src/HOL/Tools/Nitpick/nitpick_mono.ML
author blanchet
Mon Dec 06 13:30:57 2010 +0100 (2010-12-06)
changeset 40999 69d0d445c46a
parent 40998 bcd23ddeecef
child 41000 4bbff1684465
permissions -rw-r--r--
fixed bug in clause handling in monotonicity code, whereby the unsound rule False | x <--> False was used to simplify constraints
     1 (*  Title:      HOL/Tools/Nitpick/nitpick_mono.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2009, 2010
     4 
     5 Monotonicity inference for higher-order logic.
     6 *)
     7 
     8 signature NITPICK_MONO =
     9 sig
    10   type hol_context = Nitpick_HOL.hol_context
    11 
    12   val trace : bool Unsynchronized.ref
    13   val formulas_monotonic :
    14     hol_context -> bool -> int -> typ -> term list * term list -> bool
    15   val finitize_funs :
    16     hol_context -> bool -> (typ option * bool option) list -> int -> typ
    17     -> term list * term list -> term list * term list
    18 end;
    19 
    20 structure Nitpick_Mono : NITPICK_MONO =
    21 struct
    22 
    23 open Nitpick_Util
    24 open Nitpick_HOL
    25 
    26 structure PL = PropLogic
    27 
    28 datatype sign = Plus | Minus
    29 
    30 type var = int
    31 
    32 datatype annotation = Gen | New | Fls | Tru
    33 datatype annotation_atom = A of annotation | V of var
    34 
    35 type assign_literal = var * (sign * annotation)
    36 
    37 datatype mtyp =
    38   MAlpha |
    39   MFun of mtyp * annotation_atom * mtyp |
    40   MPair of mtyp * mtyp |
    41   MType of string * mtyp list |
    42   MRec of string * typ list
    43 
    44 datatype mterm =
    45   MRaw of term * mtyp |
    46   MAbs of string * typ * mtyp * annotation_atom * mterm |
    47   MApp of mterm * mterm
    48 
    49 type mdata =
    50   {hol_ctxt: hol_context,
    51    binarize: bool,
    52    alpha_T: typ,
    53    no_harmless: bool,
    54    max_fresh: int Unsynchronized.ref,
    55    datatype_mcache: ((string * typ list) * mtyp) list Unsynchronized.ref,
    56    constr_mcache: (styp * mtyp) list Unsynchronized.ref}
    57 
    58 exception UNSOLVABLE of unit
    59 exception MTYPE of string * mtyp list * typ list
    60 exception MTERM of string * mterm list
    61 
    62 val trace = Unsynchronized.ref false
    63 fun trace_msg msg = if !trace then tracing (msg ()) else ()
    64 
    65 fun string_for_sign Plus = "+"
    66   | string_for_sign Minus = "-"
    67 
    68 fun negate_sign Plus = Minus
    69   | negate_sign Minus = Plus
    70 
    71 val string_for_var = signed_string_of_int
    72 fun string_for_vars sep [] = "0\<^bsub>" ^ sep ^ "\<^esub>"
    73   | string_for_vars sep xs = space_implode sep (map string_for_var xs)
    74 fun subscript_string_for_vars sep xs =
    75   if null xs then "" else "\<^bsub>" ^ string_for_vars sep xs ^ "\<^esub>"
    76 
    77 fun string_for_annotation Gen = "G"
    78   | string_for_annotation New = "N"
    79   | string_for_annotation Fls = "F"
    80   | string_for_annotation Tru = "T"
    81 
    82 fun string_for_annotation_atom (A a) = string_for_annotation a
    83   | string_for_annotation_atom (V x) = string_for_var x
    84 
    85 fun string_for_assign_literal (x, (sn, a)) =
    86   string_for_var x ^ (case sn of Plus => " = " | Minus => " \<noteq> ") ^
    87   string_for_annotation a
    88 
    89 val bool_M = MType (@{type_name bool}, [])
    90 val dummy_M = MType (nitpick_prefix ^ "dummy", [])
    91 
    92 fun is_MRec (MRec _) = true
    93   | is_MRec _ = false
    94 fun dest_MFun (MFun z) = z
    95   | dest_MFun M = raise MTYPE ("Nitpick_Mono.dest_MFun", [M], [])
    96 
    97 val no_prec = 100
    98 
    99 fun precedence_of_mtype (MFun _) = 1
   100   | precedence_of_mtype (MPair _) = 2
   101   | precedence_of_mtype _ = no_prec
   102 
   103 val string_for_mtype =
   104   let
   105     fun aux outer_prec M =
   106       let
   107         val prec = precedence_of_mtype M
   108         val need_parens = (prec < outer_prec)
   109       in
   110         (if need_parens then "(" else "") ^
   111         (if M = dummy_M then
   112            "_"
   113          else case M of
   114              MAlpha => "\<alpha>"
   115            | MFun (M1, aa, M2) =>
   116              aux (prec + 1) M1 ^ " \<Rightarrow>\<^bsup>" ^
   117              string_for_annotation_atom aa ^ "\<^esup> " ^ aux prec M2
   118            | MPair (M1, M2) => aux (prec + 1) M1 ^ " \<times> " ^ aux prec M2
   119            | MType (s, []) =>
   120              if s = @{type_name prop} orelse s = @{type_name bool} then "o"
   121              else s
   122            | MType (s, Ms) => "(" ^ commas (map (aux 0) Ms) ^ ") " ^ s
   123            | MRec (s, _) => "[" ^ s ^ "]") ^
   124         (if need_parens then ")" else "")
   125       end
   126   in aux 0 end
   127 
   128 fun flatten_mtype (MPair (M1, M2)) = maps flatten_mtype [M1, M2]
   129   | flatten_mtype (MType (_, Ms)) = maps flatten_mtype Ms
   130   | flatten_mtype M = [M]
   131 
   132 fun precedence_of_mterm (MRaw _) = no_prec
   133   | precedence_of_mterm (MAbs _) = 1
   134   | precedence_of_mterm (MApp _) = 2
   135 
   136 fun string_for_mterm ctxt =
   137   let
   138     fun mtype_annotation M = "\<^bsup>" ^ string_for_mtype M ^ "\<^esup>"
   139     fun aux outer_prec m =
   140       let
   141         val prec = precedence_of_mterm m
   142         val need_parens = (prec < outer_prec)
   143       in
   144         (if need_parens then "(" else "") ^
   145         (case m of
   146            MRaw (t, M) => Syntax.string_of_term ctxt t ^ mtype_annotation M
   147          | MAbs (s, _, M, aa, m) =>
   148            "\<lambda>" ^ s ^ mtype_annotation M ^ ".\<^bsup>" ^
   149            string_for_annotation_atom aa ^ "\<^esup> " ^ aux prec m
   150          | MApp (m1, m2) => aux prec m1 ^ " " ^ aux (prec + 1) m2) ^
   151         (if need_parens then ")" else "")
   152       end
   153   in aux 0 end
   154 
   155 fun mtype_of_mterm (MRaw (_, M)) = M
   156   | mtype_of_mterm (MAbs (_, _, M, aa, m)) = MFun (M, aa, mtype_of_mterm m)
   157   | mtype_of_mterm (MApp (m1, _)) =
   158     case mtype_of_mterm m1 of
   159       MFun (_, _, M12) => M12
   160     | M1 => raise MTYPE ("Nitpick_Mono.mtype_of_mterm", [M1], [])
   161 
   162 fun strip_mcomb (MApp (m1, m2)) = strip_mcomb m1 ||> (fn ms => append ms [m2])
   163   | strip_mcomb m = (m, [])
   164 
   165 fun initial_mdata hol_ctxt binarize no_harmless alpha_T =
   166   ({hol_ctxt = hol_ctxt, binarize = binarize, alpha_T = alpha_T,
   167     no_harmless = no_harmless, max_fresh = Unsynchronized.ref 0,
   168     datatype_mcache = Unsynchronized.ref [],
   169     constr_mcache = Unsynchronized.ref []} : mdata)
   170 
   171 fun could_exist_alpha_subtype alpha_T (T as Type (_, Ts)) =
   172     T = alpha_T orelse (not (is_fp_iterator_type T) andalso
   173                         exists (could_exist_alpha_subtype alpha_T) Ts)
   174   | could_exist_alpha_subtype alpha_T T = (T = alpha_T)
   175 fun could_exist_alpha_sub_mtype _ (alpha_T as TFree _) T =
   176     could_exist_alpha_subtype alpha_T T
   177   | could_exist_alpha_sub_mtype ctxt alpha_T T =
   178     (T = alpha_T orelse is_datatype ctxt [(NONE, true)] T)
   179 
   180 fun exists_alpha_sub_mtype MAlpha = true
   181   | exists_alpha_sub_mtype (MFun (M1, _, M2)) =
   182     exists exists_alpha_sub_mtype [M1, M2]
   183   | exists_alpha_sub_mtype (MPair (M1, M2)) =
   184     exists exists_alpha_sub_mtype [M1, M2]
   185   | exists_alpha_sub_mtype (MType (_, Ms)) = exists exists_alpha_sub_mtype Ms
   186   | exists_alpha_sub_mtype (MRec _) = true
   187 
   188 fun exists_alpha_sub_mtype_fresh MAlpha = true
   189   | exists_alpha_sub_mtype_fresh (MFun (_, V _, _)) = true
   190   | exists_alpha_sub_mtype_fresh (MFun (_, _, M2)) =
   191     exists_alpha_sub_mtype_fresh M2
   192   | exists_alpha_sub_mtype_fresh (MPair (M1, M2)) =
   193     exists exists_alpha_sub_mtype_fresh [M1, M2]
   194   | exists_alpha_sub_mtype_fresh (MType (_, Ms)) =
   195     exists exists_alpha_sub_mtype_fresh Ms
   196   | exists_alpha_sub_mtype_fresh (MRec _) = true
   197 
   198 fun constr_mtype_for_binders z Ms =
   199   fold_rev (fn M => curry3 MFun M (A Gen)) Ms (MRec z)
   200 
   201 fun repair_mtype _ _ MAlpha = MAlpha
   202   | repair_mtype cache seen (MFun (M1, aa, M2)) =
   203     MFun (repair_mtype cache seen M1, aa, repair_mtype cache seen M2)
   204   | repair_mtype cache seen (MPair Mp) =
   205     MPair (pairself (repair_mtype cache seen) Mp)
   206   | repair_mtype cache seen (MType (s, Ms)) =
   207     MType (s, maps (flatten_mtype o repair_mtype cache seen) Ms)
   208   | repair_mtype cache seen (MRec (z as (s, _))) =
   209     case AList.lookup (op =) cache z |> the of
   210       MRec _ => MType (s, [])
   211     | M => if member (op =) seen M then MType (s, [])
   212            else repair_mtype cache (M :: seen) M
   213 
   214 fun repair_datatype_mcache cache =
   215   let
   216     fun repair_one (z, M) =
   217       Unsynchronized.change cache
   218           (AList.update (op =) (z, repair_mtype (!cache) [] M))
   219   in List.app repair_one (rev (!cache)) end
   220 
   221 fun repair_constr_mcache dtype_cache constr_mcache =
   222   let
   223     fun repair_one (x, M) =
   224       Unsynchronized.change constr_mcache
   225           (AList.update (op =) (x, repair_mtype dtype_cache [] M))
   226   in List.app repair_one (!constr_mcache) end
   227 
   228 fun is_fin_fun_supported_type @{typ prop} = true
   229   | is_fin_fun_supported_type @{typ bool} = true
   230   | is_fin_fun_supported_type (Type (@{type_name option}, _)) = true
   231   | is_fin_fun_supported_type _ = false
   232 fun fin_fun_body _ _ (t as @{term False}) = SOME t
   233   | fin_fun_body _ _ (t as Const (@{const_name None}, _)) = SOME t
   234   | fin_fun_body dom_T ran_T
   235                  ((t0 as Const (@{const_name If}, _))
   236                   $ (t1 as Const (@{const_name HOL.eq}, _) $ Bound 0 $ t1')
   237                   $ t2 $ t3) =
   238     (if loose_bvar1 (t1', 0) then
   239        NONE
   240      else case fin_fun_body dom_T ran_T t3 of
   241        NONE => NONE
   242      | SOME t3 =>
   243        SOME (t0 $ (Const (@{const_name is_unknown}, dom_T --> bool_T) $ t1')
   244                 $ (Const (@{const_name unknown}, ran_T)) $ (t0 $ t1 $ t2 $ t3)))
   245   | fin_fun_body _ _ _ = NONE
   246 
   247 (* ### FIXME: make sure wellformed! *)
   248 
   249 fun fresh_mfun_for_fun_type (mdata as {max_fresh, ...} : mdata) all_minus
   250                             T1 T2 =
   251   let
   252     val M1 = fresh_mtype_for_type mdata all_minus T1
   253     val M2 = fresh_mtype_for_type mdata all_minus T2
   254     val aa = if not all_minus andalso exists_alpha_sub_mtype_fresh M1 andalso
   255                 is_fin_fun_supported_type (body_type T2) then
   256                V (Unsynchronized.inc max_fresh)
   257              else
   258                A Gen
   259   in (M1, aa, M2) end
   260 and fresh_mtype_for_type (mdata as {hol_ctxt as {ctxt, ...}, binarize, alpha_T,
   261                                     datatype_mcache, constr_mcache, ...})
   262                          all_minus =
   263   let
   264     fun do_type T =
   265       if T = alpha_T then
   266         MAlpha
   267       else case T of
   268         Type (@{type_name fun}, [T1, T2]) =>
   269         MFun (fresh_mfun_for_fun_type mdata all_minus T1 T2)
   270       | Type (@{type_name prod}, [T1, T2]) => MPair (pairself do_type (T1, T2))
   271       | Type (z as (s, _)) =>
   272         if could_exist_alpha_sub_mtype ctxt alpha_T T then
   273           case AList.lookup (op =) (!datatype_mcache) z of
   274             SOME M => M
   275           | NONE =>
   276             let
   277               val _ = Unsynchronized.change datatype_mcache (cons (z, MRec z))
   278               val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T
   279               val (all_Ms, constr_Ms) =
   280                 fold_rev (fn (_, T') => fn (all_Ms, constr_Ms) =>
   281                              let
   282                                val binder_Ms = map do_type (binder_types T')
   283                                val new_Ms = filter exists_alpha_sub_mtype_fresh
   284                                                    binder_Ms
   285                                val constr_M = constr_mtype_for_binders z
   286                                                                        binder_Ms
   287                              in
   288                                (union (op =) new_Ms all_Ms,
   289                                 constr_M :: constr_Ms)
   290                              end)
   291                          xs ([], [])
   292               val M = MType (s, all_Ms)
   293               val _ = Unsynchronized.change datatype_mcache
   294                           (AList.update (op =) (z, M))
   295               val _ = Unsynchronized.change constr_mcache
   296                           (append (xs ~~ constr_Ms))
   297             in
   298               if forall (not o is_MRec o snd) (!datatype_mcache) then
   299                 (repair_datatype_mcache datatype_mcache;
   300                  repair_constr_mcache (!datatype_mcache) constr_mcache;
   301                  AList.lookup (op =) (!datatype_mcache) z |> the)
   302               else
   303                 M
   304             end
   305         else
   306           MType (s, [])
   307       | _ => MType (simple_string_of_typ T, [])
   308   in do_type end
   309 
   310 fun prodM_factors (MPair (M1, M2)) = maps prodM_factors [M1, M2]
   311   | prodM_factors M = [M]
   312 fun curried_strip_mtype (MFun (M1, _, M2)) =
   313     curried_strip_mtype M2 |>> append (prodM_factors M1)
   314   | curried_strip_mtype M = ([], M)
   315 fun sel_mtype_from_constr_mtype s M =
   316   let val (arg_Ms, dataM) = curried_strip_mtype M in
   317     MFun (dataM, A Gen,
   318           case sel_no_from_name s of ~1 => bool_M | n => nth arg_Ms n)
   319   end
   320 
   321 fun mtype_for_constr (mdata as {hol_ctxt = {ctxt, ...}, alpha_T, constr_mcache,
   322                                 ...}) (x as (_, T)) =
   323   if could_exist_alpha_sub_mtype ctxt alpha_T T then
   324     case AList.lookup (op =) (!constr_mcache) x of
   325       SOME M => M
   326     | NONE => if T = alpha_T then
   327                 let val M = fresh_mtype_for_type mdata false T in
   328                   (Unsynchronized.change constr_mcache (cons (x, M)); M)
   329                 end
   330               else
   331                 (fresh_mtype_for_type mdata false (body_type T);
   332                  AList.lookup (op =) (!constr_mcache) x |> the)
   333   else
   334     fresh_mtype_for_type mdata false T
   335 fun mtype_for_sel (mdata as {hol_ctxt, binarize, ...}) (x as (s, _)) =
   336   x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
   337     |> mtype_for_constr mdata |> sel_mtype_from_constr_mtype s
   338 
   339 fun resolve_annotation_atom asgs (V x) =
   340     x |> AList.lookup (op =) asgs |> Option.map A |> the_default (V x)
   341   | resolve_annotation_atom _ aa = aa
   342 fun resolve_mtype asgs =
   343   let
   344     fun aux MAlpha = MAlpha
   345       | aux (MFun (M1, aa, M2)) =
   346         MFun (aux M1, resolve_annotation_atom asgs aa, aux M2)
   347       | aux (MPair Mp) = MPair (pairself aux Mp)
   348       | aux (MType (s, Ms)) = MType (s, map aux Ms)
   349       | aux (MRec z) = MRec z
   350   in aux end
   351 
   352 datatype comp_op = Eq | Neq | Leq
   353 
   354 type comp = annotation_atom * annotation_atom * comp_op * var list
   355 type assign_clause = assign_literal list
   356 
   357 type constraint_set = comp list * assign_clause list
   358 
   359 fun string_for_comp_op Eq = "="
   360   | string_for_comp_op Neq = "\<noteq>"
   361   | string_for_comp_op Leq = "\<le>"
   362 
   363 fun string_for_comp (aa1, aa2, cmp, xs) =
   364   string_for_annotation_atom aa1 ^ " " ^ string_for_comp_op cmp ^
   365   subscript_string_for_vars " \<and> " xs ^ " " ^ string_for_annotation_atom aa2
   366 
   367 fun string_for_assign_clause NONE = "\<top>"
   368   | string_for_assign_clause (SOME []) = "\<bot>"
   369   | string_for_assign_clause (SOME asgs) =
   370     space_implode " \<or> " (map string_for_assign_literal asgs)
   371 
   372 fun add_assign_literal (x, (sn, a)) clauses =
   373   if exists (fn [(x', (sn', a'))] =>
   374                 x = x' andalso ((sn = sn' andalso a <> a') orelse
   375                                 (sn <> sn' andalso a = a'))
   376               | _ => false) clauses then
   377     NONE
   378   else
   379     SOME ([(x, a)] :: clauses)
   380 
   381 fun add_assign_disjunct _ NONE = NONE
   382   | add_assign_disjunct asg (SOME asgs) = SOME (insert (op =) asg asgs)
   383 
   384 fun add_assign_clause NONE = I
   385   | add_assign_clause (SOME clause) = insert (op =) clause
   386 
   387 fun annotation_comp Eq a1 a2 = (a1 = a2)
   388   | annotation_comp Neq a1 a2 = (a1 <> a2)
   389   | annotation_comp Leq a1 a2 = (a1 = a2 orelse a2 = Gen)
   390 
   391 fun sign_for_comp_op Eq = Plus
   392   | sign_for_comp_op Neq = Minus
   393   | sign_for_comp_op Leq = raise BAD ("sign_for_comp_op", "unexpected \"Leq\"")
   394 
   395 fun do_annotation_atom_comp Leq [] aa1 aa2 (cset as (comps, clauses)) =
   396     (case (aa1, aa2) of
   397        (A a1, A a2) => if annotation_comp Leq a1 a2 then SOME cset else NONE
   398      | _ => SOME (insert (op =) (aa1, aa2, Leq, []) comps, clauses))
   399   | do_annotation_atom_comp cmp [] aa1 aa2 (cset as (comps, clauses)) =
   400     (case (aa1, aa2) of
   401        (A a1, A a2) => if annotation_comp cmp a1 a2 then SOME cset else NONE
   402      | (V x1, A a2) =>
   403        clauses |> add_assign_literal (x1, (sign_for_comp_op cmp, a2))
   404                |> Option.map (pair comps)
   405      | (A _, V _) => do_annotation_atom_comp cmp [] aa2 aa1 cset
   406      | (V _, V _) => SOME (insert (op =) (aa1, aa2, cmp, []) comps, clauses))
   407   | do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
   408     SOME (insert (op =) (aa1, aa2, cmp, xs) comps, clauses)
   409 
   410 fun add_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
   411   (trace_msg (fn () => "*** Add " ^ string_for_comp (aa1, aa2, cmp, xs));
   412    case do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) of
   413      NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
   414    | SOME cset => cset)
   415 
   416 fun do_mtype_comp _ _ _ _ NONE = NONE
   417   | do_mtype_comp _ _ MAlpha MAlpha cset = cset
   418   | do_mtype_comp Eq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
   419                   (SOME cset) =
   420     cset |> do_annotation_atom_comp Eq xs aa1 aa2
   421          |> do_mtype_comp Eq xs M11 M21 |> do_mtype_comp Eq xs M12 M22
   422   | do_mtype_comp Leq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
   423                   (SOME cset) =
   424     (if exists_alpha_sub_mtype M11 then
   425        cset |> do_annotation_atom_comp Leq xs aa1 aa2
   426             |> do_mtype_comp Leq xs M21 M11
   427             |> (case aa2 of
   428                   A Gen => I
   429                 | A _ => do_mtype_comp Leq xs M11 M21
   430                 | V x => do_mtype_comp Leq (x :: xs) M11 M21)
   431      else
   432        SOME cset)
   433     |> do_mtype_comp Leq xs M12 M22
   434   | do_mtype_comp cmp xs (M1 as MPair (M11, M12)) (M2 as MPair (M21, M22))
   435                   cset =
   436     (cset |> fold (uncurry (do_mtype_comp cmp xs)) [(M11, M21), (M12, M22)]
   437      handle Library.UnequalLengths =>
   438             raise MTYPE ("Nitpick_Mono.do_mtype_comp", [M1, M2], []))
   439   | do_mtype_comp _ _ (MType _) (MType _) cset =
   440     cset (* no need to compare them thanks to the cache *)
   441   | do_mtype_comp cmp _ M1 M2 _ =
   442     raise MTYPE ("Nitpick_Mono.do_mtype_comp (" ^ string_for_comp_op cmp ^ ")",
   443                  [M1, M2], [])
   444 
   445 fun add_mtype_comp cmp M1 M2 cset =
   446   (trace_msg (fn () => "*** Add " ^ string_for_mtype M1 ^ " " ^
   447                        string_for_comp_op cmp ^ " " ^ string_for_mtype M2);
   448    case SOME cset |> do_mtype_comp cmp [] M1 M2 of
   449      NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
   450    | SOME cset => cset)
   451 
   452 val add_mtypes_equal = add_mtype_comp Eq
   453 val add_is_sub_mtype = add_mtype_comp Leq
   454 
   455 fun do_notin_mtype_fv _ _ _ NONE = NONE
   456   | do_notin_mtype_fv Minus _ MAlpha cset = cset
   457   | do_notin_mtype_fv Plus [] MAlpha _ = NONE
   458   | do_notin_mtype_fv Plus [asg] MAlpha (SOME clauses) =
   459     clauses |> add_assign_literal asg
   460   | do_notin_mtype_fv Plus clause MAlpha (SOME clauses) =
   461     SOME (insert (op =) clause clauses)
   462   | do_notin_mtype_fv sn clause (MFun (M1, A a, M2)) cset =
   463     cset |> (if a <> Gen andalso sn = Plus then do_notin_mtype_fv Plus clause M1
   464              else I)
   465          |> (if a = Gen orelse sn = Plus then do_notin_mtype_fv Minus clause M1
   466              else I)
   467          |> do_notin_mtype_fv sn clause M2
   468   | do_notin_mtype_fv Plus clause (MFun (M1, V x, M2)) cset =
   469     cset |> (case add_assign_disjunct (x, (Plus, Gen)) (SOME clause) of
   470                NONE => I
   471              | SOME clause' => do_notin_mtype_fv Plus clause' M1)
   472          |> do_notin_mtype_fv Minus clause M1
   473          |> do_notin_mtype_fv Plus clause M2
   474   | do_notin_mtype_fv Minus clause (MFun (M1, V x, M2)) cset =
   475     cset |> (case fold (fn a => add_assign_disjunct (x, (Plus, a))) [Fls, Tru]
   476                        (SOME clause) of
   477                NONE => I
   478              | SOME clause' => do_notin_mtype_fv Plus clause' M1)
   479          |> do_notin_mtype_fv Minus clause M2
   480   | do_notin_mtype_fv sn clause (MPair (M1, M2)) cset =
   481     cset |> fold (do_notin_mtype_fv sn clause) [M1, M2]
   482   | do_notin_mtype_fv sn clause (MType (_, Ms)) cset =
   483     cset |> fold (do_notin_mtype_fv sn clause) Ms
   484  | do_notin_mtype_fv _ _ M _ =
   485    raise MTYPE ("Nitpick_Mono.do_notin_mtype_fv", [M], [])
   486 
   487 fun add_notin_mtype_fv sn M (comps, clauses) =
   488   (trace_msg (fn () => "*** Add " ^ string_for_mtype M ^ " is " ^
   489                        (case sn of Minus => "concrete" | Plus => "complete"));
   490    case SOME clauses |> do_notin_mtype_fv sn [] M of
   491      NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
   492    | SOME clauses => (comps, clauses))
   493 
   494 val add_mtype_is_concrete = add_notin_mtype_fv Minus
   495 val add_mtype_is_complete = add_notin_mtype_fv Plus
   496 
   497 val bool_table =
   498   [(Gen, (false, false)),
   499    (New, (false, true)),
   500    (Fls, (true, false)),
   501    (Tru, (true, true))]
   502 
   503 fun fst_var n = 2 * n
   504 fun snd_var n = 2 * n + 1
   505 
   506 val bools_from_annotation = AList.lookup (op =) bool_table #> the
   507 val annotation_from_bools = AList.find (op =) bool_table #> the_single
   508 
   509 fun prop_for_bool b = if b then PL.True else PL.False
   510 fun prop_for_bool_var_equality (v1, v2) =
   511   PL.SAnd (PL.SOr (PL.BoolVar v1, PL.SNot (PL.BoolVar v2)),
   512            PL.SOr (PL.SNot (PL.BoolVar v1), PL.BoolVar v2))
   513 fun prop_for_assign (x, a) =
   514   let val (b1, b2) = bools_from_annotation a in
   515     PL.SAnd (PL.BoolVar (fst_var x) |> not b1 ? PL.SNot,
   516              PL.BoolVar (snd_var x) |> not b2 ? PL.SNot)
   517   end
   518 fun prop_for_assign_literal (x, (Plus, a)) = prop_for_assign (x, a)
   519   | prop_for_assign_literal (x, (Minus, a)) = PL.SNot (prop_for_assign (x, a))
   520 fun prop_for_atom_assign (A a', a) = prop_for_bool (a = a')
   521   | prop_for_atom_assign (V x, a) = prop_for_assign_literal (x, (Plus, a))
   522 fun prop_for_atom_equality (aa1, A a2) = prop_for_atom_assign (aa1, a2)
   523   | prop_for_atom_equality (A a1, aa2) = prop_for_atom_assign (aa2, a1)
   524   | prop_for_atom_equality (V x1, V x2) =
   525     PL.SAnd (prop_for_bool_var_equality (pairself fst_var (x1, x2)),
   526              prop_for_bool_var_equality (pairself snd_var (x1, x2)))
   527 val prop_for_assign_clause = PL.exists o map prop_for_assign_literal
   528 fun prop_for_exists_var_assign_literal xs a =
   529   PL.exists (map (fn x => prop_for_assign_literal (x, (Plus, a))) xs)
   530 fun prop_for_comp (aa1, aa2, Eq, []) =
   531     PL.SAnd (prop_for_comp (aa1, aa2, Leq, []),
   532              prop_for_comp (aa2, aa1, Leq, []))
   533   | prop_for_comp (aa1, aa2, Neq, []) =
   534     PL.SNot (prop_for_comp (aa1, aa2, Eq, []))
   535   | prop_for_comp (aa1, aa2, Leq, []) =
   536     PL.SOr (prop_for_atom_equality (aa1, aa2), prop_for_atom_assign (aa2, Gen))
   537   | prop_for_comp (aa1, aa2, cmp, xs) =
   538     PL.SOr (prop_for_exists_var_assign_literal xs Gen,
   539             prop_for_comp (aa1, aa2, cmp, []))
   540 
   541 (* The "calculus" parameter may be 1, 2, or 3, corresponding approximately to
   542    the M1, M2, and M3 calculi from Blanchette & Krauss 2011. *)
   543 fun variable_domain calculus =
   544   [Gen] @ (if calculus > 1 then [Fls] else [])
   545   @ (if calculus > 2 then [New, Tru] else [])
   546 
   547 fun prop_for_variable_domain calculus x =
   548   PL.exists (map (fn a => prop_for_assign_literal (x, (Plus, a)))
   549                  (variable_domain calculus))
   550 
   551 fun extract_assigns max_var assigns asgs =
   552   fold (fn x => fn accum =>
   553            if AList.defined (op =) asgs x then
   554              accum
   555            else case (fst_var x, snd_var x) |> pairself assigns of
   556              (NONE, NONE) => accum
   557            | bp => (x, annotation_from_bools (pairself (the_default false) bp))
   558                    :: accum)
   559        (max_var downto 1) asgs
   560 
   561 fun print_problem calculus comps clauses =
   562   trace_msg (fn () =>
   563                 "*** Problem (calculus M" ^ string_of_int calculus ^ "):\n" ^
   564                 cat_lines (map string_for_comp comps @
   565                            map (string_for_assign_clause o SOME) clauses))
   566 
   567 fun print_solution asgs =
   568   trace_msg (fn () => "*** Solution:\n" ^
   569       (asgs
   570        |> map swap
   571        |> AList.group (op =)
   572        |> map (fn (a, xs) => string_for_annotation a ^ ": " ^
   573                              string_for_vars ", " xs)
   574        |> space_implode "\n"))
   575 
   576 fun solve calculus max_var (comps, clauses) =
   577   let
   578     val asgs = map_filter (fn [(x, (_, a))] => SOME (x, a) | _ => NONE) clauses
   579     fun do_assigns assigns =
   580       SOME (extract_assigns max_var assigns asgs |> tap print_solution)
   581     val _ = print_problem calculus comps clauses
   582     val prop =
   583       map prop_for_comp comps @
   584       map prop_for_assign_clause clauses @
   585       (if calculus < 3 then
   586          map (prop_for_variable_domain calculus) (1 upto max_var)
   587        else
   588          [])
   589       |> PL.all
   590   in
   591     if PL.eval (K false) prop then
   592       do_assigns (K (SOME false))
   593     else if PL.eval (K true) prop then
   594       do_assigns (K (SOME true))
   595     else
   596       let
   597         (* use the first ML solver (to avoid startup overhead) *)
   598         val solvers = !SatSolver.solvers
   599                       |> filter (member (op =) ["dptsat", "dpll"] o fst)
   600       in
   601         case snd (hd solvers) prop of
   602           SatSolver.SATISFIABLE assigns => do_assigns assigns
   603         | _ => (trace_msg (K "*** Unsolvable"); NONE)
   604       end
   605   end
   606 
   607 type mcontext =
   608   {bound_Ts: typ list,
   609    bound_Ms: mtyp list,
   610    frame: (int * annotation_atom) list,
   611    frees: (styp * mtyp) list,
   612    consts: (styp * mtyp) list}
   613 
   614 fun string_for_bound ctxt Ms (j, aa) =
   615   Syntax.string_of_term ctxt (Bound (length Ms - j - 1)) ^ " :\<^bsup>" ^
   616   string_for_annotation_atom aa ^ "\<^esup> " ^
   617   string_for_mtype (nth Ms (length Ms - j - 1))
   618 fun string_for_free relevant_frees ((s, _), M) =
   619   if member (op =) relevant_frees s then SOME (s ^ " : " ^ string_for_mtype M)
   620   else NONE
   621 fun string_for_mcontext ctxt t {bound_Ms, frame, frees, ...} =
   622   (map_filter (string_for_free (Term.add_free_names t [])) frees @
   623    map (string_for_bound ctxt bound_Ms) frame)
   624   |> commas |> enclose "[" "]"
   625 
   626 val initial_gamma =
   627   {bound_Ts = [], bound_Ms = [], frame = [], frees = [], consts = []}
   628 
   629 fun push_bound aa T M {bound_Ts, bound_Ms, frame, frees, consts} =
   630   {bound_Ts = T :: bound_Ts, bound_Ms = M :: bound_Ms,
   631    frame = frame @ [(length bound_Ts, aa)], frees = frees, consts = consts}
   632 fun pop_bound {bound_Ts, bound_Ms, frame, frees, consts} =
   633   {bound_Ts = tl bound_Ts, bound_Ms = tl bound_Ms,
   634    frame = frame |> filter_out (fn (j, _) => j = length bound_Ts - 1),
   635    frees = frees, consts = consts}
   636   handle List.Empty => initial_gamma (* FIXME: needed? *)
   637 
   638 fun set_frame frame ({bound_Ts, bound_Ms, frees, consts, ...} : mcontext) =
   639   {bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame, frees = frees,
   640    consts = consts}
   641 
   642 (* FIXME: make sure tracing messages are complete *)
   643 
   644 fun add_comp_frame aa cmp = fold (add_annotation_atom_comp cmp [] aa o snd)
   645 
   646 fun add_bound_frame j frame =
   647   let
   648     val (new_frame, gen_frame) = List.partition (curry (op =) j o fst) frame
   649   in
   650     add_comp_frame (A New) Leq new_frame
   651     #> add_comp_frame (A Gen) Eq gen_frame
   652   end
   653 
   654 fun fresh_frame ({max_fresh, ...} : mdata) fls tru =
   655   map (apsnd (fn aa =>
   656                  case (aa, fls, tru) of
   657                    (A Fls, SOME a, _) => A a
   658                  | (A Tru, _, SOME a) => A a
   659                  | (A Gen, _, _) => A Gen
   660                  | _ => V (Unsynchronized.inc max_fresh)))
   661 
   662 fun conj_clauses res_aa aa1 aa2 =
   663   [[(aa1, (Neq, Tru)), (aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
   664    [(aa1, (Neq, Fls)), (res_aa, (Eq, Fls))],
   665    [(aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
   666    [(aa1, (Neq, Gen)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
   667    [(aa1, (Neq, New)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
   668    [(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
   669    [(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
   670 
   671 fun disj_clauses res_aa aa1 aa2 =
   672   [[(aa1, (Neq, Tru)), (res_aa, (Eq, Tru))],
   673    [(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
   674    [(aa1, (Neq, Fls)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
   675    [(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
   676    [(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
   677    [(aa1, (Eq, Tru)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
   678    [(aa1, (Eq, Tru)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
   679 
   680 fun imp_clauses res_aa aa1 aa2 =
   681   [[(aa1, (Neq, Fls)), (res_aa, (Eq, Tru))],
   682    [(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
   683    [(aa1, (Neq, Tru)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
   684    [(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
   685    [(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
   686    [(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
   687    [(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
   688 
   689 fun add_annotation_clause_from_quasi_clause _ NONE = NONE
   690   | add_annotation_clause_from_quasi_clause [] accum = accum
   691   | add_annotation_clause_from_quasi_clause ((aa, (cmp, a)) :: rest) accum =
   692     case aa of
   693       A a' => if annotation_comp cmp a' a then NONE
   694               else add_annotation_clause_from_quasi_clause rest accum
   695     | V x => add_annotation_clause_from_quasi_clause rest accum
   696              |> Option.map (cons (x, (sign_for_comp_op cmp, a)))
   697 
   698 fun assign_clause_from_quasi_clause clause =
   699   add_annotation_clause_from_quasi_clause clause (SOME [])
   700 
   701 fun add_connective_var conn mk_quasi_clauses res_aa aa1 aa2 =
   702   (trace_msg (fn () => "*** Add " ^ string_for_annotation_atom res_aa ^ " = " ^
   703                        string_for_annotation_atom aa1 ^ " " ^ conn ^ " " ^
   704                        string_for_annotation_atom aa2);
   705    fold (add_assign_clause o assign_clause_from_quasi_clause)
   706         (mk_quasi_clauses res_aa aa1 aa2))
   707 fun add_connective_frames conn mk_quasi_clauses res_frame frame1 frame2 =
   708   fold I (map3 (fn (_, res_aa) => fn (_, aa1) => fn (_, aa2) =>
   709                    add_connective_var conn mk_quasi_clauses res_aa aa1 aa2)
   710                res_frame frame1 frame2)
   711 
   712 fun kill_unused_in_frame is_in (accum as ({frame, ...}, _)) =
   713   let val (used_frame, unused_frame) = List.partition is_in frame in
   714     accum |>> set_frame used_frame
   715           ||> add_comp_frame (A Gen) Eq unused_frame
   716   end
   717 
   718 fun split_frame is_in_fun (gamma as {frame, ...}, cset) =
   719   let
   720     fun bubble fun_frame arg_frame [] cset =
   721         ((rev fun_frame, rev arg_frame), cset)
   722       | bubble fun_frame arg_frame ((bound as (_, aa)) :: rest) cset =
   723         if is_in_fun bound then
   724           bubble (bound :: fun_frame) arg_frame rest
   725                  (cset |> add_comp_frame aa Leq arg_frame)
   726         else
   727           bubble fun_frame (bound :: arg_frame) rest cset
   728   in cset |> bubble [] [] frame ||> pair gamma end
   729 
   730 fun add_annotation_atom_comp_alt _ (A Gen) _ _ = I
   731   | add_annotation_atom_comp_alt _ (A _) _ _ =
   732     (trace_msg (K "*** Expected G"); raise UNSOLVABLE ())
   733   | add_annotation_atom_comp_alt cmp (V x) aa1 aa2 =
   734     add_annotation_atom_comp cmp [x] aa1 aa2
   735 
   736 fun add_arg_order1 ((_, aa), (_, prev_aa)) = I
   737   add_annotation_atom_comp_alt Neq prev_aa (A Gen) aa
   738 fun add_app1 fun_aa ((_, res_aa), (_, arg_aa)) = I
   739   let
   740     val clause = [(arg_aa, (Eq, New)), (res_aa, (Eq, Gen))]
   741                  |> assign_clause_from_quasi_clause
   742   in
   743     trace_msg (fn () => "*** Add " ^ string_for_assign_clause clause);
   744     apsnd (add_assign_clause clause)
   745     #> add_annotation_atom_comp_alt Leq arg_aa fun_aa res_aa
   746   end
   747 fun add_app _ [] [] = I
   748   | add_app fun_aa res_frame arg_frame =
   749     add_comp_frame (A New) Leq arg_frame
   750     #> fold add_arg_order1 (tl arg_frame ~~ (fst (split_last arg_frame)))
   751     #> fold (add_app1 fun_aa) (res_frame ~~ arg_frame)
   752 
   753 fun consider_term (mdata as {hol_ctxt = {thy, ctxt, stds, ...}, alpha_T,
   754                              max_fresh, ...}) =
   755   let
   756     fun is_enough_eta_expanded t =
   757       case strip_comb t of
   758         (Const x, ts) => the_default 0 (arity_of_built_in_const thy stds x)
   759         <= length ts
   760       | _ => true
   761     val mtype_for = fresh_mtype_for_type mdata false
   762     fun plus_set_mtype_for_dom M =
   763       MFun (M, A (if exists_alpha_sub_mtype M then Fls else Gen), bool_M)
   764     fun do_all T (gamma, cset) =
   765       let
   766         val abs_M = mtype_for (domain_type (domain_type T))
   767         val body_M = mtype_for (body_type T)
   768       in
   769         (MFun (MFun (abs_M, A Gen, body_M), A Gen, body_M),
   770          (gamma, cset |> add_mtype_is_complete abs_M))
   771       end
   772     fun do_equals T (gamma, cset) =
   773       let
   774         val M = mtype_for (domain_type T)
   775         val aa = V (Unsynchronized.inc max_fresh)
   776       in
   777         (MFun (M, A Gen, MFun (M, aa, mtype_for (nth_range_type 2 T))),
   778          (gamma, cset |> add_mtype_is_concrete M
   779                       |> add_annotation_atom_comp Leq [] (A Fls) aa))
   780       end
   781     fun do_robust_set_operation T (gamma, cset) =
   782       let
   783         val set_T = domain_type T
   784         val M1 = mtype_for set_T
   785         val M2 = mtype_for set_T
   786         val M3 = mtype_for set_T
   787       in
   788         (MFun (M1, A Gen, MFun (M2, A Gen, M3)),
   789          (gamma, cset |> add_is_sub_mtype M1 M3 |> add_is_sub_mtype M2 M3))
   790       end
   791     fun do_fragile_set_operation T (gamma, cset) =
   792       let
   793         val set_T = domain_type T
   794         val set_M = mtype_for set_T
   795         fun custom_mtype_for (T as Type (@{type_name fun}, [T1, T2])) =
   796             if T = set_T then set_M
   797             else MFun (custom_mtype_for T1, A Gen, custom_mtype_for T2)
   798           | custom_mtype_for T = mtype_for T
   799       in
   800         (custom_mtype_for T, (gamma, cset |> add_mtype_is_concrete set_M))
   801       end
   802     fun do_pair_constr T accum =
   803       case mtype_for (nth_range_type 2 T) of
   804         M as MPair (a_M, b_M) =>
   805         (MFun (a_M, A Gen, MFun (b_M, A Gen, M)), accum)
   806       | M => raise MTYPE ("Nitpick_Mono.consider_term.do_pair_constr", [M], [])
   807     fun do_nth_pair_sel n T =
   808       case mtype_for (domain_type T) of
   809         M as MPair (a_M, b_M) =>
   810         pair (MFun (M, A Gen, if n = 0 then a_M else b_M))
   811       | M => raise MTYPE ("Nitpick_Mono.consider_term.do_nth_pair_sel", [M], [])
   812     fun do_bounded_quantifier t0 abs_s abs_T connective_t bound_t body_t accum =
   813       let
   814         val abs_M = mtype_for abs_T
   815         val aa = V (Unsynchronized.inc max_fresh)
   816         val (bound_m, accum) =
   817           accum |>> push_bound aa abs_T abs_M |> do_term bound_t
   818         val expected_bound_M = plus_set_mtype_for_dom abs_M
   819         val (body_m, accum) =
   820           accum ||> add_mtypes_equal expected_bound_M (mtype_of_mterm bound_m)
   821                 |> do_term body_t ||> apfst pop_bound
   822         val bound_M = mtype_of_mterm bound_m
   823         val (M1, aa', _) = dest_MFun bound_M
   824       in
   825         (MApp (MRaw (t0, MFun (bound_M, aa, bool_M)),
   826                MAbs (abs_s, abs_T, M1, aa',
   827                      MApp (MApp (MRaw (connective_t,
   828                                        mtype_for (fastype_of connective_t)),
   829                                  MApp (bound_m, MRaw (Bound 0, M1))),
   830                            body_m))), accum)
   831       end
   832     and do_connect conn mk_quasi_clauses t0 t1 t2 (accum as ({frame, ...}, _)) =
   833       let
   834         val frame1 = fresh_frame mdata (SOME Tru) NONE frame
   835         val frame2 = fresh_frame mdata (SOME Fls) NONE frame
   836         val (m1, accum) = accum |>> set_frame frame1 |> do_term t1
   837         val (m2, accum) = accum |>> set_frame frame2 |> do_term t2
   838       in
   839         (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2),
   840          accum |>> set_frame frame
   841                ||> apsnd (add_connective_frames conn mk_quasi_clauses
   842                                                 frame frame1 frame2))
   843       end
   844     and do_term t
   845             (accum as (gamma as {bound_Ts, bound_Ms, frame, frees, consts},
   846                        cset)) =
   847       (trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
   848                            " \<turnstile> " ^ Syntax.string_of_term ctxt t ^
   849                            " : _?");
   850        case t of
   851          @{const False} =>
   852          (MRaw (t, bool_M), accum ||> add_comp_frame (A Fls) Leq frame)
   853        | @{const True} =>
   854          (MRaw (t, bool_M), accum ||> add_comp_frame (A Tru) Leq frame)
   855        | Const (x as (s, T)) =>
   856          (case AList.lookup (op =) consts x of
   857             SOME M => (M, accum)
   858           | NONE =>
   859             if not (could_exist_alpha_subtype alpha_T T) then
   860               (mtype_for T, accum)
   861             else case s of
   862               @{const_name all} => do_all T accum
   863             | @{const_name "=="} => do_equals T accum
   864             | @{const_name All} => do_all T accum
   865             | @{const_name Ex} =>
   866               let val set_T = domain_type T in
   867                 do_term (Abs (Name.uu, set_T,
   868                               @{const Not} $ (HOLogic.mk_eq
   869                                   (Abs (Name.uu, domain_type set_T,
   870                                         @{const False}),
   871                                    Bound 0)))) accum
   872                 |>> mtype_of_mterm
   873               end
   874             | @{const_name HOL.eq} => do_equals T accum
   875             | @{const_name The} =>
   876               (trace_msg (K "*** The"); raise UNSOLVABLE ())
   877             | @{const_name Eps} =>
   878               (trace_msg (K "*** Eps"); raise UNSOLVABLE ())
   879             | @{const_name If} =>
   880               do_robust_set_operation (range_type T) accum
   881               |>> curry3 MFun bool_M (A Gen)
   882             | @{const_name Pair} => do_pair_constr T accum
   883             | @{const_name fst} => do_nth_pair_sel 0 T accum
   884             | @{const_name snd} => do_nth_pair_sel 1 T accum
   885             | @{const_name Id} =>
   886               (MFun (mtype_for (domain_type T), A Gen, bool_M), accum)
   887             | @{const_name converse} =>
   888               let
   889                 val x = Unsynchronized.inc max_fresh
   890                 fun mtype_for_set T =
   891                   MFun (mtype_for (domain_type T), V x, bool_M)
   892                 val ab_set_M = domain_type T |> mtype_for_set
   893                 val ba_set_M = range_type T |> mtype_for_set
   894               in (MFun (ab_set_M, A Gen, ba_set_M), accum) end
   895             | @{const_name trancl} => do_fragile_set_operation T accum
   896             | @{const_name rel_comp} =>
   897               let
   898                 val x = Unsynchronized.inc max_fresh
   899                 fun mtype_for_set T =
   900                   MFun (mtype_for (domain_type T), V x, bool_M)
   901                 val bc_set_M = domain_type T |> mtype_for_set
   902                 val ab_set_M = domain_type (range_type T) |> mtype_for_set
   903                 val ac_set_M = nth_range_type 2 T |> mtype_for_set
   904               in
   905                 (MFun (bc_set_M, A Gen, MFun (ab_set_M, A Gen, ac_set_M)),
   906                  accum)
   907               end
   908             | @{const_name image} =>
   909               let
   910                 val a_M = mtype_for (domain_type (domain_type T))
   911                 val b_M = mtype_for (range_type (domain_type T))
   912               in
   913                 (MFun (MFun (a_M, A Gen, b_M), A Gen,
   914                        MFun (plus_set_mtype_for_dom a_M, A Gen,
   915                              plus_set_mtype_for_dom b_M)), accum)
   916               end
   917             | @{const_name finite} =>
   918               let val M1 = mtype_for (domain_type (domain_type T)) in
   919                 (MFun (plus_set_mtype_for_dom M1, A Gen, bool_M), accum)
   920               end
   921             | @{const_name Sigma} =>
   922               let
   923                 val x = Unsynchronized.inc max_fresh
   924                 fun mtype_for_set T =
   925                   MFun (mtype_for (domain_type T), V x, bool_M)
   926                 val a_set_T = domain_type T
   927                 val a_M = mtype_for (domain_type a_set_T)
   928                 val b_set_M =
   929                   mtype_for_set (range_type (domain_type (range_type T)))
   930                 val a_set_M = mtype_for_set a_set_T
   931                 val a_to_b_set_M = MFun (a_M, A Gen, b_set_M)
   932                 val ab_set_M = mtype_for_set (nth_range_type 2 T)
   933               in
   934                 (MFun (a_set_M, A Gen, MFun (a_to_b_set_M, A Gen, ab_set_M)),
   935                  accum)
   936               end
   937             | _ =>
   938               if s = @{const_name safe_The} then
   939                 let
   940                   val a_set_M = mtype_for (domain_type T)
   941                   val a_M = dest_MFun a_set_M |> #1
   942                 in (MFun (a_set_M, A Gen, a_M), accum) end
   943               else if s = @{const_name ord_class.less_eq} andalso
   944                       is_set_type (domain_type T) then
   945                 do_fragile_set_operation T accum
   946               else if is_sel s then
   947                 (mtype_for_sel mdata x, accum)
   948               else if is_constr ctxt stds x then
   949                 (mtype_for_constr mdata x, accum)
   950               else if is_built_in_const thy stds x then
   951                 (fresh_mtype_for_type mdata true T, accum)
   952               else
   953                 let val M = mtype_for T in
   954                   (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
   955                         frees = frees, consts = (x, M) :: consts}, cset))
   956                 end)
   957            |>> curry MRaw t
   958            ||> apsnd (add_comp_frame (A Gen) Eq frame)
   959          | Free (x as (_, T)) =>
   960            (case AList.lookup (op =) frees x of
   961               SOME M => (M, accum)
   962             | NONE =>
   963               let val M = mtype_for T in
   964                 (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
   965                       frees = (x, M) :: frees, consts = consts}, cset))
   966               end)
   967            |>> curry MRaw t ||> apsnd (add_comp_frame (A Gen) Eq frame)
   968          | Var _ => (trace_msg (K "*** Var"); raise UNSOLVABLE ())
   969          | Bound j =>
   970            (MRaw (t, nth bound_Ms j),
   971             accum ||> add_bound_frame (length bound_Ts - j - 1) frame)
   972          | Abs (s, T, t') =>
   973            (case fin_fun_body T (fastype_of1 (T :: bound_Ts, t')) t' of
   974               SOME t' =>
   975               let
   976                 val M = mtype_for T
   977                 val (m', accum) = do_term t' (accum |>> push_bound (A Fls) T M)
   978               in (MAbs (s, T, M, A Fls, m'), accum |>> pop_bound) end
   979             | NONE =>
   980               ((case t' of
   981                   t1' $ Bound 0 =>
   982                   if not (loose_bvar1 (t1', 0)) andalso
   983                      is_enough_eta_expanded t1' then
   984                     do_term (incr_boundvars ~1 t1') accum
   985                   else
   986                     raise SAME ()
   987                 | (t11 as Const (@{const_name HOL.eq}, _)) $ Bound 0 $ t13 =>
   988                   if not (loose_bvar1 (t13, 0)) then
   989                     do_term (incr_boundvars ~1 (t11 $ t13)) accum
   990                   else
   991                     raise SAME ()
   992                 | _ => raise SAME ())
   993                handle SAME () =>
   994                       let
   995                         val M = mtype_for T
   996                         val aa = V (Unsynchronized.inc max_fresh)
   997                         val (m', accum) =
   998                           do_term t' (accum |>> push_bound aa T M)
   999                       in (MAbs (s, T, M, aa, m'), accum |>> pop_bound) end))
  1000          | (t0 as Const (@{const_name All}, _))
  1001            $ Abs (s', T', (t10 as @{const implies}) $ (t11 $ Bound 0) $ t12) =>
  1002            do_bounded_quantifier t0 s' T' t10 t11 t12 accum
  1003          | (t0 as Const (@{const_name Ex}, _))
  1004            $ Abs (s', T', (t10 as @{const conj}) $ (t11 $ Bound 0) $ t12) =>
  1005            do_bounded_quantifier t0 s' T' t10 t11 t12 accum
  1006          | @{const Not} $ t1 =>
  1007            do_connect "\<implies>" imp_clauses @{const implies} t1
  1008                       @{const False} accum
  1009          | (t0 as @{const conj}) $ t1 $ t2 =>
  1010            do_connect "\<and>" conj_clauses t0 t1 t2 accum
  1011          | (t0 as @{const disj}) $ t1 $ t2 =>
  1012            do_connect "\<or>" disj_clauses t0 t1 t2 accum
  1013          | (t0 as @{const implies}) $ t1 $ t2 =>
  1014            do_connect "\<implies>" imp_clauses t0 t1 t2 accum
  1015          | Const (@{const_name Let}, _) $ t1 $ t2 =>
  1016            do_term (betapply (t2, t1)) accum
  1017          | t1 $ t2 =>
  1018            let
  1019              fun is_in t (j, _) = loose_bvar1 (t, length bound_Ts - j - 1)
  1020              val accum as ({frame, ...}, _) =
  1021                accum |> kill_unused_in_frame (is_in t)
  1022              val ((frame1a, frame1b), accum) = accum |> split_frame (is_in t1)
  1023              val frame2a = frame1a |> map (apsnd (K (A Gen)))
  1024              val frame2b =
  1025                frame1b |> map (apsnd (fn _ => V (Unsynchronized.inc max_fresh)))
  1026              val frame2 = frame2a @ frame2b
  1027              val (m1, accum) = accum |>> set_frame frame1a |> do_term t1
  1028              val (m2, accum) = accum |>> set_frame frame2 |> do_term t2
  1029            in
  1030              let
  1031                val (M11, aa, _) = mtype_of_mterm m1 |> dest_MFun
  1032                val M2 = mtype_of_mterm m2
  1033              in
  1034                (MApp (m1, m2),
  1035                 accum |>> set_frame frame
  1036                       ||> add_is_sub_mtype M2 M11
  1037                       ||> add_app aa frame1b frame2b)
  1038              end
  1039            end)
  1040         |> tap (fn (m, (gamma, _)) =>
  1041                    trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
  1042                                        " \<turnstile> " ^
  1043                                        string_for_mterm ctxt m))
  1044   in do_term end
  1045 
  1046 fun force_minus_funs 0 _ = I
  1047   | force_minus_funs n (M as MFun (M1, _, M2)) =
  1048     add_mtypes_equal M (MFun (M1, A Gen, M2)) #> force_minus_funs (n - 1) M2
  1049   | force_minus_funs _ M =
  1050     raise MTYPE ("Nitpick_Mono.force_minus_funs", [M], [])
  1051 fun consider_general_equals mdata def (x as (_, T)) t1 t2 accum =
  1052   let
  1053     val (m1, accum) = consider_term mdata t1 accum
  1054     val (m2, accum) = consider_term mdata t2 accum
  1055     val M1 = mtype_of_mterm m1
  1056     val M2 = mtype_of_mterm m2
  1057     val accum = accum ||> add_mtypes_equal M1 M2
  1058     val body_M = fresh_mtype_for_type mdata false (nth_range_type 2 T)
  1059     val m = MApp (MApp (MRaw (Const x,
  1060                            MFun (M1, A Gen, MFun (M2, A Gen, body_M))), m1), m2)
  1061   in
  1062     (m, if def then
  1063           let val (head_m, arg_ms) = strip_mcomb m1 in
  1064             accum ||> force_minus_funs (length arg_ms) (mtype_of_mterm head_m)
  1065           end
  1066         else
  1067           accum)
  1068   end
  1069 
  1070 fun consider_general_formula (mdata as {hol_ctxt = {ctxt, ...}, ...}) =
  1071   let
  1072     val mtype_for = fresh_mtype_for_type mdata false
  1073     val do_term = consider_term mdata
  1074     fun do_formula sn t (accum as (gamma, _)) =
  1075         let
  1076           fun do_quantifier (quant_x as (quant_s, _)) abs_s abs_T body_t =
  1077             let
  1078               val abs_M = mtype_for abs_T
  1079               val a = Gen (* FIXME: strengthen *)
  1080               val side_cond = ((sn = Minus) = (quant_s = @{const_name Ex}))
  1081               val (body_m, accum) =
  1082                 accum ||> side_cond ? add_mtype_is_complete abs_M
  1083                       |>> push_bound (A a) abs_T abs_M |> do_formula sn body_t
  1084               val body_M = mtype_of_mterm body_m
  1085             in
  1086               (MApp (MRaw (Const quant_x,
  1087                            MFun (MFun (abs_M, A Gen, body_M), A Gen, body_M)),
  1088                      MAbs (abs_s, abs_T, abs_M, A Gen, body_m)),
  1089                accum |>> pop_bound)
  1090             end
  1091           fun do_equals x t1 t2 =
  1092             case sn of
  1093               Plus => do_term t accum
  1094             | Minus => consider_general_equals mdata false x t1 t2 accum
  1095         in
  1096           (trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
  1097                                " \<turnstile> " ^ Syntax.string_of_term ctxt t ^
  1098                                " : o\<^sup>" ^ string_for_sign sn ^ "?");
  1099            case t of
  1100              Const (x as (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
  1101              do_quantifier x s1 T1 t1
  1102            | Const (x as (@{const_name "=="}, _)) $ t1 $ t2 => do_equals x t1 t2
  1103            | @{const Trueprop} $ t1 =>
  1104              let val (m1, accum) = do_formula sn t1 accum in
  1105                (MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),
  1106                       m1), accum)
  1107              end
  1108            | @{const Not} $ t1 =>
  1109              let val (m1, accum) = do_formula (negate_sign sn) t1 accum in
  1110                (MApp (MRaw (@{const Not}, mtype_for (bool_T --> bool_T)), m1),
  1111                 accum)
  1112              end
  1113            | Const (x as (@{const_name All}, _)) $ Abs (s1, T1, t1) =>
  1114              do_quantifier x s1 T1 t1
  1115            | Const (x0 as (@{const_name Ex}, T0))
  1116              $ (t1 as Abs (s1, T1, t1')) =>
  1117              (case sn of
  1118                 Plus => do_quantifier x0 s1 T1 t1'
  1119               | Minus =>
  1120                 (* FIXME: Move elsewhere *)
  1121                 do_term (@{const Not}
  1122                          $ (HOLogic.eq_const (domain_type T0) $ t1
  1123                             $ Abs (Name.uu, T1, @{const False}))) accum)
  1124            | Const (x as (@{const_name HOL.eq}, _)) $ t1 $ t2 =>
  1125              do_equals x t1 t2
  1126            | Const (@{const_name Let}, _) $ t1 $ t2 =>
  1127              do_formula sn (betapply (t2, t1)) accum
  1128            | (t0 as Const (s0, _)) $ t1 $ t2 =>
  1129              if s0 = @{const_name "==>"} orelse
  1130                 s0 = @{const_name Pure.conjunction} orelse
  1131                 s0 = @{const_name conj} orelse
  1132                 s0 = @{const_name disj} orelse
  1133                 s0 = @{const_name implies} then
  1134                let
  1135                  val impl = (s0 = @{const_name "==>"} orelse
  1136                              s0 = @{const_name implies})
  1137                  val (m1, accum) =
  1138                    do_formula (sn |> impl ? negate_sign) t1 accum
  1139                  val (m2, accum) = do_formula sn t2 accum
  1140                in
  1141                  (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2),
  1142                   accum)
  1143                end
  1144              else
  1145                do_term t accum
  1146            | _ => do_term t accum)
  1147         end
  1148         |> tap (fn (m, (gamma, _)) =>
  1149                    trace_msg (fn () => string_for_mcontext ctxt t gamma ^
  1150                                        " \<turnstile> " ^
  1151                                        string_for_mterm ctxt m ^ " : o\<^sup>" ^
  1152                                        string_for_sign sn))
  1153   in do_formula end
  1154 
  1155 (* The harmless axiom optimization below is somewhat too aggressive in the face
  1156    of (rather peculiar) user-defined axioms. *)
  1157 val harmless_consts =
  1158   [@{const_name ord_class.less}, @{const_name ord_class.less_eq}]
  1159 val bounteous_consts = [@{const_name bisim}]
  1160 
  1161 fun is_harmless_axiom ({no_harmless = true, ...} : mdata) _ = false
  1162   | is_harmless_axiom {hol_ctxt = {thy, stds, ...}, ...} t =
  1163     Term.add_consts t []
  1164     |> filter_out (is_built_in_const thy stds)
  1165     |> (forall (member (op =) harmless_consts o original_name o fst) orf
  1166         exists (member (op =) bounteous_consts o fst))
  1167 
  1168 fun consider_nondefinitional_axiom mdata t =
  1169   if is_harmless_axiom mdata t then pair (MRaw (t, dummy_M))
  1170   else consider_general_formula mdata Plus t
  1171 
  1172 fun consider_definitional_axiom (mdata as {hol_ctxt = {ctxt, ...}, ...}) t =
  1173   if not (is_constr_pattern_formula ctxt t) then
  1174     consider_nondefinitional_axiom mdata t
  1175   else if is_harmless_axiom mdata t then
  1176     pair (MRaw (t, dummy_M))
  1177   else
  1178     let
  1179       val mtype_for = fresh_mtype_for_type mdata false
  1180       val do_term = consider_term mdata
  1181       fun do_all quant_t abs_s abs_T body_t accum =
  1182         let
  1183           val abs_M = mtype_for abs_T
  1184           val (body_m, accum) =
  1185             accum |>> push_bound (A Gen) abs_T abs_M |> do_formula body_t
  1186           val body_M = mtype_of_mterm body_m
  1187         in
  1188           (MApp (MRaw (quant_t, MFun (MFun (abs_M, A Gen, body_M), A Gen,
  1189                        body_M)),
  1190                  MAbs (abs_s, abs_T, abs_M, A Gen, body_m)),
  1191            accum |>> pop_bound)
  1192         end
  1193       and do_conjunction t0 t1 t2 accum =
  1194         let
  1195           val (m1, accum) = do_formula t1 accum
  1196           val (m2, accum) = do_formula t2 accum
  1197         in
  1198           (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
  1199         end
  1200       and do_implies t0 t1 t2 accum =
  1201         let
  1202           val (m1, accum) = do_term t1 accum
  1203           val (m2, accum) = do_formula t2 accum
  1204         in
  1205           (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
  1206         end
  1207       and do_formula t accum =
  1208           case t of
  1209             (t0 as Const (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
  1210             do_all t0 s1 T1 t1 accum
  1211           | @{const Trueprop} $ t1 =>
  1212             let val (m1, accum) = do_formula t1 accum in
  1213               (MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),
  1214                      m1), accum)
  1215             end
  1216           | Const (x as (@{const_name "=="}, _)) $ t1 $ t2 =>
  1217             consider_general_equals mdata true x t1 t2 accum
  1218           | (t0 as @{const "==>"}) $ t1 $ t2 => do_implies t0 t1 t2 accum
  1219           | (t0 as @{const Pure.conjunction}) $ t1 $ t2 =>
  1220             do_conjunction t0 t1 t2 accum
  1221           | (t0 as Const (@{const_name All}, _)) $ Abs (s0, T1, t1) =>
  1222             do_all t0 s0 T1 t1 accum
  1223           | Const (x as (@{const_name HOL.eq}, _)) $ t1 $ t2 =>
  1224             consider_general_equals mdata true x t1 t2 accum
  1225           | (t0 as @{const conj}) $ t1 $ t2 => do_conjunction t0 t1 t2 accum
  1226           | (t0 as @{const implies}) $ t1 $ t2 => do_implies t0 t1 t2 accum
  1227           | _ => raise TERM ("Nitpick_Mono.consider_definitional_axiom.\
  1228                              \do_formula", [t])
  1229     in do_formula t end
  1230 
  1231 fun string_for_mtype_of_term ctxt asgs t M =
  1232   Syntax.string_of_term ctxt t ^ " : " ^ string_for_mtype (resolve_mtype asgs M)
  1233 
  1234 fun print_mcontext ctxt asgs ({frees, consts, ...} : mcontext) =
  1235   trace_msg (fn () =>
  1236       map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Free x) M) frees @
  1237       map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Const x) M) consts
  1238       |> cat_lines)
  1239 
  1240 fun amass f t (ms, accum) =
  1241   let val (m, accum) = f t accum in (m :: ms, accum) end
  1242 
  1243 fun infer which no_harmless (hol_ctxt as {ctxt, ...}) binarize calculus alpha_T
  1244           (nondef_ts, def_ts) =
  1245   let
  1246     val _ = trace_msg (fn () => "****** " ^ which ^ " analysis: " ^
  1247                                 string_for_mtype MAlpha ^ " is " ^
  1248                                 Syntax.string_of_typ ctxt alpha_T)
  1249     val mdata as {max_fresh, constr_mcache, ...} =
  1250       initial_mdata hol_ctxt binarize no_harmless alpha_T
  1251     val accum = (initial_gamma, ([], []))
  1252     val (nondef_ms, accum) =
  1253       ([], accum) |> amass (consider_general_formula mdata Plus) (hd nondef_ts)
  1254                   |> fold (amass (consider_nondefinitional_axiom mdata))
  1255                           (tl nondef_ts)
  1256     val (def_ms, (gamma, cset)) =
  1257       ([], accum) |> fold (amass (consider_definitional_axiom mdata)) def_ts
  1258   in
  1259     case solve calculus (!max_fresh) cset of
  1260       SOME asgs => (print_mcontext ctxt asgs gamma;
  1261                     SOME (asgs, (nondef_ms, def_ms), !constr_mcache))
  1262     | _ => NONE
  1263   end
  1264   handle UNSOLVABLE () => NONE
  1265        | MTYPE (loc, Ms, Ts) =>
  1266          raise BAD (loc, commas (map string_for_mtype Ms @
  1267                                  map (Syntax.string_of_typ ctxt) Ts))
  1268        | MTERM (loc, ms) =>
  1269          raise BAD (loc, commas (map (string_for_mterm ctxt) ms))
  1270 
  1271 fun formulas_monotonic hol_ctxt =
  1272   is_some oooo infer "Monotonicity" false hol_ctxt
  1273 
  1274 fun fin_fun_constr T1 T2 =
  1275   (@{const_name FinFun}, (T1 --> T2) --> Type (@{type_name fin_fun}, [T1, T2]))
  1276 
  1277 fun finitize_funs (hol_ctxt as {thy, ctxt, stds, constr_cache, ...}) binarize
  1278                   finitizes calculus alpha_T tsp =
  1279   case infer "Finiteness" true hol_ctxt binarize calculus alpha_T tsp of
  1280     SOME (asgs, msp, constr_mtypes) =>
  1281     if forall (curry (op =) Gen o snd) asgs then
  1282       tsp
  1283     else
  1284       let
  1285         fun should_finitize T aa =
  1286           case triple_lookup (type_match thy) finitizes T of
  1287             SOME (SOME false) => false
  1288           | _ => resolve_annotation_atom asgs aa = A Fls
  1289         fun type_from_mtype T M =
  1290           case (M, T) of
  1291             (MAlpha, _) => T
  1292           | (MFun (M1, aa, M2), Type (@{type_name fun}, Ts)) =>
  1293             Type (if should_finitize T aa then @{type_name fin_fun}
  1294                   else @{type_name fun}, map2 type_from_mtype Ts [M1, M2])
  1295           | (MPair (M1, M2), Type (@{type_name prod}, Ts)) =>
  1296             Type (@{type_name prod}, map2 type_from_mtype Ts [M1, M2])
  1297           | (MType _, _) => T
  1298           | _ => raise MTYPE ("Nitpick_Mono.finitize_funs.type_from_mtype",
  1299                               [M], [T])
  1300         fun finitize_constr (x as (s, T)) =
  1301           (s, case AList.lookup (op =) constr_mtypes x of
  1302                 SOME M => type_from_mtype T M
  1303               | NONE => T)
  1304         fun term_from_mterm new_Ts old_Ts m =
  1305           case m of
  1306             MRaw (t, M) =>
  1307             let
  1308               val T = fastype_of1 (old_Ts, t)
  1309               val T' = type_from_mtype T M
  1310             in
  1311               case t of
  1312                 Const (x as (s, _)) =>
  1313                 if s = @{const_name finite} then
  1314                   case domain_type T' of
  1315                     set_T' as Type (@{type_name fin_fun}, _) =>
  1316                     Abs (Name.uu, set_T', @{const True})
  1317                   | _ => Const (s, T')
  1318                 else if s = @{const_name "=="} orelse
  1319                         s = @{const_name HOL.eq} then
  1320                   let
  1321                     val T =
  1322                       case T' of
  1323                         Type (_, [T1, Type (_, [T2, T3])]) =>
  1324                         T1 --> T2 --> T3
  1325                       | _ => raise TYPE ("Nitpick_Mono.finitize_funs.\
  1326                                          \term_from_mterm", [T, T'], [])
  1327                   in coerce_term hol_ctxt new_Ts T' T (Const (s, T)) end
  1328                 else if is_built_in_const thy stds x then
  1329                   coerce_term hol_ctxt new_Ts T' T t
  1330                 else if is_constr ctxt stds x then
  1331                   Const (finitize_constr x)
  1332                 else if is_sel s then
  1333                   let
  1334                     val n = sel_no_from_name s
  1335                     val x' =
  1336                       x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
  1337                         |> finitize_constr
  1338                     val x'' =
  1339                       binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
  1340                                                              x' n
  1341                   in Const x'' end
  1342                 else
  1343                   Const (s, T')
  1344               | Free (s, T) => Free (s, type_from_mtype T M)
  1345               | Bound _ => t
  1346               | _ => raise MTERM ("Nitpick_Mono.finitize_funs.term_from_mterm",
  1347                                   [m])
  1348             end
  1349           | MApp (m1, m2) =>
  1350             let
  1351               val (t1, t2) = pairself (term_from_mterm new_Ts old_Ts) (m1, m2)
  1352               val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)
  1353               val (t1', T2') =
  1354                 case T1 of
  1355                   Type (s, [T11, T12]) =>
  1356                   (if s = @{type_name fin_fun} then
  1357                      select_nth_constr_arg ctxt stds (fin_fun_constr T11 T12) t1
  1358                                            0 (T11 --> T12)
  1359                    else
  1360                      t1, T11)
  1361                 | _ => raise TYPE ("Nitpick_Mono.finitize_funs.term_from_mterm",
  1362                                    [T1], [])
  1363             in betapply (t1', coerce_term hol_ctxt new_Ts T2' T2 t2) end
  1364           | MAbs (s, old_T, M, aa, m') =>
  1365             let
  1366               val new_T = type_from_mtype old_T M
  1367               val t' = term_from_mterm (new_T :: new_Ts) (old_T :: old_Ts) m'
  1368               val T' = fastype_of1 (new_T :: new_Ts, t')
  1369             in
  1370               Abs (s, new_T, t')
  1371               |> should_finitize (new_T --> T') aa
  1372                  ? construct_value ctxt stds (fin_fun_constr new_T T') o single
  1373             end
  1374       in
  1375         Unsynchronized.change constr_cache (map (apsnd (map finitize_constr)));
  1376         pairself (map (term_from_mterm [] [])) msp
  1377       end
  1378   | NONE => tsp
  1379 
  1380 end;