src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Sun Apr 25 00:10:30 2010 +0200 (2010-04-25)
changeset 36389 8228b3a4a2ba
parent 36388 30f7ce76712d
child 36390 eee4ee6a5cbe
permissions -rw-r--r--
remove "skolemize" option from Nitpick, since Skolemization is always useful
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(*  Title:      HOL/Tools/Nitpick/nitpick_model.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2009, 2010
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Model reconstruction for Nitpick.
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*)
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signature NITPICK_MODEL =
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sig
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  type styp = Nitpick_Util.styp
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  type scope = Nitpick_Scope.scope
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  type rep = Nitpick_Rep.rep
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  type nut = Nitpick_Nut.nut
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  type params = {
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    show_skolems: bool,
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    show_datatypes: bool,
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    show_consts: bool}
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  type term_postprocessor =
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    Proof.context -> string -> (typ -> term list) -> typ -> term -> term
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  structure NameTable : TABLE
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  val irrelevant : string
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  val unknown : string
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  val unrep : string
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  val register_term_postprocessor :
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    typ -> term_postprocessor -> theory -> theory
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  val unregister_term_postprocessor : typ -> theory -> theory
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  val tuple_list_for_name :
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    nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
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  val dest_plain_fun : term -> bool * (term list * term list)
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  val reconstruct_hol_model :
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    params -> scope -> (term option * int list) list -> styp list -> nut list
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    -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
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    -> Pretty.T * bool
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  val prove_hol_model :
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    scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
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    -> Kodkod.raw_bound list -> term -> bool option
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end;
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structure Nitpick_Model : NITPICK_MODEL =
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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_Scope
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open Nitpick_Peephole
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open Nitpick_Rep
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open Nitpick_Nut
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structure KK = Kodkod
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type params = {
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  show_skolems: bool,
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  show_datatypes: bool,
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  show_consts: bool}
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type term_postprocessor =
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  Proof.context -> string -> (typ -> term list) -> typ -> term -> term
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structure Data = Theory_Data(
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  type T = (typ * term_postprocessor) list
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  val empty = []
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  val extend = I
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  fun merge (ps1, ps2) = AList.merge (op =) (K true) (ps1, ps2))
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val irrelevant = "_"
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val unknown = "?"
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val unrep = "\<dots>"
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val maybe_mixfix = "_\<^sup>?"
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val base_mixfix = "_\<^bsub>base\<^esub>"
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val step_mixfix = "_\<^bsub>step\<^esub>"
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val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
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val arg_var_prefix = "x"
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val cyclic_co_val_name = "\<omega>"
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val cyclic_const_prefix = "\<xi>"
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val cyclic_type_name = nitpick_prefix ^ cyclic_const_prefix
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val opt_flag = nitpick_prefix ^ "opt"
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val non_opt_flag = nitpick_prefix ^ "non_opt"
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type atom_pool = ((string * int) * int list) list
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fun add_wacky_syntax ctxt =
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  let
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    val name_of = fst o dest_Const
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    val thy = ProofContext.theory_of ctxt |> Context.reject_draft
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    val (maybe_t, thy) =
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      Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
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                          Mixfix (maybe_mixfix, [1000], 1000)) thy
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    val (abs_t, thy) =
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      Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
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                          Mixfix (abs_mixfix, [40], 40)) thy
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    val (base_t, thy) =
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      Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
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                          Mixfix (base_mixfix, [1000], 1000)) thy
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    val (step_t, thy) =
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      Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
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                          Mixfix (step_mixfix, [1000], 1000)) thy
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  in
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    (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
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     ProofContext.transfer_syntax thy ctxt)
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  end
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(** Term reconstruction **)
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fun nth_atom_suffix pool s j k =
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  (case AList.lookup (op =) (!pool) (s, k) of
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     SOME js =>
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     (case find_index (curry (op =) j) js of
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        ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));
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               length js + 1)
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      | n => length js - n)
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   | NONE => (Unsynchronized.change pool (cons ((s, k), [j])); 1))
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  |> nat_subscript
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  |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
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     ? prefix "\<^isub>,"
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fun nth_atom_name pool prefix (Type (s, _)) j k =
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    let val s' = shortest_name s in
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      prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
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      nth_atom_suffix pool s j k
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    end
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  | nth_atom_name pool prefix (TFree (s, _)) j k =
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    prefix ^ perhaps (try (unprefix "'")) s ^ nth_atom_suffix pool s j k
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  | nth_atom_name _ _ T _ _ =
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    raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
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fun nth_atom pool for_auto T j k =
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  if for_auto then
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    Free (nth_atom_name pool (hd (space_explode "." nitpick_prefix)) T j k, T)
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  else
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    Const (nth_atom_name pool "" T j k, T)
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fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
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    real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
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  | extract_real_number t = real (snd (HOLogic.dest_number t))
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fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
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  | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
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    handle TERM ("dest_number", _) =>
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           case tp of
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             (t11 $ t12, t21 $ t22) =>
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             (case nice_term_ord (t11, t21) of
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                EQUAL => nice_term_ord (t12, t22)
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              | ord => ord)
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           | _ => Term_Ord.fast_term_ord tp
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fun register_term_postprocessor T p = Data.map (cons (T, p))
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fun unregister_term_postprocessor T = Data.map (AList.delete (op =) T)
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fun tuple_list_for_name rel_table bounds name =
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  the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
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fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =
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    unarize_unbox_etc_term t1
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  | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
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    unarize_unbox_etc_term t1
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  | unarize_unbox_etc_term
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        (Const (@{const_name PairBox},
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                Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
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         $ t1 $ t2) =
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    let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
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      Const (@{const_name Pair}, Ts ---> Type (@{type_name "*"}, Ts))
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      $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
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    end
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  | unarize_unbox_etc_term (Const (s, T)) =
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    Const (s, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (t1 $ t2) =
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    unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
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  | unarize_unbox_etc_term (Free (s, T)) =
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    Free (s, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (Var (x, T)) =
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    Var (x, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (Bound j) = Bound j
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  | unarize_unbox_etc_term (Abs (s, T, t')) =
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    Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
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fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))
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                     (T2 as Type (@{type_name "*"}, [T21, T22])) =
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    let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
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      if n1 = n2 then
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        let
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          val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
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        in
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          ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),
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           (Type (@{type_name "*"}, [T21, T21']), opt_T22'))
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        end
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      else if n1 < n2 then
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        case factor_out_types T1 T21 of
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          (p1, (T21', NONE)) => (p1, (T21', SOME T22))
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        | (p1, (T21', SOME T22')) =>
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          (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))
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      else
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        swap (factor_out_types T2 T1)
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    end
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  | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =
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    ((T11, SOME T12), (T2, NONE))
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  | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =
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    ((T1, NONE), (T21, SOME T22))
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  | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
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fun make_plain_fun maybe_opt T1 T2 =
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  let
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    fun aux T1 T2 [] =
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        Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
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      | aux T1 T2 ((t1, t2) :: tps) =
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        Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
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        $ aux T1 T2 tps $ t1 $ t2
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  in aux T1 T2 o rev end
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fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
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  | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
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    is_plain_fun t0
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  | is_plain_fun _ = false
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val dest_plain_fun =
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  let
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    fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
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      | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
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      | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
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        let val (maybe_opt, (ts1, ts2)) = aux t0 in
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          (maybe_opt, (t1 :: ts1, t2 :: ts2))
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        end
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      | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
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  in apsnd (pairself rev) o aux end
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fun break_in_two T T1 T2 t =
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  let
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    val ps = HOLogic.flat_tupleT_paths T
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    val cut = length (HOLogic.strip_tupleT T1)
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    val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
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    val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
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  in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
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fun pair_up (Type (@{type_name "*"}, [T1', T2']))
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            (t1 as Const (@{const_name Pair},
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                          Type (@{type_name fun},
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                                [_, Type (@{type_name fun}, [_, T1])]))
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             $ t11 $ t12) t2 =
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    if T1 = T1' then HOLogic.mk_prod (t1, t2)
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    else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
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  | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
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fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
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fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =
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    let
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      fun do_curry T1 T1a T1b T2 t =
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        let
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          val (maybe_opt, tsp) = dest_plain_fun t
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          val tps =
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            tsp |>> map (break_in_two T1 T1a T1b)
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                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
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                |> AList.coalesce (op =)
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                |> map (apsnd (make_plain_fun maybe_opt T1b T2))
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        in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
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      and do_uncurry T1 T2 t =
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        let
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          val (maybe_opt, tsp) = dest_plain_fun t
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          val tps =
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            tsp |> op ~~
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                |> maps (fn (t1, t2) =>
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                            multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
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        in make_plain_fun maybe_opt T1 T2 tps end
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      and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
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        | do_arrow T1' T2' T1 T2
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                   (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
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          Const (@{const_name fun_upd},
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                 (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
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          $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
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        | do_arrow _ _ _ _ t =
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          raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
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      and do_fun T1' T2' T1 T2 t =
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        case factor_out_types T1' T1 of
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          ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
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        | ((_, NONE), (T1a, SOME T1b)) =>
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          t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
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        | ((T1a', SOME T1b'), (_, NONE)) =>
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          t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
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        | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
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      and do_term (Type (@{type_name fun}, [T1', T2']))
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                  (Type (@{type_name fun}, [T1, T2])) t =
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          do_fun T1' T2' T1 T2 t
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        | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))
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                  (Type (@{type_name "*"}, [T1, T2]))
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                  (Const (@{const_name Pair}, _) $ t1 $ t2) =
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          Const (@{const_name Pair}, Ts' ---> T')
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          $ do_term T1' T1 t1 $ do_term T2' T2 t2
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        | do_term T' T t =
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          if T = T' then t
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          else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
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   286
    in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
blanchet@34998
   287
  | typecast_fun T' _ _ _ =
blanchet@34998
   288
    raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
blanchet@33192
   289
blanchet@33192
   290
fun truth_const_sort_key @{const True} = "0"
blanchet@33192
   291
  | truth_const_sort_key @{const False} = "2"
blanchet@33192
   292
  | truth_const_sort_key _ = "1"
blanchet@33192
   293
blanchet@35665
   294
fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =
blanchet@33192
   295
    HOLogic.mk_prod (mk_tuple T1 ts,
blanchet@33192
   296
        mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
blanchet@33192
   297
  | mk_tuple _ (t :: _) = t
blanchet@34124
   298
  | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
blanchet@33192
   299
blanchet@35711
   300
fun varified_type_match thy (candid_T, pat_T) =
wenzelm@35845
   301
  strict_type_match thy (candid_T, Logic.varifyT_global pat_T)
blanchet@35711
   302
blanchet@35712
   303
fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
blanchet@35712
   304
                       sel_names rel_table bounds card T =
blanchet@35712
   305
  let
blanchet@35712
   306
    val card = if card = 0 then card_of_type card_assigns T else card
blanchet@35712
   307
    fun nth_value_of_type n =
blanchet@35712
   308
      let
blanchet@35712
   309
        fun term unfold =
blanchet@35712
   310
          reconstruct_term unfold pool wacky_names scope sel_names rel_table
blanchet@35712
   311
                           bounds T T (Atom (card, 0)) [[n]]
blanchet@35712
   312
      in
blanchet@35712
   313
        case term false of
blanchet@35712
   314
          t as Const (s, _) =>
blanchet@35712
   315
          if String.isPrefix cyclic_const_prefix s then
blanchet@35712
   316
            HOLogic.mk_eq (t, term true)
blanchet@35712
   317
          else
blanchet@35712
   318
            t
blanchet@35712
   319
        | t => t
blanchet@35712
   320
      end
blanchet@35712
   321
  in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
blanchet@35712
   322
and reconstruct_term unfold pool (wacky_names as ((maybe_name, abs_name), _))
blanchet@35712
   323
        (scope as {hol_ctxt as {ctxt, thy, stds, ...}, binarize, card_assigns,
blanchet@35712
   324
                   bits, datatypes, ofs, ...}) sel_names rel_table bounds =
blanchet@33192
   325
  let
blanchet@33192
   326
    val for_auto = (maybe_name = "")
blanchet@34124
   327
    fun value_of_bits jss =
blanchet@34124
   328
      let
blanchet@34124
   329
        val j0 = offset_of_type ofs @{typ unsigned_bit}
blanchet@34124
   330
        val js = map (Integer.add (~ j0) o the_single) jss
blanchet@34124
   331
      in
blanchet@34124
   332
        fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
blanchet@34124
   333
             js 0
blanchet@34124
   334
      end
blanchet@35712
   335
    val all_values =
blanchet@35712
   336
      all_values_of_type pool wacky_names scope sel_names rel_table bounds 0
blanchet@35712
   337
    fun postprocess_term (Type (@{type_name fun}, _)) = I
blanchet@35712
   338
      | postprocess_term T =
blanchet@35712
   339
        if null (Data.get thy) then
blanchet@35712
   340
          I
blanchet@35712
   341
        else case AList.lookup (varified_type_match thy) (Data.get thy) T of
blanchet@35712
   342
          SOME postproc => postproc ctxt maybe_name all_values T
blanchet@35712
   343
        | NONE => I
blanchet@35712
   344
    fun postprocess_subterms Ts (t1 $ t2) =
blanchet@35712
   345
        let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
blanchet@35712
   346
          postprocess_term (fastype_of1 (Ts, t)) t
blanchet@35712
   347
        end
blanchet@35712
   348
      | postprocess_subterms Ts (Abs (s, T, t')) =
blanchet@35712
   349
        Abs (s, T, postprocess_subterms (T :: Ts) t')
blanchet@35712
   350
      | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
blanchet@35388
   351
    fun make_set maybe_opt T1 T2 tps =
blanchet@33192
   352
      let
wenzelm@35402
   353
        val empty_const = Const (@{const_abbrev Set.empty}, T1 --> T2)
blanchet@33192
   354
        val insert_const = Const (@{const_name insert},
blanchet@34124
   355
                                  T1 --> (T1 --> T2) --> T1 --> T2)
blanchet@33192
   356
        fun aux [] =
blanchet@35385
   357
            if maybe_opt andalso not (is_complete_type datatypes false T1) then
blanchet@33192
   358
              insert_const $ Const (unrep, T1) $ empty_const
blanchet@33192
   359
            else
blanchet@33192
   360
              empty_const
blanchet@33192
   361
          | aux ((t1, t2) :: zs) =
blanchet@35388
   362
            aux zs
blanchet@35388
   363
            |> t2 <> @{const False}
blanchet@35388
   364
               ? curry (op $)
blanchet@35388
   365
                       (insert_const
blanchet@35388
   366
                        $ (t1 |> t2 <> @{const True}
blanchet@35388
   367
                                 ? curry (op $)
blanchet@35388
   368
                                         (Const (maybe_name, T1 --> T1))))
blanchet@35388
   369
      in
blanchet@35388
   370
        if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
blanchet@35388
   371
                  tps then
blanchet@35388
   372
          Const (unknown, T1 --> T2)
blanchet@35388
   373
        else
blanchet@35388
   374
          aux tps
blanchet@35388
   375
      end
blanchet@35665
   376
    fun make_map maybe_opt T1 T2 T2' =
blanchet@33192
   377
      let
blanchet@33192
   378
        val update_const = Const (@{const_name fun_upd},
blanchet@34124
   379
                                  (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
wenzelm@35402
   380
        fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
blanchet@35712
   381
          | aux' ((t1, t2) :: tps) =
blanchet@33192
   382
            (case t2 of
blanchet@35712
   383
               Const (@{const_name None}, _) => aux' tps
blanchet@35712
   384
             | _ => update_const $ aux' tps $ t1 $ t2)
blanchet@35712
   385
        fun aux tps =
blanchet@35665
   386
          if maybe_opt andalso not (is_complete_type datatypes false T1) then
blanchet@35712
   387
            update_const $ aux' tps $ Const (unrep, T1)
blanchet@33192
   388
            $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
blanchet@33192
   389
          else
blanchet@35712
   390
            aux' tps
blanchet@33192
   391
      in aux end
blanchet@34982
   392
    fun polish_funs Ts t =
blanchet@33192
   393
      (case fastype_of1 (Ts, t) of
blanchet@35665
   394
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
   395
         if is_plain_fun t then
blanchet@33192
   396
           case T2 of
blanchet@33192
   397
             @{typ bool} =>
blanchet@33192
   398
             let
blanchet@33192
   399
               val (maybe_opt, ts_pair) =
blanchet@34982
   400
                 dest_plain_fun t ||> pairself (map (polish_funs Ts))
blanchet@33192
   401
             in
blanchet@33192
   402
               make_set maybe_opt T1 T2
blanchet@33192
   403
                        (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
blanchet@33192
   404
             end
blanchet@33192
   405
           | Type (@{type_name option}, [T2']) =>
blanchet@33192
   406
             let
blanchet@35665
   407
               val (maybe_opt, ts_pair) =
blanchet@35665
   408
                 dest_plain_fun t ||> pairself (map (polish_funs Ts))
blanchet@35665
   409
             in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
blanchet@33192
   410
           | _ => raise SAME ()
blanchet@33192
   411
         else
blanchet@33192
   412
           raise SAME ()
blanchet@33192
   413
       | _ => raise SAME ())
blanchet@33192
   414
      handle SAME () =>
blanchet@33192
   415
             case t of
blanchet@34982
   416
               (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
blanchet@34982
   417
               $ (t2 as Const (s, _)) =>
blanchet@34982
   418
               if s = unknown then polish_funs Ts t11
blanchet@34982
   419
               else polish_funs Ts t1 $ polish_funs Ts t2
blanchet@34982
   420
             | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
blanchet@34982
   421
             | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
blanchet@35665
   422
             | Const (s, Type (@{type_name fun}, [T1, T2])) =>
blanchet@34982
   423
               if s = opt_flag orelse s = non_opt_flag then
blanchet@35712
   424
                 Abs ("x", T1,
blanchet@35712
   425
                      Const (if is_complete_type datatypes false T1 then
blanchet@35712
   426
                               irrelevant
blanchet@35712
   427
                             else
blanchet@35712
   428
                               unknown, T2))
blanchet@34982
   429
               else
blanchet@34982
   430
                 t
blanchet@34982
   431
             | t => t
blanchet@33192
   432
    fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
blanchet@34126
   433
      ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
blanchet@34998
   434
                 |> make_plain_fun maybe_opt T1 T2
blanchet@35665
   435
                 |> unarize_unbox_etc_term
blanchet@35665
   436
                 |> typecast_fun (uniterize_unarize_unbox_etc_type T')
blanchet@35665
   437
                                 (uniterize_unarize_unbox_etc_type T1)
blanchet@35665
   438
                                 (uniterize_unarize_unbox_etc_type T2)
blanchet@35665
   439
    fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
blanchet@33192
   440
        let
blanchet@33192
   441
          val k1 = card_of_type card_assigns T1
blanchet@33192
   442
          val k2 = card_of_type card_assigns T2
blanchet@33192
   443
        in
blanchet@35665
   444
          term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
blanchet@33192
   445
                       [nth_combination (replicate k1 (k2, 0)) j]
blanchet@33192
   446
          handle General.Subscript =>
blanchet@33232
   447
                 raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
blanchet@33192
   448
                            signed_string_of_int j ^ " for " ^
blanchet@33192
   449
                            string_for_rep (Vect (k1, Atom (k2, 0))))
blanchet@33192
   450
        end
blanchet@35665
   451
      | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =
blanchet@35075
   452
        let
blanchet@35075
   453
          val k1 = card_of_type card_assigns T1
blanchet@35075
   454
          val k2 = k div k1
blanchet@35075
   455
        in
blanchet@33192
   456
          list_comb (HOLogic.pair_const T1 T2,
blanchet@35075
   457
                     map3 (fn T => term_for_atom seen T T) [T1, T2]
blanchet@35075
   458
                          [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
blanchet@33192
   459
        end
blanchet@35075
   460
      | term_for_atom seen @{typ prop} _ j k =
blanchet@35075
   461
        HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
blanchet@35075
   462
      | term_for_atom _ @{typ bool} _ j _ =
blanchet@33192
   463
        if j = 0 then @{const False} else @{const True}
blanchet@35075
   464
      | term_for_atom _ @{typ unit} _ _ _ = @{const Unity}
blanchet@35075
   465
      | term_for_atom seen T _ j k =
blanchet@35220
   466
        if T = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@33192
   467
          HOLogic.mk_number nat_T j
blanchet@33192
   468
        else if T = int_T then
blanchet@35075
   469
          HOLogic.mk_number int_T (int_for_atom (k, 0) j)
blanchet@33192
   470
        else if is_fp_iterator_type T then
blanchet@35075
   471
          HOLogic.mk_number nat_T (k - j - 1)
blanchet@33192
   472
        else if T = @{typ bisim_iterator} then
blanchet@33192
   473
          HOLogic.mk_number nat_T j
blanchet@33192
   474
        else case datatype_spec datatypes T of
blanchet@35076
   475
          NONE => nth_atom pool for_auto T j k
blanchet@35076
   476
        | SOME {deep = false, ...} => nth_atom pool for_auto T j k
blanchet@35179
   477
        | SOME {co, standard, constrs, ...} =>
blanchet@33192
   478
          let
blanchet@33192
   479
            fun tuples_for_const (s, T) =
blanchet@33192
   480
              tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
blanchet@35180
   481
            fun cyclic_atom () =
blanchet@35180
   482
              nth_atom pool for_auto (Type (cyclic_type_name, [])) j k
blanchet@35180
   483
            fun cyclic_var () = Var ((nth_atom_name pool "" T j k, 0), T)
blanchet@35180
   484
blanchet@33192
   485
            val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
blanchet@33192
   486
                                 constrs
blanchet@33192
   487
            val real_j = j + offset_of_type ofs T
blanchet@33192
   488
            val constr_x as (constr_s, constr_T) =
blanchet@33192
   489
              get_first (fn (jss, {const, ...}) =>
blanchet@34121
   490
                            if member (op =) jss [real_j] then SOME const
blanchet@34121
   491
                            else NONE)
blanchet@33192
   492
                        (discr_jsss ~~ constrs) |> the
blanchet@33192
   493
            val arg_Ts = curried_binder_types constr_T
blanchet@35190
   494
            val sel_xs =
blanchet@35190
   495
              map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
blanchet@35190
   496
                                                          constr_x)
blanchet@35190
   497
                  (index_seq 0 (length arg_Ts))
blanchet@33192
   498
            val sel_Rs =
blanchet@33192
   499
              map (fn x => get_first
blanchet@33192
   500
                               (fn ConstName (s', T', R) =>
blanchet@33192
   501
                                   if (s', T') = x then SOME R else NONE
blanchet@33232
   502
                                 | u => raise NUT ("Nitpick_Model.reconstruct_\
blanchet@33192
   503
                                                   \term.term_for_atom", [u]))
blanchet@33192
   504
                               sel_names |> the) sel_xs
blanchet@33192
   505
            val arg_Rs = map (snd o dest_Func) sel_Rs
blanchet@33192
   506
            val sel_jsss = map tuples_for_const sel_xs
blanchet@33192
   507
            val arg_jsss =
blanchet@33192
   508
              map (map_filter (fn js => if hd js = real_j then SOME (tl js)
blanchet@33192
   509
                                        else NONE)) sel_jsss
blanchet@33192
   510
            val uncur_arg_Ts = binder_types constr_T
blanchet@35179
   511
            val maybe_cyclic = co orelse not standard
blanchet@33192
   512
          in
blanchet@35180
   513
            if maybe_cyclic andalso not (null seen) andalso
blanchet@35188
   514
               member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
blanchet@35180
   515
              cyclic_var ()
blanchet@34124
   516
            else if constr_s = @{const_name Word} then
blanchet@34124
   517
              HOLogic.mk_number
blanchet@34124
   518
                  (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
blanchet@34124
   519
                  (value_of_bits (the_single arg_jsss))
blanchet@33192
   520
            else
blanchet@33192
   521
              let
blanchet@35179
   522
                val seen = seen |> maybe_cyclic ? cons (T, j)
blanchet@33192
   523
                val ts =
blanchet@33192
   524
                  if length arg_Ts = 0 then
blanchet@33192
   525
                    []
blanchet@33192
   526
                  else
blanchet@35665
   527
                    map3 (fn Ts =>
blanchet@35665
   528
                             term_for_rep (constr_s <> @{const_name FinFun})
blanchet@35665
   529
                                          seen Ts Ts) arg_Ts arg_Rs arg_jsss
blanchet@33192
   530
                    |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
blanchet@33192
   531
                    |> dest_n_tuple (length uncur_arg_Ts)
blanchet@33192
   532
                val t =
blanchet@33192
   533
                  if constr_s = @{const_name Abs_Frac} then
blanchet@35711
   534
                    case ts of
blanchet@35711
   535
                      [Const (@{const_name Pair}, _) $ t1 $ t2] =>
blanchet@35711
   536
                      frac_from_term_pair (body_type T) t1 t2
blanchet@35711
   537
                    | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
blanchet@35711
   538
                                       \term_for_atom (Abs_Frac)", ts)
blanchet@34936
   539
                  else if not for_auto andalso
blanchet@34936
   540
                          (is_abs_fun thy constr_x orelse
blanchet@34936
   541
                           constr_s = @{const_name Quot}) then
blanchet@33192
   542
                    Const (abs_name, constr_T) $ the_single ts
blanchet@33192
   543
                  else
blanchet@33192
   544
                    list_comb (Const constr_x, ts)
blanchet@33192
   545
              in
blanchet@35179
   546
                if maybe_cyclic then
blanchet@35180
   547
                  let val var = cyclic_var () in
blanchet@35188
   548
                    if unfold andalso not standard andalso
blanchet@35180
   549
                       length seen = 1 andalso
blanchet@35180
   550
                       exists_subterm (fn Const (s, _) =>
blanchet@35188
   551
                                          String.isPrefix cyclic_const_prefix s
blanchet@35180
   552
                                        | t' => t' = var) t then
blanchet@35188
   553
                      subst_atomic [(var, cyclic_atom ())] t
blanchet@35180
   554
                    else if exists_subterm (curry (op =) var) t then
blanchet@35179
   555
                      if co then
blanchet@35179
   556
                        Const (@{const_name The}, (T --> bool_T) --> T)
blanchet@35179
   557
                        $ Abs (cyclic_co_val_name, T,
blanchet@35179
   558
                               Const (@{const_name "op ="}, T --> T --> bool_T)
blanchet@35180
   559
                               $ Bound 0 $ abstract_over (var, t))
blanchet@35179
   560
                      else
blanchet@35180
   561
                        cyclic_atom ()
blanchet@33192
   562
                    else
blanchet@33192
   563
                      t
blanchet@33192
   564
                  end
blanchet@33192
   565
                else
blanchet@33192
   566
                  t
blanchet@33192
   567
              end
blanchet@33192
   568
          end
blanchet@33192
   569
    and term_for_vect seen k R T1 T2 T' js =
blanchet@35075
   570
      make_fun true T1 T2 T'
blanchet@35075
   571
               (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
blanchet@35665
   572
               (map (term_for_rep true seen T2 T2 R o single)
blanchet@33192
   573
                    (batch_list (arity_of_rep R) js))
blanchet@35665
   574
    and term_for_rep _ seen T T' Unit [[]] = term_for_atom seen T T' 0 1
blanchet@35665
   575
      | term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
blanchet@35075
   576
        if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
blanchet@33232
   577
        else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
blanchet@35665
   578
      | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _
blanchet@35665
   579
                     (Struct [R1, R2]) [js] =
blanchet@33192
   580
        let
blanchet@33192
   581
          val arity1 = arity_of_rep R1
blanchet@33192
   582
          val (js1, js2) = chop arity1 js
blanchet@33192
   583
        in
blanchet@33192
   584
          list_comb (HOLogic.pair_const T1 T2,
blanchet@35665
   585
                     map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
blanchet@33192
   586
                          [[js1], [js2]])
blanchet@33192
   587
        end
blanchet@35665
   588
      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   589
                     (Vect (k, R')) [js] =
blanchet@33192
   590
        term_for_vect seen k R' T1 T2 T' js
blanchet@35665
   591
      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   592
                     (Func (R1, Formula Neut)) jss =
blanchet@33192
   593
        let
blanchet@33192
   594
          val jss1 = all_combinations_for_rep R1
blanchet@35665
   595
          val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
blanchet@33192
   596
          val ts2 =
blanchet@35665
   597
            map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
blanchet@35385
   598
                                       [[int_from_bool (member (op =) jss js)]])
blanchet@34121
   599
                jss1
blanchet@33192
   600
        in make_fun false T1 T2 T' ts1 ts2 end
blanchet@35665
   601
      | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   602
                     (Func (R1, R2)) jss =
blanchet@33192
   603
        let
blanchet@33192
   604
          val arity1 = arity_of_rep R1
blanchet@33192
   605
          val jss1 = all_combinations_for_rep R1
blanchet@35665
   606
          val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
blanchet@33192
   607
          val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
blanchet@35665
   608
          val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
blanchet@33192
   609
                         o AList.lookup (op =) grouped_jss2) jss1
blanchet@35665
   610
        in make_fun maybe_opt T1 T2 T' ts1 ts2 end
blanchet@35665
   611
      | term_for_rep _ seen T T' (Opt R) jss =
blanchet@35665
   612
        if null jss then Const (unknown, T)
blanchet@35665
   613
        else term_for_rep true seen T T' R jss
blanchet@35665
   614
      | term_for_rep _ _ T _ R jss =
blanchet@33232
   615
        raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
blanchet@33192
   616
                   Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
blanchet@33192
   617
                   string_of_int (length jss))
blanchet@35712
   618
  in
blanchet@35712
   619
    postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
blanchet@35712
   620
    oooo term_for_rep true []
blanchet@35712
   621
  end
blanchet@33192
   622
blanchet@35718
   623
(** Constant postprocessing **)
blanchet@35718
   624
blanchet@35718
   625
fun dest_n_tuple_type 1 T = [T]
blanchet@35718
   626
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@35718
   627
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@35718
   628
  | dest_n_tuple_type _ T =
blanchet@35718
   629
    raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
blanchet@35718
   630
blanchet@35718
   631
fun const_format thy def_table (x as (s, T)) =
blanchet@35718
   632
  if String.isPrefix unrolled_prefix s then
blanchet@35718
   633
    const_format thy def_table (original_name s, range_type T)
blanchet@35718
   634
  else if String.isPrefix skolem_prefix s then
blanchet@35718
   635
    let
blanchet@35718
   636
      val k = unprefix skolem_prefix s
blanchet@35718
   637
              |> strip_first_name_sep |> fst |> space_explode "@"
blanchet@35718
   638
              |> hd |> Int.fromString |> the
blanchet@35718
   639
    in [k, num_binder_types T - k] end
blanchet@35718
   640
  else if original_name s <> s then
blanchet@35718
   641
    [num_binder_types T]
blanchet@35718
   642
  else case def_of_const thy def_table x of
blanchet@35718
   643
    SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
blanchet@35718
   644
                 let val k = length (strip_abs_vars t') in
blanchet@35718
   645
                   [k, num_binder_types T - k]
blanchet@35718
   646
                 end
blanchet@35718
   647
               else
blanchet@35718
   648
                 [num_binder_types T]
blanchet@35718
   649
  | NONE => [num_binder_types T]
blanchet@35718
   650
fun intersect_formats _ [] = []
blanchet@35718
   651
  | intersect_formats [] _ = []
blanchet@35718
   652
  | intersect_formats ks1 ks2 =
blanchet@35718
   653
    let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
blanchet@35718
   654
      intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
blanchet@35718
   655
                        (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
blanchet@35718
   656
      [Int.min (k1, k2)]
blanchet@35718
   657
    end
blanchet@35718
   658
blanchet@35718
   659
fun lookup_format thy def_table formats t =
blanchet@35718
   660
  case AList.lookup (fn (SOME x, SOME y) =>
blanchet@35718
   661
                        (term_match thy) (x, y) | _ => false)
blanchet@35718
   662
                    formats (SOME t) of
blanchet@35718
   663
    SOME format => format
blanchet@35718
   664
  | NONE => let val format = the (AList.lookup (op =) formats NONE) in
blanchet@35718
   665
              case t of
blanchet@35718
   666
                Const x => intersect_formats format
blanchet@35718
   667
                                             (const_format thy def_table x)
blanchet@35718
   668
              | _ => format
blanchet@35718
   669
            end
blanchet@35718
   670
blanchet@35718
   671
fun format_type default_format format T =
blanchet@35718
   672
  let
blanchet@35718
   673
    val T = uniterize_unarize_unbox_etc_type T
blanchet@35718
   674
    val format = format |> filter (curry (op <) 0)
blanchet@35718
   675
  in
blanchet@35718
   676
    if forall (curry (op =) 1) format then
blanchet@35718
   677
      T
blanchet@35718
   678
    else
blanchet@35718
   679
      let
blanchet@35718
   680
        val (binder_Ts, body_T) = strip_type T
blanchet@35718
   681
        val batched =
blanchet@35718
   682
          binder_Ts
blanchet@35718
   683
          |> map (format_type default_format default_format)
blanchet@35718
   684
          |> rev |> chunk_list_unevenly (rev format)
blanchet@35718
   685
          |> map (HOLogic.mk_tupleT o rev)
blanchet@35718
   686
      in List.foldl (op -->) body_T batched end
blanchet@35718
   687
  end
blanchet@35718
   688
fun format_term_type thy def_table formats t =
blanchet@35718
   689
  format_type (the (AList.lookup (op =) formats NONE))
blanchet@35718
   690
              (lookup_format thy def_table formats t) (fastype_of t)
blanchet@35718
   691
blanchet@35718
   692
fun repair_special_format js m format =
blanchet@35718
   693
  m - 1 downto 0 |> chunk_list_unevenly (rev format)
blanchet@35718
   694
                 |> map (rev o filter_out (member (op =) js))
blanchet@35718
   695
                 |> filter_out null |> map length |> rev
blanchet@35718
   696
blanchet@35718
   697
fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}
blanchet@35718
   698
                         : hol_context) (base_name, step_name) formats =
blanchet@35718
   699
  let
blanchet@35718
   700
    val default_format = the (AList.lookup (op =) formats NONE)
blanchet@35718
   701
    fun do_const (x as (s, T)) =
blanchet@35718
   702
      (if String.isPrefix special_prefix s then
blanchet@35718
   703
         let
blanchet@35718
   704
           val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
blanchet@35718
   705
           val (x' as (_, T'), js, ts) =
blanchet@35718
   706
             AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
blanchet@35718
   707
             |> the_single
blanchet@35718
   708
           val max_j = List.last js
blanchet@35718
   709
           val Ts = List.take (binder_types T', max_j + 1)
blanchet@35718
   710
           val missing_js = filter_out (member (op =) js) (0 upto max_j)
blanchet@35718
   711
           val missing_Ts = filter_indices missing_js Ts
blanchet@35718
   712
           fun nth_missing_var n =
blanchet@35718
   713
             ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
blanchet@35718
   714
           val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
blanchet@35718
   715
           val vars = special_bounds ts @ missing_vars
blanchet@35718
   716
           val ts' =
blanchet@35718
   717
             map (fn j =>
blanchet@35718
   718
                     case AList.lookup (op =) (js ~~ ts) j of
blanchet@35718
   719
                       SOME t => do_term t
blanchet@35718
   720
                     | NONE =>
blanchet@35718
   721
                       Var (nth missing_vars
blanchet@35718
   722
                                (find_index (curry (op =) j) missing_js)))
blanchet@35718
   723
                 (0 upto max_j)
blanchet@35718
   724
           val t = do_const x' |> fst
blanchet@35718
   725
           val format =
blanchet@35718
   726
             case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
blanchet@35718
   727
                                 | _ => false) formats (SOME t) of
blanchet@35718
   728
               SOME format =>
blanchet@35718
   729
               repair_special_format js (num_binder_types T') format
blanchet@35718
   730
             | NONE =>
blanchet@35718
   731
               const_format thy def_table x'
blanchet@35718
   732
               |> repair_special_format js (num_binder_types T')
blanchet@35718
   733
               |> intersect_formats default_format
blanchet@35718
   734
         in
blanchet@35718
   735
           (list_comb (t, ts') |> fold_rev abs_var vars,
blanchet@35718
   736
            format_type default_format format T)
blanchet@35718
   737
         end
blanchet@35718
   738
       else if String.isPrefix uncurry_prefix s then
blanchet@35718
   739
         let
blanchet@35718
   740
           val (ss, s') = unprefix uncurry_prefix s
blanchet@35718
   741
                          |> strip_first_name_sep |>> space_explode "@"
blanchet@35718
   742
         in
blanchet@35718
   743
           if String.isPrefix step_prefix s' then
blanchet@35718
   744
             do_const (s', T)
blanchet@35718
   745
           else
blanchet@35718
   746
             let
blanchet@35718
   747
               val k = the (Int.fromString (hd ss))
blanchet@35718
   748
               val j = the (Int.fromString (List.last ss))
blanchet@35718
   749
               val (before_Ts, (tuple_T, rest_T)) =
blanchet@35718
   750
                 strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
blanchet@35718
   751
               val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
blanchet@35718
   752
             in do_const (s', T') end
blanchet@35718
   753
         end
blanchet@35718
   754
       else if String.isPrefix unrolled_prefix s then
blanchet@35718
   755
         let val t = Const (original_name s, range_type T) in
blanchet@35718
   756
           (lambda (Free (iter_var_prefix, nat_T)) t,
blanchet@35718
   757
            format_type default_format
blanchet@35718
   758
                        (lookup_format thy def_table formats t) T)
blanchet@35718
   759
         end
blanchet@35718
   760
       else if String.isPrefix base_prefix s then
blanchet@35718
   761
         (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
blanchet@35718
   762
          format_type default_format default_format T)
blanchet@35718
   763
       else if String.isPrefix step_prefix s then
blanchet@35718
   764
         (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
blanchet@35718
   765
          format_type default_format default_format T)
blanchet@35718
   766
       else if String.isPrefix quot_normal_prefix s then
blanchet@35718
   767
         let val t = Const (nitpick_prefix ^ "normalize quotient type", T) in
blanchet@35718
   768
           (t, format_term_type thy def_table formats t)
blanchet@35718
   769
         end
blanchet@35718
   770
       else if String.isPrefix skolem_prefix s then
blanchet@35718
   771
         let
blanchet@35718
   772
           val ss = the (AList.lookup (op =) (!skolems) s)
blanchet@35718
   773
           val (Ts, Ts') = chop (length ss) (binder_types T)
blanchet@35718
   774
           val frees = map Free (ss ~~ Ts)
blanchet@35718
   775
           val s' = original_name s
blanchet@35718
   776
         in
blanchet@35718
   777
           (fold lambda frees (Const (s', Ts' ---> T)),
blanchet@35718
   778
            format_type default_format
blanchet@35718
   779
                        (lookup_format thy def_table formats (Const x)) T)
blanchet@35718
   780
         end
blanchet@35718
   781
       else if String.isPrefix eval_prefix s then
blanchet@35718
   782
         let
blanchet@35718
   783
           val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
blanchet@35718
   784
         in (t, format_term_type thy def_table formats t) end
blanchet@35718
   785
       else if s = @{const_name undefined_fast_The} then
blanchet@35718
   786
         (Const (nitpick_prefix ^ "The fallback", T),
blanchet@35718
   787
          format_type default_format
blanchet@35718
   788
                      (lookup_format thy def_table formats
blanchet@35718
   789
                           (Const (@{const_name The}, (T --> bool_T) --> T))) T)
blanchet@35718
   790
       else if s = @{const_name undefined_fast_Eps} then
blanchet@35718
   791
         (Const (nitpick_prefix ^ "Eps fallback", T),
blanchet@35718
   792
          format_type default_format
blanchet@35718
   793
                      (lookup_format thy def_table formats
blanchet@35718
   794
                           (Const (@{const_name Eps}, (T --> bool_T) --> T))) T)
blanchet@35718
   795
       else
blanchet@35718
   796
         let val t = Const (original_name s, T) in
blanchet@35718
   797
           (t, format_term_type thy def_table formats t)
blanchet@35718
   798
         end)
blanchet@35718
   799
      |>> map_types uniterize_unarize_unbox_etc_type
blanchet@35718
   800
      |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
blanchet@35718
   801
  in do_const end
blanchet@35718
   802
blanchet@35718
   803
fun assign_operator_for_const (s, T) =
blanchet@35718
   804
  if String.isPrefix ubfp_prefix s then
blanchet@35718
   805
    if is_fun_type T then "\<subseteq>" else "\<le>"
blanchet@35718
   806
  else if String.isPrefix lbfp_prefix s then
blanchet@35718
   807
    if is_fun_type T then "\<supseteq>" else "\<ge>"
blanchet@35718
   808
  else if original_name s <> s then
blanchet@35718
   809
    assign_operator_for_const (strip_first_name_sep s |> snd, T)
blanchet@35718
   810
  else
blanchet@35718
   811
    "="
blanchet@35718
   812
blanchet@35718
   813
(** Model reconstruction **)
blanchet@35718
   814
blanchet@35180
   815
fun term_for_name pool scope sel_names rel_table bounds name =
blanchet@33192
   816
  let val T = type_of name in
blanchet@33192
   817
    tuple_list_for_name rel_table bounds name
blanchet@35280
   818
    |> reconstruct_term false pool (("", ""), ("", "")) scope sel_names
blanchet@35280
   819
                        rel_table bounds T T (rep_of name)
blanchet@33192
   820
  end
blanchet@33192
   821
blanchet@33192
   822
fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
blanchet@33192
   823
                                   $ Abs (s, T, Const (@{const_name "op ="}, _)
blanchet@33192
   824
                                                $ Bound 0 $ t')) =
blanchet@33192
   825
    betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
blanchet@33192
   826
  | unfold_outer_the_binders t = t
blanchet@33192
   827
fun bisimilar_values _ 0 _ = true
blanchet@33192
   828
  | bisimilar_values coTs max_depth (t1, t2) =
blanchet@33192
   829
    let val T = fastype_of t1 in
blanchet@33192
   830
      if exists_subtype (member (op =) coTs) T then
blanchet@33192
   831
        let
blanchet@33192
   832
          val ((head1, args1), (head2, args2)) =
blanchet@33192
   833
            pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
blanchet@34121
   834
          val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
blanchet@33192
   835
        in
blanchet@34936
   836
          head1 = head2 andalso
blanchet@34936
   837
          forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
blanchet@33192
   838
        end
blanchet@33192
   839
      else
blanchet@33192
   840
        t1 = t2
blanchet@33192
   841
    end
blanchet@33192
   842
blanchet@33192
   843
fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
blanchet@35280
   844
        ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,
blanchet@35280
   845
                      debug, binary_ints, destroy_constrs, specialize,
blanchet@36389
   846
                      star_linear_preds, fast_descrs, tac_timeout, evals,
blanchet@36389
   847
                      case_names, def_table, nondef_table, user_nondefs,
blanchet@36388
   848
                      simp_table, psimp_table, choice_spec_table, intro_table,
blanchet@36388
   849
                      ground_thm_table, ersatz_table, skolems, special_funs,
blanchet@36388
   850
                      unrolled_preds, wf_cache, constr_cache},
blanchet@35190
   851
         binarize, card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
blanchet@34124
   852
        formats all_frees free_names sel_names nonsel_names rel_table bounds =
blanchet@33192
   853
  let
blanchet@35180
   854
    val pool = Unsynchronized.ref []
blanchet@35280
   855
    val (wacky_names as (_, base_step_names), ctxt) =
blanchet@33192
   856
      add_wacky_syntax ctxt
blanchet@35070
   857
    val hol_ctxt =
blanchet@33192
   858
      {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
blanchet@34982
   859
       stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
blanchet@34124
   860
       binary_ints = binary_ints, destroy_constrs = destroy_constrs,
blanchet@36389
   861
       specialize = specialize, star_linear_preds = star_linear_preds,
blanchet@36389
   862
       fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
blanchet@36389
   863
       case_names = case_names, def_table = def_table,
blanchet@36389
   864
       nondef_table = nondef_table, user_nondefs = user_nondefs,
blanchet@36389
   865
       simp_table = simp_table, psimp_table = psimp_table,
blanchet@36389
   866
       choice_spec_table = choice_spec_table, intro_table = intro_table,
blanchet@36389
   867
       ground_thm_table = ground_thm_table, ersatz_table = ersatz_table,
blanchet@36389
   868
       skolems = skolems, special_funs = special_funs,
blanchet@36389
   869
       unrolled_preds = unrolled_preds, wf_cache = wf_cache,
blanchet@36389
   870
       constr_cache = constr_cache}
blanchet@36388
   871
    val scope =
blanchet@36388
   872
      {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
blanchet@36388
   873
       bits = bits, bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}
blanchet@35188
   874
    fun term_for_rep unfold =
blanchet@35188
   875
      reconstruct_term unfold pool wacky_names scope sel_names rel_table bounds
blanchet@35180
   876
    fun nth_value_of_type card T n =
blanchet@35188
   877
      let
blanchet@35188
   878
        fun aux unfold = term_for_rep unfold T T (Atom (card, 0)) [[n]]
blanchet@35188
   879
      in
blanchet@35188
   880
        case aux false of
blanchet@35188
   881
          t as Const (s, _) =>
blanchet@35188
   882
          if String.isPrefix cyclic_const_prefix s then
blanchet@35188
   883
            HOLogic.mk_eq (t, aux true)
blanchet@35188
   884
          else
blanchet@35188
   885
            t
blanchet@35188
   886
        | t => t
blanchet@35188
   887
      end
blanchet@35712
   888
    val all_values =
blanchet@35712
   889
      all_values_of_type pool wacky_names scope sel_names rel_table bounds
blanchet@33192
   890
    fun is_codatatype_wellformed (cos : dtype_spec list)
blanchet@33192
   891
                                 ({typ, card, ...} : dtype_spec) =
blanchet@33192
   892
      let
blanchet@35712
   893
        val ts = all_values card typ
blanchet@33192
   894
        val max_depth = Integer.sum (map #card cos)
blanchet@33192
   895
      in
blanchet@33192
   896
        forall (not o bisimilar_values (map #typ cos) max_depth)
blanchet@33192
   897
               (all_distinct_unordered_pairs_of ts)
blanchet@33192
   898
      end
blanchet@33192
   899
    fun pretty_for_assign name =
blanchet@33192
   900
      let
blanchet@33192
   901
        val (oper, (t1, T'), T) =
blanchet@33192
   902
          case name of
blanchet@33192
   903
            FreeName (s, T, _) =>
blanchet@35665
   904
            let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
blanchet@33192
   905
              ("=", (t, format_term_type thy def_table formats t), T)
blanchet@33192
   906
            end
blanchet@33192
   907
          | ConstName (s, T, _) =>
blanchet@33192
   908
            (assign_operator_for_const (s, T),
blanchet@35280
   909
             user_friendly_const hol_ctxt base_step_names formats (s, T), T)
blanchet@33232
   910
          | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
blanchet@33192
   911
                            \pretty_for_assign", [name])
blanchet@33192
   912
        val t2 = if rep_of name = Any then
blanchet@33192
   913
                   Const (@{const_name undefined}, T')
blanchet@33192
   914
                 else
blanchet@33192
   915
                   tuple_list_for_name rel_table bounds name
blanchet@35180
   916
                   |> term_for_rep false T T' (rep_of name)
blanchet@33192
   917
      in
blanchet@33192
   918
        Pretty.block (Pretty.breaks
blanchet@33571
   919
            [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
blanchet@33192
   920
             Pretty.str oper, Syntax.pretty_term ctxt t2])
blanchet@33192
   921
      end
blanchet@34123
   922
    fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
blanchet@33192
   923
      Pretty.block (Pretty.breaks
blanchet@35665
   924
          (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::
blanchet@35665
   925
           (case typ of
blanchet@35665
   926
              Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]
blanchet@35665
   927
            | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
blanchet@35665
   928
            | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
blanchet@35665
   929
            | _ => []) @
blanchet@35665
   930
           [Pretty.str "=",
blanchet@35665
   931
            Pretty.enum "," "{" "}"
blanchet@35712
   932
                (map (Syntax.pretty_term ctxt) (all_values card typ) @
blanchet@35665
   933
                 (if fun_from_pair complete false then []
blanchet@35665
   934
                  else [Pretty.str unrep]))]))
blanchet@33192
   935
    fun integer_datatype T =
blanchet@33192
   936
      [{typ = T, card = card_of_type card_assigns T, co = false,
blanchet@35385
   937
        standard = true, complete = (false, false), concrete = (true, true),
blanchet@35385
   938
        deep = true, constrs = []}]
blanchet@33232
   939
      handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
blanchet@33192
   940
    val (codatatypes, datatypes) =
blanchet@34982
   941
      datatypes |> filter #deep |> List.partition #co
blanchet@35220
   942
                ||> append (integer_datatype int_T
blanchet@35220
   943
                            |> is_standard_datatype thy stds nat_T
blanchet@35220
   944
                               ? append (integer_datatype nat_T))
blanchet@33192
   945
    val block_of_datatypes =
blanchet@33192
   946
      if show_datatypes andalso not (null datatypes) then
blanchet@33192
   947
        [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
blanchet@33192
   948
                         (map pretty_for_datatype datatypes)]
blanchet@33192
   949
      else
blanchet@33192
   950
        []
blanchet@33192
   951
    val block_of_codatatypes =
blanchet@33192
   952
      if show_datatypes andalso not (null codatatypes) then
blanchet@33192
   953
        [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
blanchet@33192
   954
                         (map pretty_for_datatype codatatypes)]
blanchet@33192
   955
      else
blanchet@33192
   956
        []
blanchet@33192
   957
    fun block_of_names show title names =
blanchet@33192
   958
      if show andalso not (null names) then
blanchet@33192
   959
        Pretty.str (title ^ plural_s_for_list names ^ ":")
blanchet@33192
   960
        :: map (Pretty.indent indent_size o pretty_for_assign)
blanchet@33192
   961
               (sort_wrt (original_name o nickname_of) names)
blanchet@33192
   962
      else
blanchet@33192
   963
        []
blanchet@33192
   964
    val (skolem_names, nonskolem_nonsel_names) =
blanchet@33192
   965
      List.partition is_skolem_name nonsel_names
blanchet@33192
   966
    val (eval_names, noneval_nonskolem_nonsel_names) =
blanchet@33192
   967
      List.partition (String.isPrefix eval_prefix o nickname_of)
blanchet@33192
   968
                     nonskolem_nonsel_names
blanchet@35665
   969
      ||> filter_out (member (op =) [@{const_name bisim},
blanchet@35665
   970
                                     @{const_name bisim_iterator_max}]
blanchet@34121
   971
                      o nickname_of)
blanchet@33192
   972
    val free_names =
blanchet@33192
   973
      map (fn x as (s, T) =>
blanchet@34121
   974
              case filter (curry (op =) x
blanchet@35280
   975
                       o pairf nickname_of
blanchet@35665
   976
                               (uniterize_unarize_unbox_etc_type o type_of))
blanchet@35190
   977
                       free_names of
blanchet@33192
   978
                [name] => name
blanchet@33192
   979
              | [] => FreeName (s, T, Any)
blanchet@33232
   980
              | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
blanchet@33192
   981
                                 [Const x])) all_frees
blanchet@33192
   982
    val chunks = block_of_names true "Free variable" free_names @
blanchet@33192
   983
                 block_of_names show_skolems "Skolem constant" skolem_names @
blanchet@33192
   984
                 block_of_names true "Evaluated term" eval_names @
blanchet@33192
   985
                 block_of_datatypes @ block_of_codatatypes @
blanchet@33192
   986
                 block_of_names show_consts "Constant"
blanchet@33192
   987
                                noneval_nonskolem_nonsel_names
blanchet@33192
   988
  in
blanchet@33192
   989
    (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
blanchet@33192
   990
                    else chunks),
blanchet@34936
   991
     bisim_depth >= 0 orelse
blanchet@34936
   992
     forall (is_codatatype_wellformed codatatypes) codatatypes)
blanchet@33192
   993
  end
blanchet@33192
   994
blanchet@35280
   995
fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
blanchet@34998
   996
                               card_assigns, ...})
blanchet@33192
   997
                    auto_timeout free_names sel_names rel_table bounds prop =
blanchet@33192
   998
  let
blanchet@35076
   999
    val pool = Unsynchronized.ref []
blanchet@33192
  1000
    fun free_type_assm (T, k) =
blanchet@33192
  1001
      let
blanchet@35076
  1002
        fun atom j = nth_atom pool true T j k
blanchet@33192
  1003
        fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
blanchet@33192
  1004
        val eqs = map equation_for_atom (index_seq 0 k)
blanchet@33192
  1005
        val compreh_assm =
blanchet@33192
  1006
          Const (@{const_name All}, (T --> bool_T) --> bool_T)
blanchet@33192
  1007
              $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
blanchet@33192
  1008
        val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
blanchet@34998
  1009
      in s_conj (compreh_assm, distinct_assm) end
blanchet@33192
  1010
    fun free_name_assm name =
blanchet@33192
  1011
      HOLogic.mk_eq (Free (nickname_of name, type_of name),
blanchet@35180
  1012
                     term_for_name pool scope sel_names rel_table bounds name)
blanchet@33192
  1013
    val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
blanchet@33192
  1014
    val model_assms = map free_name_assm free_names
blanchet@34998
  1015
    val assm = foldr1 s_conj (freeT_assms @ model_assms)
blanchet@33192
  1016
    fun try_out negate =
blanchet@33192
  1017
      let
blanchet@33192
  1018
        val concl = (negate ? curry (op $) @{const Not})
wenzelm@35625
  1019
                    (Object_Logic.atomize_term thy prop)
blanchet@34998
  1020
        val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
blanchet@33192
  1021
                   |> map_types (map_type_tfree
blanchet@34998
  1022
                                     (fn (s, []) => TFree (s, HOLogic.typeS)
blanchet@34998
  1023
                                       | x => TFree x))
blanchet@34998
  1024
       val _ = if debug then
blanchet@34998
  1025
                 priority ((if negate then "Genuineness" else "Spuriousness") ^
blanchet@34998
  1026
                           " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
blanchet@34998
  1027
               else
blanchet@34998
  1028
                 ()
blanchet@34998
  1029
        val goal = prop |> cterm_of thy |> Goal.init
blanchet@33192
  1030
      in
blanchet@33192
  1031
        (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
blanchet@33192
  1032
                                        (auto_tac (clasimpset_of ctxt)))
blanchet@33192
  1033
              |> the |> Goal.finish ctxt; true)
blanchet@33192
  1034
        handle THM _ => false
blanchet@33192
  1035
             | TimeLimit.TimeOut => false
blanchet@33192
  1036
      end
blanchet@33192
  1037
  in
blanchet@33705
  1038
    if try_out false then SOME true
blanchet@33705
  1039
    else if try_out true then SOME false
blanchet@33192
  1040
    else NONE
blanchet@33192
  1041
  end
blanchet@33192
  1042
blanchet@33192
  1043
end;