ t1 $ t2 =>
blanchet@37928
   607
          s_disj (pairself (aux ss Ts js skolemizable polar) (t1, t2))
haftmann@38786
   608
        | @{const HOL.implies} $ t1 $ t2 =>
haftmann@38786
   609
          @{const HOL.implies} $ aux ss Ts js skolemizable (flip_polarity polar) t1
blanchet@37928
   610
          $ aux ss Ts js skolemizable polar t2
blanchet@35280
   611
        | (t0 as Const (@{const_name Let}, _)) $ t1 $ t2 =>
blanchet@37928
   612
          t0 $ t1 $ aux ss Ts js skolemizable polar t2
blanchet@35070
   613
        | Const (x as (s, T)) =>
blanchet@38205
   614
          if is_real_inductive_pred hol_ctxt x andalso
blanchet@38205
   615
             not (is_real_equational_fun hol_ctxt x) andalso
blanchet@35070
   616
             not (is_well_founded_inductive_pred hol_ctxt x) then
blanchet@35070
   617
            let
blanchet@35070
   618
              val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@37476
   619
              val (pref, connective) =
haftmann@38795
   620
                if gfp then (lbfp_prefix, @{const HOL.disj})
haftmann@38795
   621
                else (ubfp_prefix, @{const HOL.conj})
blanchet@35070
   622
              fun pos () = unrolled_inductive_pred_const hol_ctxt gfp x
blanchet@37928
   623
                           |> aux ss Ts js skolemizable polar
blanchet@35070
   624
              fun neg () = Const (pref ^ s, T)
blanchet@35070
   625
            in
blanchet@37476
   626
              case polar |> gfp ? flip_polarity of
blanchet@37476
   627
                Pos => pos ()
blanchet@37476
   628
              | Neg => neg ()
blanchet@37476
   629
              | Neut =>
blanchet@37476
   630
                let
blanchet@37476
   631
                  val arg_Ts = binder_types T
blanchet@37476
   632
                  fun app f =
blanchet@37476
   633
                    list_comb (f (), map Bound (length arg_Ts - 1 downto 0))
blanchet@37476
   634
                in
blanchet@37476
   635
                  List.foldr absdummy (connective $ app pos $ app neg) arg_Ts
blanchet@37476
   636
                end
blanchet@35070
   637
            end
blanchet@35070
   638
          else
blanchet@35070
   639
            Const x
blanchet@35070
   640
        | t1 $ t2 =>
blanchet@38166
   641
          s_betapply Ts (aux ss Ts js false polar t1,
blanchet@38166
   642
                         aux ss Ts js false Neut t2)
blanchet@37928
   643
        | Abs (s, T, t1) =>
blanchet@37928
   644
          Abs (s, T, aux ss Ts (incrs js) skolemizable polar t1)
blanchet@35070
   645
        | _ => t
blanchet@35070
   646
      end
blanchet@37928
   647
  in aux [] [] [] true Pos end
blanchet@35070
   648
blanchet@35070
   649
(** Function specialization **)
blanchet@35070
   650
blanchet@35070
   651
fun params_in_equation (@{const "==>"} $ _ $ t2) = params_in_equation t2
blanchet@35070
   652
  | params_in_equation (@{const Trueprop} $ t1) = params_in_equation t1
haftmann@38864
   653
  | params_in_equation (Const (@{const_name HOL.eq}, _) $ t1 $ _) =
blanchet@35070
   654
    snd (strip_comb t1)
blanchet@35070
   655
  | params_in_equation _ = []
blanchet@35070
   656
blanchet@35070
   657
fun specialize_fun_axiom x x' fixed_js fixed_args extra_args t =
blanchet@35070
   658
  let
blanchet@35070
   659
    val k = fold Integer.max (map maxidx_of_term (fixed_args @ extra_args)) 0
blanchet@35070
   660
            + 1
blanchet@35070
   661
    val t = map_aterms (fn Var ((s, i), T) => Var ((s, k + i), T) | t' => t') t
blanchet@35070
   662
    val fixed_params = filter_indices fixed_js (params_in_equation t)
blanchet@35070
   663
    fun aux args (Abs (s, T, t)) = list_comb (Abs (s, T, aux [] t), args)
blanchet@35070
   664
      | aux args (t1 $ t2) = aux (aux [] t2 :: args) t1
blanchet@35070
   665
      | aux args t =
blanchet@35070
   666
        if t = Const x then
blanchet@35070
   667
          list_comb (Const x', extra_args @ filter_out_indices fixed_js args)
blanchet@35070
   668
        else
blanchet@35070
   669
          let val j = find_index (curry (op =) t) fixed_params in
blanchet@35070
   670
            list_comb (if j >= 0 then nth fixed_args j else t, args)
blanchet@35070
   671
          end
blanchet@35070
   672
  in aux [] t end
blanchet@35070
   673
blanchet@35070
   674
fun static_args_in_term ({ersatz_table, ...} : hol_context) x t =
blanchet@35070
   675
  let
blanchet@35070
   676
    fun fun_calls (Abs (_, _, t)) _ = fun_calls t []
blanchet@35070
   677
      | fun_calls (t1 $ t2) args = fun_calls t2 [] #> fun_calls t1 (t2 :: args)
blanchet@35070
   678
      | fun_calls t args =
blanchet@35070
   679
        (case t of
blanchet@35070
   680
           Const (x' as (s', T')) =>
blanchet@35070
   681
           x = x' orelse (case AList.lookup (op =) ersatz_table s' of
blanchet@35070
   682
                            SOME s'' => x = (s'', T')
blanchet@35070
   683
                          | NONE => false)
blanchet@35070
   684
         | _ => false) ? cons args
blanchet@35070
   685
    fun call_sets [] [] vs = [vs]
blanchet@35070
   686
      | call_sets [] uss vs = vs :: call_sets uss [] []
blanchet@35070
   687
      | call_sets ([] :: _) _ _ = []
blanchet@35070
   688
      | call_sets ((t :: ts) :: tss) uss vs =
wenzelm@39687
   689
        Ord_List.insert Term_Ord.term_ord t vs |> call_sets tss (ts :: uss)
blanchet@35070
   690
    val sets = call_sets (fun_calls t [] []) [] []
blanchet@35070
   691
    val indexed_sets = sets ~~ (index_seq 0 (length sets))
blanchet@35070
   692
  in
blanchet@35070
   693
    fold_rev (fn (set, j) =>
blanchet@35070
   694
                 case set of
blanchet@35070
   695
                   [Var _] => AList.lookup (op =) indexed_sets set = SOME j
blanchet@35070
   696
                              ? cons (j, NONE)
blanchet@35070
   697
                 | [t as Const _] => cons (j, SOME t)
blanchet@35070
   698
                 | [t as Free _] => cons (j, SOME t)
blanchet@35070
   699
                 | _ => I) indexed_sets []
blanchet@35070
   700
  end
blanchet@35070
   701
fun static_args_in_terms hol_ctxt x =
blanchet@35070
   702
  map (static_args_in_term hol_ctxt x)
wenzelm@39687
   703
  #> fold1 (Ord_List.inter (prod_ord int_ord (option_ord Term_Ord.term_ord)))
blanchet@35070
   704
blanchet@35070
   705
fun overlapping_indices [] _ = []
blanchet@35070
   706
  | overlapping_indices _ [] = []
blanchet@35070
   707
  | overlapping_indices (ps1 as (j1, t1) :: ps1') (ps2 as (j2, t2) :: ps2') =
blanchet@35070
   708
    if j1 < j2 then overlapping_indices ps1' ps2
blanchet@35070
   709
    else if j1 > j2 then overlapping_indices ps1 ps2'
blanchet@35070
   710
    else overlapping_indices ps1' ps2' |> the_default t2 t1 = t2 ? cons j1
blanchet@35070
   711
blanchet@35070
   712
fun is_eligible_arg Ts t =
blanchet@35070
   713
  let val bad_Ts = map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t) in
blanchet@35070
   714
    null bad_Ts orelse
blanchet@35070
   715
    (is_higher_order_type (fastype_of1 (Ts, t)) andalso
blanchet@35070
   716
     forall (not o is_higher_order_type) bad_Ts)
blanchet@35070
   717
  end
blanchet@35070
   718
blanchet@35070
   719
fun special_prefix_for j = special_prefix ^ string_of_int j ^ name_sep
blanchet@35070
   720
blanchet@35070
   721
(* If a constant's definition is picked up deeper than this threshold, we
blanchet@35070
   722
   prevent excessive specialization by not specializing it. *)
blanchet@35070
   723
val special_max_depth = 20
blanchet@35070
   724
blanchet@35070
   725
val bound_var_prefix = "b"
blanchet@35070
   726
blanchet@38165
   727
fun special_fun_aconv ((x1, js1, ts1), (x2, js2, ts2)) =
blanchet@38165
   728
  x1 = x2 andalso js1 = js2 andalso length ts1 = length ts2 andalso
blanchet@38165
   729
  forall (op aconv) (ts1 ~~ ts2)
blanchet@38165
   730
blanchet@38204
   731
fun specialize_consts_in_term
blanchet@39359
   732
        (hol_ctxt as {ctxt, thy, stds, specialize, def_table, simp_table,
blanchet@39359
   733
                      special_funs, ...}) def depth t =
blanchet@35070
   734
  if not specialize orelse depth > special_max_depth then
blanchet@35070
   735
    t
blanchet@35070
   736
  else
blanchet@35070
   737
    let
blanchet@38206
   738
      val blacklist =
blanchet@38206
   739
        if def then case term_under_def t of Const x => [x] | _ => [] else []
blanchet@35070
   740
      fun aux args Ts (Const (x as (s, T))) =
blanchet@35070
   741
          ((if not (member (op =) blacklist x) andalso not (null args) andalso
blanchet@35070
   742
               not (String.isPrefix special_prefix s) andalso
blanchet@39359
   743
               not (is_built_in_const thy stds x) andalso
blanchet@38204
   744
               (is_equational_fun_but_no_plain_def hol_ctxt x orelse
blanchet@38204
   745
                (is_some (def_of_const thy def_table x) andalso
blanchet@38204
   746
                 not (is_of_class_const thy x) andalso
blanchet@38204
   747
                 not (is_constr ctxt stds x) andalso
blanchet@38204
   748
                 not (is_choice_spec_fun hol_ctxt x))) then
blanchet@35070
   749
              let
blanchet@35070
   750
                val eligible_args = filter (is_eligible_arg Ts o snd)
blanchet@35070
   751
                                           (index_seq 0 (length args) ~~ args)
blanchet@35070
   752
                val _ = not (null eligible_args) orelse raise SAME ()
blanchet@35070
   753
                val old_axs = equational_fun_axioms hol_ctxt x
blanchet@35220
   754
                              |> map (destroy_existential_equalities hol_ctxt)
blanchet@35070
   755
                val static_params = static_args_in_terms hol_ctxt x old_axs
blanchet@35070
   756
                val fixed_js = overlapping_indices static_params eligible_args
blanchet@35070
   757
                val _ = not (null fixed_js) orelse raise SAME ()
blanchet@35070
   758
                val fixed_args = filter_indices fixed_js args
blanchet@35070
   759
                val vars = fold Term.add_vars fixed_args []
wenzelm@35408
   760
                           |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@35070
   761
                val bound_js = fold (fn t => fn js => add_loose_bnos (t, 0, js))
blanchet@35070
   762
                                    fixed_args []
blanchet@35070
   763
                               |> sort int_ord
blanchet@35070
   764
                val live_args = filter_out_indices fixed_js args
blanchet@35070
   765
                val extra_args = map Var vars @ map Bound bound_js @ live_args
blanchet@35070
   766
                val extra_Ts = map snd vars @ filter_indices bound_js Ts
blanchet@35070
   767
                val k = maxidx_of_term t + 1
blanchet@35070
   768
                fun var_for_bound_no j =
blanchet@35070
   769
                  Var ((bound_var_prefix ^
blanchet@35070
   770
                        nat_subscript (find_index (curry (op =) j) bound_js
blanchet@35070
   771
                                       + 1), k),
blanchet@35070
   772
                       nth Ts j)
blanchet@35070
   773
                val fixed_args_in_axiom =
blanchet@35070
   774
                  map (curry subst_bounds
blanchet@35070
   775
                             (map var_for_bound_no (index_seq 0 (length Ts))))
blanchet@35070
   776
                      fixed_args
blanchet@35070
   777
              in
blanchet@38165
   778
                case AList.lookup special_fun_aconv (!special_funs)
blanchet@35070
   779
                                  (x, fixed_js, fixed_args_in_axiom) of
blanchet@35070
   780
                  SOME x' => list_comb (Const x', extra_args)
blanchet@35070
   781
                | NONE =>
blanchet@35070
   782
                  let
blanchet@35070
   783
                    val extra_args_in_axiom =
blanchet@35070
   784
                      map Var vars @ map var_for_bound_no bound_js
blanchet@35070
   785
                    val x' as (s', _) =
blanchet@35070
   786
                      (special_prefix_for (length (!special_funs) + 1) ^ s,
blanchet@35070
   787
                       extra_Ts @ filter_out_indices fixed_js (binder_types T)
blanchet@35070
   788
                       ---> body_type T)
blanchet@35070
   789
                    val new_axs =
blanchet@35070
   790
                      map (specialize_fun_axiom x x' fixed_js
blanchet@35070
   791
                               fixed_args_in_axiom extra_args_in_axiom) old_axs
blanchet@35070
   792
                    val _ =
blanchet@35070
   793
                      Unsynchronized.change special_funs
blanchet@35070
   794
                          (cons ((x, fixed_js, fixed_args_in_axiom), x'))
blanchet@35070
   795
                    val _ = add_simps simp_table s' new_axs
blanchet@35070
   796
                  in list_comb (Const x', extra_args) end
blanchet@35070
   797
              end
blanchet@35070
   798
            else
blanchet@35070
   799
              raise SAME ())
blanchet@35070
   800
           handle SAME () => list_comb (Const x, args))
blanchet@35070
   801
        | aux args Ts (Abs (s, T, t)) =
blanchet@35070
   802
          list_comb (Abs (s, T, aux [] (T :: Ts) t), args)
blanchet@35070
   803
        | aux args Ts (t1 $ t2) = aux (aux [] Ts t2 :: args) Ts t1
blanchet@35070
   804
        | aux args _ t = list_comb (t, args)
blanchet@35070
   805
    in aux [] [] t end
blanchet@35070
   806
blanchet@35070
   807
type special_triple = int list * term list * styp
blanchet@35070
   808
blanchet@35070
   809
val cong_var_prefix = "c"
blanchet@35070
   810
blanchet@35280
   811
fun special_congruence_axiom T (js1, ts1, x1) (js2, ts2, x2) =
blanchet@35070
   812
  let
blanchet@35070
   813
    val (bounds1, bounds2) = pairself (map Var o special_bounds) (ts1, ts2)
blanchet@35070
   814
    val Ts = binder_types T
blanchet@35070
   815
    val max_j = fold (fold Integer.max) [js1, js2] ~1
blanchet@35070
   816
    val (eqs, (args1, args2)) =
blanchet@35070
   817
      fold (fn j => case pairself (fn ps => AList.lookup (op =) ps j)
blanchet@35070
   818
                                  (js1 ~~ ts1, js2 ~~ ts2) of
blanchet@35070
   819
                      (SOME t1, SOME t2) => apfst (cons (t1, t2))
blanchet@35070
   820
                    | (SOME t1, NONE) => apsnd (apsnd (cons t1))
blanchet@35070
   821
                    | (NONE, SOME t2) => apsnd (apfst (cons t2))
blanchet@35070
   822
                    | (NONE, NONE) =>
blanchet@35070
   823
                      let val v = Var ((cong_var_prefix ^ nat_subscript j, 0),
blanchet@35070
   824
                                       nth Ts j) in
blanchet@35070
   825
                        apsnd (pairself (cons v))
blanchet@35070
   826
                      end) (max_j downto 0) ([], ([], []))
blanchet@35070
   827
  in
blanchet@38165
   828
    Logic.list_implies (eqs |> filter_out (op aconv) |> distinct (op =)
blanchet@35070
   829
                            |> map Logic.mk_equals,
blanchet@35070
   830
                        Logic.mk_equals (list_comb (Const x1, bounds1 @ args1),
blanchet@35070
   831
                                         list_comb (Const x2, bounds2 @ args2)))
blanchet@35070
   832
  end
blanchet@35070
   833
blanchet@38170
   834
fun special_congruence_axioms (hol_ctxt as {special_funs, ...}) ts =
blanchet@35070
   835
  let
blanchet@35070
   836
    val groups =
blanchet@35070
   837
      !special_funs
blanchet@35070
   838
      |> map (fn ((x, js, ts), x') => (x, (js, ts, x')))
blanchet@35070
   839
      |> AList.group (op =)
blanchet@35070
   840
      |> filter_out (is_equational_fun_surely_complete hol_ctxt o fst)
blanchet@38170
   841
      |> map (fn (x, zs) =>
blanchet@38170
   842
                 (x, zs |> member (op =) ts (Const x) ? cons ([], [], x)))
blanchet@35070
   843
    fun generality (js, _, _) = ~(length js)
blanchet@35070
   844
    fun is_more_specific (j1, t1, x1) (j2, t2, x2) =
blanchet@38165
   845
      x1 <> x2 andalso length j2 < length j1 andalso
wenzelm@39687
   846
      Ord_List.subset (prod_ord int_ord Term_Ord.term_ord) (j2 ~~ t2, j1 ~~ t1)
blanchet@35070
   847
    fun do_pass_1 _ [] [_] [_] = I
blanchet@35280
   848
      | do_pass_1 T skipped _ [] = do_pass_2 T skipped
blanchet@35280
   849
      | do_pass_1 T skipped all (z :: zs) =
blanchet@35070
   850
        case filter (is_more_specific z) all
blanchet@35070
   851
             |> sort (int_ord o pairself generality) of
blanchet@35280
   852
          [] => do_pass_1 T (z :: skipped) all zs
blanchet@35280
   853
        | (z' :: _) => cons (special_congruence_axiom T z z')
blanchet@35280
   854
                       #> do_pass_1 T skipped all zs
blanchet@35070
   855
    and do_pass_2 _ [] = I
blanchet@35280
   856
      | do_pass_2 T (z :: zs) =
blanchet@35280
   857
        fold (cons o special_congruence_axiom T z) zs #> do_pass_2 T zs
blanchet@35280
   858
  in fold (fn ((_, T), zs) => do_pass_1 T [] zs zs) groups [] end
blanchet@35070
   859
blanchet@35070
   860
(** Axiom selection **)
blanchet@35070
   861
blanchet@38169
   862
fun defined_free_by_assumption t =
blanchet@38169
   863
  let
blanchet@38170
   864
    fun do_equals x def =
blanchet@38170
   865
      if exists_subterm (curry (op aconv) (Free x)) def then NONE else SOME x
blanchet@38169
   866
  in
blanchet@38169
   867
    case t of
blanchet@38170
   868
      Const (@{const_name "=="}, _) $ Free x $ def => do_equals x def
blanchet@38170
   869
    | @{const Trueprop} $ (Const (@{const_name "=="}, _) $ Free x $ def) =>
blanchet@38170
   870
      do_equals x def
blanchet@38169
   871
    | _ => NONE
blanchet@38169
   872
  end
blanchet@38169
   873
blanchet@38169
   874
fun assumption_exclusively_defines_free assm_ts t =
blanchet@38169
   875
  case defined_free_by_assumption t of
blanchet@38170
   876
    SOME x =>
blanchet@38170
   877
    length (filter ((fn SOME x' => x = x' | NONE => false)
blanchet@38169
   878
                     o defined_free_by_assumption) assm_ts) = 1
blanchet@38169
   879
  | NONE => false
blanchet@38169
   880
blanchet@35070
   881
fun all_table_entries table = Symtab.fold (append o snd) table []
blanchet@35070
   882
fun extra_table table s = Symtab.make [(s, all_table_entries table)]
blanchet@35070
   883
blanchet@35070
   884
fun eval_axiom_for_term j t =
blanchet@35070
   885
  Logic.mk_equals (Const (eval_prefix ^ string_of_int j, fastype_of t), t)
blanchet@35070
   886
blanchet@35070
   887
val is_trivial_equation = the_default false o try (op aconv o Logic.dest_equals)
blanchet@35070
   888
blanchet@35070
   889
(* Prevents divergence in case of cyclic or infinite axiom dependencies. *)
blanchet@35070
   890
val axioms_max_depth = 255
blanchet@35070
   891
blanchet@35070
   892
fun axioms_for_term
blanchet@35311
   893
        (hol_ctxt as {thy, ctxt, max_bisim_depth, stds, user_axioms,
blanchet@39359
   894
                      evals, def_table, nondef_table, choice_spec_table,
blanchet@39359
   895
                      user_nondefs, ...}) assm_ts neg_t =
blanchet@35070
   896
  let
blanchet@38170
   897
    val (def_assm_ts, nondef_assm_ts) =
blanchet@38170
   898
      List.partition (assumption_exclusively_defines_free assm_ts) assm_ts
blanchet@38170
   899
    val def_assm_table = map (`(the o defined_free_by_assumption)) def_assm_ts
blanchet@35070
   900
    type accumulator = styp list * (term list * term list)
blanchet@38206
   901
    fun add_axiom get app def depth t (accum as (seen, axs)) =
blanchet@35070
   902
      let
blanchet@35070
   903
        val t = t |> unfold_defs_in_term hol_ctxt
blanchet@38206
   904
                  |> skolemize_term_and_more hol_ctxt ~1 (* FIXME: why ~1? *)
blanchet@35070
   905
      in
blanchet@35070
   906
        if is_trivial_equation t then
blanchet@35070
   907
          accum
blanchet@35070
   908
        else
blanchet@38206
   909
          let val t' = t |> specialize_consts_in_term hol_ctxt def depth in
blanchet@35070
   910
            if exists (member (op aconv) (get axs)) [t, t'] then accum
blanchet@38170
   911
            else add_axioms_for_term (depth + 1) t' (seen, app (cons t') axs)
blanchet@35070
   912
          end
blanchet@35070
   913
      end
blanchet@38206
   914
    and add_def_axiom depth = add_axiom fst apfst true depth
blanchet@38206
   915
    and add_nondef_axiom depth = add_axiom snd apsnd false depth
blanchet@35070
   916
    and add_maybe_def_axiom depth t =
blanchet@35070
   917
      (if head_of t <> @{const "==>"} then add_def_axiom
blanchet@35070
   918
       else add_nondef_axiom) depth t
blanchet@35070
   919
    and add_eq_axiom depth t =
blanchet@37256
   920
      (if is_constr_pattern_formula ctxt t then add_def_axiom
blanchet@35070
   921
       else add_nondef_axiom) depth t
blanchet@38170
   922
    and add_axioms_for_term depth t (accum as (seen, axs)) =
blanchet@35070
   923
      case t of
blanchet@35070
   924
        t1 $ t2 => accum |> fold (add_axioms_for_term depth) [t1, t2]
blanchet@35070
   925
      | Const (x as (s, T)) =>
blanchet@39359
   926
        (if member (op aconv) seen t orelse is_built_in_const thy stds x then
blanchet@35070
   927
           accum
blanchet@35070
   928
         else
blanchet@38170
   929
           let val accum = (t :: seen, axs) in
blanchet@35070
   930
             if depth > axioms_max_depth then
blanchet@35070
   931
               raise TOO_LARGE ("Nitpick_Preproc.axioms_for_term.\
blanchet@35070
   932
                                \add_axioms_for_term",
blanchet@35070
   933
                                "too many nested axioms (" ^
blanchet@35070
   934
                                string_of_int depth ^ ")")
blanchet@37260
   935
             else if is_of_class_const thy x then
blanchet@35070
   936
               let
blanchet@35070
   937
                 val class = Logic.class_of_const s
blanchet@35070
   938
                 val of_class = Logic.mk_of_class (TVar (("'a", 0), [class]),
blanchet@35070
   939
                                                   class)
blanchet@36555
   940
                 val ax1 = try (specialize_type thy x) of_class
blanchet@36555
   941
                 val ax2 = Option.map (specialize_type thy x o snd)
blanchet@37260
   942
                                      (get_class_def thy class)
blanchet@35070
   943
               in
blanchet@35070
   944
                 fold (add_maybe_def_axiom depth) (map_filter I [ax1, ax2])
blanchet@35070
   945
                      accum
blanchet@35070
   946
               end
blanchet@37256
   947
             else if is_constr ctxt stds x then
blanchet@35070
   948
               accum
blanchet@37271
   949
             else if is_descr (original_name s) then
blanchet@37271
   950
               fold (add_nondef_axiom depth) (equational_fun_axioms hol_ctxt x)
blanchet@37271
   951
                    accum
blanchet@38202
   952
             else if is_equational_fun_but_no_plain_def hol_ctxt x then
blanchet@35070
   953
               fold (add_eq_axiom depth) (equational_fun_axioms hol_ctxt x)
blanchet@35070
   954
                    accum
blanchet@35807
   955
             else if is_choice_spec_fun hol_ctxt x then
blanchet@35807
   956
               fold (add_nondef_axiom depth)
blanchet@35807
   957
                    (nondef_props_for_const thy true choice_spec_table x) accum
blanchet@37256
   958
             else if is_abs_fun ctxt x then
blanchet@38215
   959
               accum |> fold (add_nondef_axiom depth)
blanchet@38215
   960
                             (nondef_props_for_const thy false nondef_table x)
blanchet@38240
   961
                     |> (is_funky_typedef ctxt (range_type T) orelse
blanchet@38215
   962
                         range_type T = nat_T)
blanchet@38215
   963
                        ? fold (add_maybe_def_axiom depth)
blanchet@38215
   964
                               (nondef_props_for_const thy true
blanchet@35070
   965
                                                    (extra_table def_table s) x)
blanchet@37256
   966
             else if is_rep_fun ctxt x then
blanchet@38215
   967
               accum |> fold (add_nondef_axiom depth)
blanchet@38215
   968
                             (nondef_props_for_const thy false nondef_table x)
blanchet@38240
   969
                     |> (is_funky_typedef ctxt (range_type T) orelse
blanchet@38215
   970
                         range_type T = nat_T)
blanchet@38215
   971
                        ? fold (add_maybe_def_axiom depth)
blanchet@38215
   972
                               (nondef_props_for_const thy true
blanchet@35070
   973
                                                    (extra_table def_table s) x)
blanchet@38215
   974
                     |> add_axioms_for_term depth
blanchet@38215
   975
                                            (Const (mate_of_rep_fun ctxt x))
blanchet@38215
   976
                     |> fold (add_def_axiom depth)
blanchet@38215
   977
                             (inverse_axioms_for_rep_fun ctxt x)
blanchet@37253
   978
             else if s = @{const_name TYPE} then
blanchet@37253
   979
               accum
blanchet@38202
   980
             else case def_of_const thy def_table x of
blanchet@39345
   981
               SOME _ =>
blanchet@38202
   982
               fold (add_eq_axiom depth) (equational_fun_axioms hol_ctxt x)
blanchet@38202
   983
                    accum
blanchet@38202
   984
             | NONE =>
blanchet@35070
   985
               accum |> user_axioms <> SOME false
blanchet@35070
   986
                        ? fold (add_nondef_axiom depth)
blanchet@35070
   987
                               (nondef_props_for_const thy false nondef_table x)
blanchet@35070
   988
           end)
blanchet@35070
   989
        |> add_axioms_for_type depth T
blanchet@38170
   990
      | Free (x as (_, T)) =>
blanchet@38170
   991
        (if member (op aconv) seen t then
blanchet@38170
   992
           accum
blanchet@38170
   993
         else case AList.lookup (op =) def_assm_table x of
blanchet@38170
   994
           SOME t => add_def_axiom depth t accum
blanchet@38170
   995
         | NONE => accum)
blanchet@38170
   996
        |> add_axioms_for_type depth T
blanchet@35070
   997
      | Var (_, T) => add_axioms_for_type depth T accum
blanchet@35070
   998
      | Bound _ => accum
blanchet@35070
   999
      | Abs (_, T, t) => accum |> add_axioms_for_term depth t
blanchet@35070
  1000
                               |> add_axioms_for_type depth T
blanchet@35070
  1001
    and add_axioms_for_type depth T =
blanchet@35070
  1002
      case T of
blanchet@35665
  1003
        Type (@{type_name fun}, Ts) => fold (add_axioms_for_type depth) Ts
blanchet@38190
  1004
      | Type (@{type_name prod}, Ts) => fold (add_axioms_for_type depth) Ts
blanchet@35070
  1005
      | @{typ prop} => I
blanchet@35070
  1006
      | @{typ bool} => I
blanchet@35070
  1007
      | TFree (_, S) => add_axioms_for_sort depth T S
blanchet@35070
  1008
      | TVar (_, S) => add_axioms_for_sort depth T S
blanchet@35280
  1009
      | Type (z as (_, Ts)) =>
blanchet@35070
  1010
        fold (add_axioms_for_type depth) Ts
blanchet@37256
  1011
        #> (if is_pure_typedef ctxt T then
blanchet@37256
  1012
              fold (add_maybe_def_axiom depth) (optimized_typedef_axioms ctxt z)
blanchet@38240
  1013
            else if is_quot_type ctxt T then
blanchet@35311
  1014
              fold (add_def_axiom depth)
blanchet@35311
  1015
                   (optimized_quot_type_axioms ctxt stds z)
blanchet@38240
  1016
            else if max_bisim_depth >= 0 andalso is_codatatype ctxt T then
blanchet@35070
  1017
              fold (add_maybe_def_axiom depth)
blanchet@35070
  1018
                   (codatatype_bisim_axioms hol_ctxt T)
blanchet@35070
  1019
            else
blanchet@35070
  1020
              I)
blanchet@35070
  1021
    and add_axioms_for_sort depth T S =
blanchet@35070
  1022
      let
blanchet@35070
  1023
        val supers = Sign.complete_sort thy S
blanchet@35070
  1024
        val class_axioms =
blanchet@35070
  1025
          maps (fn class => map prop_of (AxClass.get_info thy class |> #axioms
blanchet@35070
  1026
                                         handle ERROR _ => [])) supers
blanchet@35070
  1027
        val monomorphic_class_axioms =
blanchet@35070
  1028
          map (fn t => case Term.add_tvars t [] of
blanchet@35070
  1029
                         [] => t
blanchet@35070
  1030
                       | [(x, S)] =>
blanchet@36555
  1031
                         monomorphic_term (Vartab.make [(x, (S, T))]) t
blanchet@35070
  1032
                       | _ => raise TERM ("Nitpick_Preproc.axioms_for_term.\
blanchet@35070
  1033
                                          \add_axioms_for_sort", [t]))
blanchet@35070
  1034
              class_axioms
blanchet@35070
  1035
      in fold (add_nondef_axiom depth) monomorphic_class_axioms end
blanchet@35070
  1036
    val (mono_user_nondefs, poly_user_nondefs) =
blanchet@35070
  1037
      List.partition (null o Term.hidden_polymorphism) user_nondefs
blanchet@35070
  1038
    val eval_axioms = map2 eval_axiom_for_term (index_seq 0 (length evals))
blanchet@35070
  1039
                           evals
blanchet@38170
  1040
    val (seen, (defs, nondefs)) =
blanchet@38169
  1041
      ([], ([], []))
blanchet@38169
  1042
      |> add_axioms_for_term 1 neg_t
blanchet@38169
  1043
      |> fold_rev (add_nondef_axiom 1) nondef_assm_ts
blanchet@38169
  1044
      |> fold_rev (add_def_axiom 1) eval_axioms
blanchet@38169
  1045
      |> user_axioms = SOME true ? fold (add_nondef_axiom 1) mono_user_nondefs
blanchet@38170
  1046
    val defs = defs @ special_congruence_axioms hol_ctxt seen
blanchet@35386
  1047
    val got_all_mono_user_axioms =
blanchet@35386
  1048
      (user_axioms = SOME true orelse null mono_user_nondefs)
blanchet@38169
  1049
  in
blanchet@38169
  1050
    (neg_t :: nondefs, defs, got_all_mono_user_axioms, null poly_user_nondefs)
blanchet@38169
  1051
  end
blanchet@35070
  1052
blanchet@35070
  1053
(** Simplification of constructor/selector terms **)
blanchet@35070
  1054
blanchet@37256
  1055
fun simplify_constrs_and_sels ctxt t =
blanchet@35070
  1056
  let
blanchet@35070
  1057
    fun is_nth_sel_on t' n (Const (s, _) $ t) =
blanchet@35070
  1058
        (t = t' andalso is_sel_like_and_no_discr s andalso
blanchet@35070
  1059
         sel_no_from_name s = n)
blanchet@35070
  1060
      | is_nth_sel_on _ _ _ = false
blanchet@35070
  1061
    fun do_term (Const (@{const_name Rep_Frac}, _)
blanchet@35070
  1062
                 $ (Const (@{const_name Abs_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@35070
  1063
      | do_term (Const (@{const_name Abs_Frac}, _)
blanchet@35070
  1064
                 $ (Const (@{const_name Rep_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@35070
  1065
      | do_term (t1 $ t2) args = do_term t1 (do_term t2 [] :: args)
blanchet@35070
  1066
      | do_term (t as Const (x as (s, T))) (args as _ :: _) =
blanchet@37256
  1067
        ((if is_constr_like ctxt x then
blanchet@35070
  1068
            if length args = num_binder_types T then
blanchet@35070
  1069
              case hd args of
blanchet@35280
  1070
                Const (_, T') $ t' =>
blanchet@35070
  1071
                if domain_type T' = body_type T andalso
blanchet@35070
  1072
                   forall (uncurry (is_nth_sel_on t'))
blanchet@35070
  1073
                          (index_seq 0 (length args) ~~ args) then
blanchet@35070
  1074
                  t'
blanchet@35070
  1075
                else
blanchet@35070
  1076
                  raise SAME ()
blanchet@35070
  1077
              | _ => raise SAME ()
blanchet@35070
  1078
            else
blanchet@35070
  1079
              raise SAME ()
blanchet@35070
  1080
          else if is_sel_like_and_no_discr s then
blanchet@35070
  1081
            case strip_comb (hd args) of
blanchet@35070
  1082
              (Const (x' as (s', T')), ts') =>
blanchet@37256
  1083
              if is_constr_like ctxt x' andalso
blanchet@35070
  1084
                 constr_name_for_sel_like s = s' andalso
blanchet@35070
  1085
                 not (exists is_pair_type (binder_types T')) then
blanchet@35070
  1086
                list_comb (nth ts' (sel_no_from_name s), tl args)
blanchet@35070
  1087
              else
blanchet@35070
  1088
                raise SAME ()
blanchet@35070
  1089
            | _ => raise SAME ()
blanchet@35070
  1090
          else
blanchet@35070
  1091
            raise SAME ())
blanchet@37476
  1092
         handle SAME () => s_betapplys [] (t, args))
blanchet@35070
  1093
      | do_term (Abs (s, T, t')) args =
blanchet@37476
  1094
        s_betapplys [] (Abs (s, T, do_term t' []), args)
blanchet@37476
  1095
      | do_term t args = s_betapplys [] (t, args)
blanchet@35070
  1096
  in do_term t [] end
blanchet@35070
  1097
blanchet@35070
  1098
(** Quantifier massaging: Distributing quantifiers **)
blanchet@35070
  1099
blanchet@35070
  1100
fun distribute_quantifiers t =
blanchet@35070
  1101
  case t of
blanchet@35070
  1102
    (t0 as Const (@{const_name All}, T0)) $ Abs (s, T1, t1) =>
blanchet@35070
  1103
    (case t1 of
haftmann@38795
  1104
       (t10 as @{const HOL.conj}) $ t11 $ t12 =>
blanchet@35070
  1105
       t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
blanchet@35070
  1106
           $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
blanchet@35070
  1107
     | (t10 as @{const Not}) $ t11 =>
blanchet@35070
  1108
       t10 $ distribute_quantifiers (Const (@{const_name Ex}, T0)
blanchet@35070
  1109
                                     $ Abs (s, T1, t11))
blanchet@35070
  1110
     | t1 =>
blanchet@35070
  1111
       if not (loose_bvar1 (t1, 0)) then
blanchet@35070
  1112
         distribute_quantifiers (incr_boundvars ~1 t1)
blanchet@35070
  1113
       else
blanchet@35070
  1114
         t0 $ Abs (s, T1, distribute_quantifiers t1))
blanchet@35070
  1115
  | (t0 as Const (@{const_name Ex}, T0)) $ Abs (s, T1, t1) =>
blanchet@35070
  1116
    (case distribute_quantifiers t1 of
haftmann@38795
  1117
       (t10 as @{const HOL.disj}) $ t11 $ t12 =>
blanchet@35070
  1118
       t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
blanchet@35070
  1119
           $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
haftmann@38786
  1120
     | (t10 as @{const HOL.implies}) $ t11 $ t12 =>
blanchet@35070
  1121
       t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
blanchet@35070
  1122
                                     $ Abs (s, T1, t11))
blanchet@35070
  1123
           $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
blanchet@35070
  1124
     | (t10 as @{const Not}) $ t11 =>
blanchet@35070
  1125
       t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
blanchet@35070
  1126
                                     $ Abs (s, T1, t11))
blanchet@35070
  1127
     | t1 =>
blanchet@35070
  1128
       if not (loose_bvar1 (t1, 0)) then
blanchet@35070
  1129
         distribute_quantifiers (incr_boundvars ~1 t1)
blanchet@35070
  1130
       else
blanchet@35070
  1131
         t0 $ Abs (s, T1, distribute_quantifiers t1))
blanchet@35070
  1132
  | t1 $ t2 => distribute_quantifiers t1 $ distribute_quantifiers t2
blanchet@35070
  1133
  | Abs (s, T, t') => Abs (s, T, distribute_quantifiers t')
blanchet@35070
  1134
  | _ => t
blanchet@35070
  1135
blanchet@35070
  1136
(** Quantifier massaging: Pushing quantifiers inward **)
blanchet@35070
  1137
blanchet@35070
  1138
fun renumber_bounds j n f t =
blanchet@35070
  1139
  case t of
blanchet@35070
  1140
    t1 $ t2 => renumber_bounds j n f t1 $ renumber_bounds j n f t2
blanchet@35070
  1141
  | Abs (s, T, t') => Abs (s, T, renumber_bounds (j + 1) n f t')
blanchet@35070
  1142
  | Bound j' =>
blanchet@35070
  1143
    Bound (if j' >= j andalso j' < j + n then f (j' - j) + j else j')
blanchet@35070
  1144
  | _ => t
blanchet@35070
  1145
blanchet@35070
  1146
(* Maximum number of quantifiers in a cluster for which the exponential
blanchet@35070
  1147
   algorithm is used. Larger clusters use a heuristic inspired by Claessen &
blanchet@35386
  1148
   Soerensson's polynomial binary splitting procedure (p. 5 of their MODEL 2003
blanchet@35070
  1149
   paper). *)
blanchet@35070
  1150
val quantifier_cluster_threshold = 7
blanchet@35070
  1151
blanchet@35280
  1152
val push_quantifiers_inward =
blanchet@35070
  1153
  let
blanchet@35070
  1154
    fun aux quant_s ss Ts t =
blanchet@35070
  1155
      (case t of
blanchet@35280
  1156
         Const (s0, _) $ Abs (s1, T1, t1 as _ $ _) =>
blanchet@35070
  1157
         if s0 = quant_s then
blanchet@35070
  1158
           aux s0 (s1 :: ss) (T1 :: Ts) t1
blanchet@35070
  1159
         else if quant_s = "" andalso
blanchet@35070
  1160
                 (s0 = @{const_name All} orelse s0 = @{const_name Ex}) then
blanchet@35070
  1161
           aux s0 [s1] [T1] t1
blanchet@35070
  1162
         else
blanchet@35070
  1163
           raise SAME ()
blanchet@35070
  1164
       | _ => raise SAME ())
blanchet@35070
  1165
      handle SAME () =>
blanchet@35070
  1166
             case t of
blanchet@35070
  1167
               t1 $ t2 =>
blanchet@35070
  1168
               if quant_s = "" then
blanchet@35070
  1169
                 aux "" [] [] t1 $ aux "" [] [] t2
blanchet@35070
  1170
               else
blanchet@35070
  1171
                 let
blanchet@35070
  1172
                   val typical_card = 4
blanchet@35070
  1173
                   fun big_union proj ps =
blanchet@35070
  1174
                     fold (fold (insert (op =)) o proj) ps []
blanchet@35070
  1175
                   val (ts, connective) = strip_any_connective t
blanchet@35070
  1176
                   val T_costs =
blanchet@35070
  1177
                     map (bounded_card_of_type 65536 typical_card []) Ts
blanchet@35070
  1178
                   val t_costs = map size_of_term ts
blanchet@35070
  1179
                   val num_Ts = length Ts
blanchet@35070
  1180
                   val flip = curry (op -) (num_Ts - 1)
blanchet@35070
  1181
                   val t_boundss = map (map flip o loose_bnos) ts
blanchet@35070
  1182
                   fun merge costly_boundss [] = costly_boundss
blanchet@35070
  1183
                     | merge costly_boundss (j :: js) =
blanchet@35070
  1184
                       let
blanchet@35070
  1185
                         val (yeas, nays) =
blanchet@35070
  1186
                           List.partition (fn (bounds, _) =>
blanchet@35070
  1187
                                              member (op =) bounds j)
blanchet@35070
  1188
                                          costly_boundss
blanchet@35070
  1189
                         val yeas_bounds = big_union fst yeas
blanchet@35070
  1190
                         val yeas_cost = Integer.sum (map snd yeas)
blanchet@35070
  1191
                                         * nth T_costs j
blanchet@35070
  1192
                       in merge ((yeas_bounds, yeas_cost) :: nays) js end
blanchet@35070
  1193
                   val cost = Integer.sum o map snd oo merge
blanchet@35070
  1194
                   fun heuristically_best_permutation _ [] = []
blanchet@35070
  1195
                     | heuristically_best_permutation costly_boundss js =
blanchet@35070
  1196
                       let
blanchet@35070
  1197
                         val (costly_boundss, (j, js)) =
blanchet@35070
  1198
                           js |> map (`(merge costly_boundss o single))
blanchet@35070
  1199
                              |> sort (int_ord
blanchet@35070
  1200
                                       o pairself (Integer.sum o map snd o fst))
blanchet@35070
  1201
                              |> split_list |>> hd ||> pairf hd tl
blanchet@35070
  1202
                       in
blanchet@35070
  1203
                         j :: heuristically_best_permutation costly_boundss js
blanchet@35070
  1204
                       end
blanchet@35070
  1205
                   val js =
blanchet@35070
  1206
                     if length Ts <= quantifier_cluster_threshold then
blanchet@35070
  1207
                       all_permutations (index_seq 0 num_Ts)
blanchet@35070
  1208
                       |> map (`(cost (t_boundss ~~ t_costs)))
blanchet@35070
  1209
                       |> sort (int_ord o pairself fst) |> hd |> snd
blanchet@35070
  1210
                     else
blanchet@35070
  1211
                       heuristically_best_permutation (t_boundss ~~ t_costs)
blanchet@35070
  1212
                                                      (index_seq 0 num_Ts)
blanchet@35070
  1213
                   val back_js = map (fn j => find_index (curry (op =) j) js)
blanchet@35070
  1214
                                     (index_seq 0 num_Ts)
blanchet@35070
  1215
                   val ts = map (renumber_bounds 0 num_Ts (nth back_js o flip))
blanchet@35070
  1216
                                ts
blanchet@35070
  1217
                   fun mk_connection [] =
blanchet@35070
  1218
                       raise ARG ("Nitpick_Preproc.push_quantifiers_inward.aux.\
blanchet@35070
  1219
                                  \mk_connection", "")
blanchet@35070
  1220
                     | mk_connection ts_cum_bounds =
blanchet@35070
  1221
                       ts_cum_bounds |> map fst
blanchet@35070
  1222
                       |> foldr1 (fn (t1, t2) => connective $ t1 $ t2)
blanchet@35070
  1223
                   fun build ts_cum_bounds [] = ts_cum_bounds |> mk_connection
blanchet@35070
  1224
                     | build ts_cum_bounds (j :: js) =
blanchet@35070
  1225
                       let
blanchet@35070
  1226
                         val (yeas, nays) =
blanchet@35070
  1227
                           List.partition (fn (_, bounds) =>
blanchet@35070
  1228
                                              member (op =) bounds j)
blanchet@35070
  1229
                                          ts_cum_bounds
blanchet@35070
  1230
                           ||> map (apfst (incr_boundvars ~1))
blanchet@35070
  1231
                       in
blanchet@35070
  1232
                         if null yeas then
blanchet@35070
  1233
                           build nays js
blanchet@35070
  1234
                         else
blanchet@35070
  1235
                           let val T = nth Ts (flip j) in
blanchet@35070
  1236
                             build ((Const (quant_s, (T --> bool_T) --> bool_T)
blanchet@35070
  1237
                                     $ Abs (nth ss (flip j), T,
blanchet@35070
  1238
                                            mk_connection yeas),
blanchet@35070
  1239
                                      big_union snd yeas) :: nays) js
blanchet@35070
  1240
                           end
blanchet@35070
  1241
                       end
blanchet@35070
  1242
                 in build (ts ~~ t_boundss) js end
blanchet@35070
  1243
             | Abs (s, T, t') => Abs (s, T, aux "" [] [] t')
blanchet@35070
  1244
             | _ => t
blanchet@35070
  1245
  in aux "" [] [] end
blanchet@35070
  1246
blanchet@35070
  1247
(** Preprocessor entry point **)
blanchet@35070
  1248
blanchet@37928
  1249
val max_skolem_depth = 3
blanchet@36389
  1250
blanchet@38169
  1251
fun preprocess_formulas
blanchet@38169
  1252
        (hol_ctxt as {thy, ctxt, stds, binary_ints, destroy_constrs, boxes,
blanchet@41052
  1253
                      ...}) assm_ts neg_t =
blanchet@35070
  1254
  let
blanchet@35386
  1255
    val (nondef_ts, def_ts, got_all_mono_user_axioms, no_poly_user_axioms) =
blanchet@38169
  1256
      neg_t |> unfold_defs_in_term hol_ctxt
blanchet@38169
  1257
            |> close_form
blanchet@38169
  1258
            |> skolemize_term_and_more hol_ctxt max_skolem_depth
blanchet@38206
  1259
            |> specialize_consts_in_term hol_ctxt false 0
blanchet@38169
  1260
            |> axioms_for_term hol_ctxt assm_ts
blanchet@35070
  1261
    val binarize =
blanchet@35220
  1262
      is_standard_datatype thy stds nat_T andalso
blanchet@35070
  1263
      case binary_ints of
blanchet@35070
  1264
        SOME false => false
blanchet@35718
  1265
      | _ => forall (may_use_binary_ints false) nondef_ts andalso
blanchet@35718
  1266
             forall (may_use_binary_ints true) def_ts andalso
blanchet@35220
  1267
             (binary_ints = SOME true orelse
blanchet@35386
  1268
              exists should_use_binary_ints (nondef_ts @ def_ts))
blanchet@35070
  1269
    val box = exists (not_equal (SOME false) o snd) boxes
blanchet@35070
  1270
    val table =
blanchet@35386
  1271
      Termtab.empty
blanchet@37256
  1272
      |> box ? fold (add_to_uncurry_table ctxt) (nondef_ts @ def_ts)
blanchet@35280
  1273
    fun do_rest def =
blanchet@35070
  1274
      binarize ? binarize_nat_and_int_in_term
blanchet@36388
  1275
      #> box ? uncurry_term table
blanchet@35070
  1276
      #> box ? box_fun_and_pair_in_term hol_ctxt def
blanchet@35220
  1277
      #> destroy_constrs ? (pull_out_universal_constrs hol_ctxt def
blanchet@35220
  1278
                            #> pull_out_existential_constrs hol_ctxt
blanchet@35070
  1279
                            #> destroy_pulled_out_constrs hol_ctxt def)
blanchet@35070
  1280
      #> curry_assms
blanchet@35070
  1281
      #> destroy_universal_equalities
blanchet@35220
  1282
      #> destroy_existential_equalities hol_ctxt
blanchet@37256
  1283
      #> simplify_constrs_and_sels ctxt
blanchet@35070
  1284
      #> distribute_quantifiers
blanchet@35280
  1285
      #> push_quantifiers_inward
blanchet@35078
  1286
      #> close_form
blanchet@35070
  1287
      #> Term.map_abs_vars shortest_name
blanchet@35386
  1288
    val nondef_ts = map (do_rest false) nondef_ts
blanchet@35384
  1289
    val def_ts = map (do_rest true) def_ts
blanchet@35070
  1290
  in
blanchet@35386
  1291
    (nondef_ts, def_ts, got_all_mono_user_axioms, no_poly_user_axioms, binarize)
blanchet@35070
  1292
  end
blanchet@35070
  1293
blanchet@35070
  1294
end;