src/HOL/Library/Old_SMT/old_smt_translate.ML
author wenzelm
Wed Jun 17 11:03:05 2015 +0200 (2015-06-17)
changeset 60500 903bb1495239
parent 58058 1a0b18176548
permissions -rw-r--r--
isabelle update_cartouches;
     1 (*  Title:      HOL/Library/Old_SMT/old_smt_translate.ML
     2     Author:     Sascha Boehme, TU Muenchen
     3 
     4 Translate theorems into an SMT intermediate format and serialize them.
     5 *)
     6 
     7 signature OLD_SMT_TRANSLATE =
     8 sig
     9   (*intermediate term structure*)
    10   datatype squant = SForall | SExists
    11   datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
    12   datatype sterm =
    13     SVar of int |
    14     SApp of string * sterm list |
    15     SLet of string * sterm * sterm |
    16     SQua of squant * string list * sterm spattern list * int option * sterm
    17 
    18   (*translation configuration*)
    19   type prefixes = {sort_prefix: string, func_prefix: string}
    20   type sign = {
    21     header: string list,
    22     sorts: string list,
    23     dtyps: (string * (string * (string * string) list) list) list list,
    24     funcs: (string * (string list * string)) list }
    25   type config = {
    26     prefixes: prefixes,
    27     header: term list -> string list,
    28     is_fol: bool,
    29     has_datatypes: bool,
    30     serialize: string list -> sign -> sterm list -> string }
    31   type recon = {
    32     context: Proof.context,
    33     typs: typ Symtab.table,
    34     terms: term Symtab.table,
    35     rewrite_rules: thm list,
    36     assms: (int * thm) list }
    37 
    38   (*translation*)
    39   val add_config: Old_SMT_Utils.class * (Proof.context -> config) ->
    40     Context.generic -> Context.generic 
    41   val translate: Proof.context -> string list -> (int * thm) list ->
    42     string * recon
    43 end
    44 
    45 structure Old_SMT_Translate: OLD_SMT_TRANSLATE =
    46 struct
    47 
    48 
    49 (* intermediate term structure *)
    50 
    51 datatype squant = SForall | SExists
    52 
    53 datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
    54 
    55 datatype sterm =
    56   SVar of int |
    57   SApp of string * sterm list |
    58   SLet of string * sterm * sterm |
    59   SQua of squant * string list * sterm spattern list * int option * sterm
    60 
    61 
    62 
    63 (* translation configuration *)
    64 
    65 type prefixes = {sort_prefix: string, func_prefix: string}
    66 
    67 type sign = {
    68   header: string list,
    69   sorts: string list,
    70   dtyps: (string * (string * (string * string) list) list) list list,
    71   funcs: (string * (string list * string)) list }
    72 
    73 type config = {
    74   prefixes: prefixes,
    75   header: term list -> string list,
    76   is_fol: bool,
    77   has_datatypes: bool,
    78   serialize: string list -> sign -> sterm list -> string }
    79 
    80 type recon = {
    81   context: Proof.context,
    82   typs: typ Symtab.table,
    83   terms: term Symtab.table,
    84   rewrite_rules: thm list,
    85   assms: (int * thm) list }
    86 
    87 
    88 
    89 (* translation context *)
    90 
    91 fun make_tr_context {sort_prefix, func_prefix} =
    92   (sort_prefix, 1, Typtab.empty, func_prefix, 1, Termtab.empty)
    93 
    94 fun string_of_index pre i = pre ^ string_of_int i
    95 
    96 fun add_typ T proper (cx as (sp, Tidx, typs, fp, idx, terms)) =
    97   (case Typtab.lookup typs T of
    98     SOME (n, _) => (n, cx)
    99   | NONE =>
   100       let
   101         val n = string_of_index sp Tidx
   102         val typs' = Typtab.update (T, (n, proper)) typs
   103       in (n, (sp, Tidx+1, typs', fp, idx, terms)) end)
   104 
   105 fun add_fun t sort (cx as (sp, Tidx, typs, fp, idx, terms)) =
   106   (case Termtab.lookup terms t of
   107     SOME (n, _) => (n, cx)
   108   | NONE => 
   109       let
   110         val n = string_of_index fp idx
   111         val terms' = Termtab.update (t, (n, sort)) terms
   112       in (n, (sp, Tidx, typs, fp, idx+1, terms')) end)
   113 
   114 fun sign_of header dtyps (_, _, typs, _, _, terms) = {
   115   header = header,
   116   sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
   117   dtyps = dtyps,
   118   funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
   119 
   120 fun recon_of ctxt rules thms ithms (_, _, typs, _, _, terms) =
   121   let
   122     fun add_typ (T, (n, _)) = Symtab.update (n, T)
   123     val typs' = Typtab.fold add_typ typs Symtab.empty
   124 
   125     fun add_fun (t, (n, _)) = Symtab.update (n, t)
   126     val terms' = Termtab.fold add_fun terms Symtab.empty
   127 
   128     val assms = map (pair ~1) thms @ ithms
   129   in
   130     {context=ctxt, typs=typs', terms=terms', rewrite_rules=rules, assms=assms}
   131   end
   132 
   133 
   134 
   135 (* preprocessing *)
   136 
   137 (** datatype declarations **)
   138 
   139 fun collect_datatypes_and_records (tr_context, ctxt) ts =
   140   let
   141     val (declss, ctxt') =
   142       fold (Term.fold_types Old_SMT_Datatypes.add_decls) ts ([], ctxt)
   143 
   144     fun is_decl_typ T = exists (exists (equal T o fst)) declss
   145 
   146     fun add_typ' T proper =
   147       (case Old_SMT_Builtin.dest_builtin_typ ctxt' T of
   148         SOME n => pair n
   149       | NONE => add_typ T proper)
   150 
   151     fun tr_select sel =
   152       let val T = Term.range_type (Term.fastype_of sel)
   153       in add_fun sel NONE ##>> add_typ' T (not (is_decl_typ T)) end
   154     fun tr_constr (constr, selects) =
   155       add_fun constr NONE ##>> fold_map tr_select selects
   156     fun tr_typ (T, cases) = add_typ' T false ##>> fold_map tr_constr cases
   157     val (declss', tr_context') = fold_map (fold_map tr_typ) declss tr_context
   158 
   159     fun add (constr, selects) =
   160       Termtab.update (constr, length selects) #>
   161       fold (Termtab.update o rpair 1) selects
   162     val funcs = fold (fold (fold add o snd)) declss Termtab.empty
   163   in ((funcs, declss', tr_context', ctxt'), ts) end
   164     (* FIXME: also return necessary datatype and record theorems *)
   165 
   166 
   167 (** eta-expand quantifiers, let expressions and built-ins *)
   168 
   169 local
   170   fun eta f T t = Abs (Name.uu, T, f (Term.incr_boundvars 1 t $ Bound 0))
   171 
   172   fun exp f T = eta f (Term.domain_type (Term.domain_type T))
   173 
   174   fun exp2 T q =
   175     let val U = Term.domain_type T
   176     in Abs (Name.uu, U, q $ eta I (Term.domain_type U) (Bound 0)) end
   177 
   178   fun exp2' T l =
   179     let val (U1, U2) = Term.dest_funT T ||> Term.domain_type
   180     in Abs (Name.uu, U1, eta I U2 (l $ Bound 0)) end
   181 
   182   fun expf k i T t =
   183     let val Ts = drop i (fst (Old_SMT_Utils.dest_funT k T))
   184     in
   185       Term.incr_boundvars (length Ts) t
   186       |> fold_rev (fn i => fn u => u $ Bound i) (0 upto length Ts - 1)
   187       |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts
   188     end
   189 in
   190 
   191 fun eta_expand ctxt is_fol funcs =
   192   let
   193     fun exp_func t T ts =
   194       (case Termtab.lookup funcs t of
   195         SOME k =>
   196           Term.list_comb (t, ts)
   197           |> k <> length ts ? expf k (length ts) T
   198       | NONE => Term.list_comb (t, ts))
   199 
   200     fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
   201       | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp expand T t
   202       | expand (q as Const (@{const_name All}, T)) = exp2 T q
   203       | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
   204       | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp expand T t
   205       | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
   206       | expand ((l as Const (@{const_name Let}, _)) $ t $ Abs a) =
   207           if is_fol then expand (Term.betapply (Abs a, t))
   208           else l $ expand t $ abs_expand a
   209       | expand ((l as Const (@{const_name Let}, T)) $ t $ u) =
   210           if is_fol then expand (u $ t)
   211           else l $ expand t $ exp expand (Term.range_type T) u
   212       | expand ((l as Const (@{const_name Let}, T)) $ t) =
   213           if is_fol then
   214             let val U = Term.domain_type (Term.range_type T)
   215             in Abs (Name.uu, U, Bound 0 $ Term.incr_boundvars 1 t) end
   216           else exp2 T (l $ expand t)
   217       | expand (l as Const (@{const_name Let}, T)) =
   218           if is_fol then 
   219             let val U = Term.domain_type (Term.range_type T)
   220             in
   221               Abs (Name.uu, Term.domain_type T, Abs (Name.uu, U,
   222                 Bound 0 $ Bound 1))
   223             end
   224           else exp2' T l
   225       | expand t =
   226           (case Term.strip_comb t of
   227             (u as Const (c as (_, T)), ts) =>
   228               (case Old_SMT_Builtin.dest_builtin ctxt c ts of
   229                 SOME (_, k, us, mk) =>
   230                   if k = length us then mk (map expand us)
   231                   else if k < length us then
   232                     chop k (map expand us) |>> mk |> Term.list_comb
   233                   else expf k (length ts) T (mk (map expand us))
   234               | NONE => exp_func u T (map expand ts))
   235           | (u as Free (_, T), ts) => exp_func u T (map expand ts)
   236           | (Abs a, ts) => Term.list_comb (abs_expand a, map expand ts)
   237           | (u, ts) => Term.list_comb (u, map expand ts))
   238 
   239     and abs_expand (n, T, t) = Abs (n, T, expand t)
   240   
   241   in map expand end
   242 
   243 end
   244 
   245 
   246 (** introduce explicit applications **)
   247 
   248 local
   249   (*
   250     Make application explicit for functions with varying number of arguments.
   251   *)
   252 
   253   fun add t i = apfst (Termtab.map_default (t, i) (Integer.min i))
   254   fun add_type T = apsnd (Typtab.update (T, ()))
   255 
   256   fun min_arities t =
   257     (case Term.strip_comb t of
   258       (u as Const _, ts) => add u (length ts) #> fold min_arities ts
   259     | (u as Free _, ts) => add u (length ts) #> fold min_arities ts
   260     | (Abs (_, T, u), ts) => add_type T #> min_arities u #> fold min_arities ts
   261     | (_, ts) => fold min_arities ts)
   262 
   263   fun minimize types t i =
   264     let
   265       fun find_min j [] _ = j
   266         | find_min j (U :: Us) T =
   267             if Typtab.defined types T then j
   268             else find_min (j + 1) Us (U --> T)
   269 
   270       val (Ts, T) = Term.strip_type (Term.type_of t)
   271     in find_min 0 (take i (rev Ts)) T end
   272 
   273   fun app u (t, T) =
   274     (Const (@{const_name fun_app}, T --> T) $ t $ u, Term.range_type T)
   275 
   276   fun apply i t T ts =
   277     let
   278       val (ts1, ts2) = chop i ts
   279       val (_, U) = Old_SMT_Utils.dest_funT i T
   280     in fst (fold app ts2 (Term.list_comb (t, ts1), U)) end
   281 in
   282 
   283 fun intro_explicit_application ctxt funcs ts =
   284   let
   285     val (arities, types) = fold min_arities ts (Termtab.empty, Typtab.empty)
   286     val arities' = Termtab.map (minimize types) arities
   287 
   288     fun app_func t T ts =
   289       if is_some (Termtab.lookup funcs t) then Term.list_comb (t, ts)
   290       else apply (the (Termtab.lookup arities' t)) t T ts
   291 
   292     fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
   293 
   294     fun traverse Ts t =
   295       (case Term.strip_comb t of
   296         (q as Const (@{const_name All}, _), [Abs (x, T, u)]) =>
   297           q $ Abs (x, T, in_trigger (T :: Ts) u)
   298       | (q as Const (@{const_name Ex}, _), [Abs (x, T, u)]) =>
   299           q $ Abs (x, T, in_trigger (T :: Ts) u)
   300       | (q as Const (@{const_name Let}, _), [u1, u2 as Abs _]) =>
   301           q $ traverse Ts u1 $ traverse Ts u2
   302       | (u as Const (c as (_, T)), ts) =>
   303           (case Old_SMT_Builtin.dest_builtin ctxt c ts of
   304             SOME (_, k, us, mk) =>
   305               let
   306                 val (ts1, ts2) = chop k (map (traverse Ts) us)
   307                 val U = Term.strip_type T |>> snd o chop k |> (op --->)
   308               in apply 0 (mk ts1) U ts2 end
   309           | NONE => app_func u T (map (traverse Ts) ts))
   310       | (u as Free (_, T), ts) => app_func u T (map (traverse Ts) ts)
   311       | (u as Bound i, ts) => apply 0 u (nth Ts i) (map (traverse Ts) ts)
   312       | (Abs (n, T, u), ts) => traverses Ts (Abs (n, T, traverse (T::Ts) u)) ts
   313       | (u, ts) => traverses Ts u ts)
   314     and in_trigger Ts ((c as @{const trigger}) $ p $ t) =
   315           c $ in_pats Ts p $ in_weight Ts t
   316       | in_trigger Ts t = in_weight Ts t
   317     and in_pats Ts ps =
   318       in_list @{typ "pattern list"}
   319         (in_list @{typ pattern} (in_pat Ts)) ps
   320     and in_pat Ts ((p as Const (@{const_name pat}, _)) $ t) =
   321           p $ traverse Ts t
   322       | in_pat Ts ((p as Const (@{const_name nopat}, _)) $ t) =
   323           p $ traverse Ts t
   324       | in_pat _ t = raise TERM ("bad pattern", [t])
   325     and in_weight Ts ((c as @{const weight}) $ w $ t) =
   326           c $ w $ traverse Ts t
   327       | in_weight Ts t = traverse Ts t 
   328     and traverses Ts t ts = Term.list_comb (t, map (traverse Ts) ts)
   329   in map (traverse []) ts end
   330 
   331 val fun_app_eq = mk_meta_eq @{thm fun_app_def}
   332 
   333 end
   334 
   335 
   336 (** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
   337 
   338 local
   339   val term_bool = @{lemma "term_true ~= term_false"
   340     by (simp add: term_true_def term_false_def)}
   341 
   342   val is_quant = member (op =) [@{const_name All}, @{const_name Ex}]
   343 
   344   val fol_rules = [
   345     Let_def,
   346     mk_meta_eq @{thm term_true_def},
   347     mk_meta_eq @{thm term_false_def},
   348     @{lemma "P = True == P" by (rule eq_reflection) simp},
   349     @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
   350 
   351   fun as_term t = @{const HOL.eq (bool)} $ t $ @{const term_true}
   352 
   353   exception BAD_PATTERN of unit
   354 
   355   fun wrap_in_if pat t =
   356     if pat then
   357       raise BAD_PATTERN ()
   358     else
   359       @{const If (bool)} $ t $ @{const term_true} $ @{const term_false}
   360 
   361   fun is_builtin_conn_or_pred ctxt c ts =
   362     is_some (Old_SMT_Builtin.dest_builtin_conn ctxt c ts) orelse
   363     is_some (Old_SMT_Builtin.dest_builtin_pred ctxt c ts)
   364 
   365   fun builtin b ctxt c ts =
   366     (case (Const c, ts) of
   367       (@{const HOL.eq (bool)}, [t, u]) =>
   368         if t = @{const term_true} orelse u = @{const term_true} then
   369           Old_SMT_Builtin.dest_builtin_eq ctxt t u
   370         else b ctxt c ts
   371     | _ => b ctxt c ts)
   372 in
   373 
   374 fun folify ctxt =
   375   let
   376     fun in_list T f t = HOLogic.mk_list T (map_filter f (HOLogic.dest_list t))
   377 
   378     fun in_term pat t =
   379       (case Term.strip_comb t of
   380         (@{const True}, []) => @{const term_true}
   381       | (@{const False}, []) => @{const term_false}
   382       | (u as Const (@{const_name If}, _), [t1, t2, t3]) =>
   383           if pat then raise BAD_PATTERN ()
   384           else u $ in_form t1 $ in_term pat t2 $ in_term pat t3
   385       | (Const (c as (n, _)), ts) =>
   386           if is_builtin_conn_or_pred ctxt c ts then wrap_in_if pat (in_form t)
   387           else if is_quant n then wrap_in_if pat (in_form t)
   388           else Term.list_comb (Const c, map (in_term pat) ts)
   389       | (Free c, ts) => Term.list_comb (Free c, map (in_term pat) ts)
   390       | _ => t)
   391 
   392     and in_weight ((c as @{const weight}) $ w $ t) = c $ w $ in_form t
   393       | in_weight t = in_form t 
   394 
   395     and in_pat ((p as Const (@{const_name pat}, _)) $ t) =
   396           p $ in_term true t
   397       | in_pat ((p as Const (@{const_name nopat}, _)) $ t) =
   398           p $ in_term true t
   399       | in_pat t = raise TERM ("bad pattern", [t])
   400 
   401     and in_pats ps =
   402       in_list @{typ "pattern list"}
   403         (SOME o in_list @{typ pattern} (try in_pat)) ps
   404 
   405     and in_trigger ((c as @{const trigger}) $ p $ t) =
   406           c $ in_pats p $ in_weight t
   407       | in_trigger t = in_weight t
   408 
   409     and in_form t =
   410       (case Term.strip_comb t of
   411         (q as Const (qn, _), [Abs (n, T, u)]) =>
   412           if is_quant qn then q $ Abs (n, T, in_trigger u)
   413           else as_term (in_term false t)
   414       | (Const c, ts) =>
   415           (case Old_SMT_Builtin.dest_builtin_conn ctxt c ts of
   416             SOME (_, _, us, mk) => mk (map in_form us)
   417           | NONE =>
   418               (case Old_SMT_Builtin.dest_builtin_pred ctxt c ts of
   419                 SOME (_, _, us, mk) => mk (map (in_term false) us)
   420               | NONE => as_term (in_term false t)))
   421       | _ => as_term (in_term false t))
   422   in
   423     map in_form #>
   424     cons (Old_SMT_Utils.prop_of term_bool) #>
   425     pair (fol_rules, [term_bool], builtin)
   426   end
   427 
   428 end
   429 
   430 
   431 (* translation into intermediate format *)
   432 
   433 (** utility functions **)
   434 
   435 val quantifier = (fn
   436     @{const_name All} => SOME SForall
   437   | @{const_name Ex} => SOME SExists
   438   | _ => NONE)
   439 
   440 fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
   441       if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
   442   | group_quant _ Ts t = (Ts, t)
   443 
   444 fun dest_weight (@{const weight} $ w $ t) =
   445       (SOME (snd (HOLogic.dest_number w)), t)
   446   | dest_weight t = (NONE, t)
   447 
   448 fun dest_pat (Const (@{const_name pat}, _) $ t) = (t, true)
   449   | dest_pat (Const (@{const_name nopat}, _) $ t) = (t, false)
   450   | dest_pat t = raise TERM ("bad pattern", [t])
   451 
   452 fun dest_pats [] = I
   453   | dest_pats ts =
   454       (case map dest_pat ts |> split_list ||> distinct (op =) of
   455         (ps, [true]) => cons (SPat ps)
   456       | (ps, [false]) => cons (SNoPat ps)
   457       | _ => raise TERM ("bad multi-pattern", ts))
   458 
   459 fun dest_trigger (@{const trigger} $ tl $ t) =
   460       (rev (fold (dest_pats o HOLogic.dest_list) (HOLogic.dest_list tl) []), t)
   461   | dest_trigger t = ([], t)
   462 
   463 fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
   464   let
   465     val (Ts, u) = group_quant qn [T] t
   466     val (ps, p) = dest_trigger u
   467     val (w, b) = dest_weight p
   468   in (q, rev Ts, ps, w, b) end)
   469 
   470 fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
   471   | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
   472 
   473 
   474 (** translation from Isabelle terms into SMT intermediate terms **)
   475 
   476 fun intermediate header dtyps builtin ctxt ts trx =
   477   let
   478     fun transT (T as TFree _) = add_typ T true
   479       | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
   480       | transT (T as Type _) =
   481           (case Old_SMT_Builtin.dest_builtin_typ ctxt T of
   482             SOME n => pair n
   483           | NONE => add_typ T true)
   484 
   485     fun app n ts = SApp (n, ts)
   486 
   487     fun trans t =
   488       (case Term.strip_comb t of
   489         (Const (qn, _), [Abs (_, T, t1)]) =>
   490           (case dest_quant qn T t1 of
   491             SOME (q, Ts, ps, w, b) =>
   492               fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
   493               trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', w, b'))
   494           | NONE => raise TERM ("unsupported quantifier", [t]))
   495       | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
   496           transT T ##>> trans t1 ##>> trans t2 #>>
   497           (fn ((U, u1), u2) => SLet (U, u1, u2))
   498       | (u as Const (c as (_, T)), ts) =>
   499           (case builtin ctxt c ts of
   500             SOME (n, _, us, _) => fold_map trans us #>> app n
   501           | NONE => transs u T ts)
   502       | (u as Free (_, T), ts) => transs u T ts
   503       | (Bound i, []) => pair (SVar i)
   504       | _ => raise TERM ("bad SMT term", [t]))
   505  
   506     and transs t T ts =
   507       let val (Us, U) = Old_SMT_Utils.dest_funT (length ts) T
   508       in
   509         fold_map transT Us ##>> transT U #-> (fn Up =>
   510         add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
   511       end
   512 
   513     val (us, trx') = fold_map trans ts trx
   514   in ((sign_of (header ts) dtyps trx', us), trx') end
   515 
   516 
   517 
   518 (* translation *)
   519 
   520 structure Configs = Generic_Data
   521 (
   522   type T = (Proof.context -> config) Old_SMT_Utils.dict
   523   val empty = []
   524   val extend = I
   525   fun merge data = Old_SMT_Utils.dict_merge fst data
   526 )
   527 
   528 fun add_config (cs, cfg) = Configs.map (Old_SMT_Utils.dict_update (cs, cfg))
   529 
   530 fun get_config ctxt = 
   531   let val cs = Old_SMT_Config.solver_class_of ctxt
   532   in
   533     (case Old_SMT_Utils.dict_get (Configs.get (Context.Proof ctxt)) cs of
   534       SOME cfg => cfg ctxt
   535     | NONE => error ("SMT: no translation configuration found " ^
   536         "for solver class " ^ quote (Old_SMT_Utils.string_of_class cs)))
   537   end
   538 
   539 fun translate ctxt comments ithms =
   540   let
   541     val {prefixes, is_fol, header, has_datatypes, serialize} = get_config ctxt
   542 
   543     val with_datatypes =
   544       has_datatypes andalso Config.get ctxt Old_SMT_Config.datatypes
   545 
   546     fun no_dtyps (tr_context, ctxt) ts =
   547       ((Termtab.empty, [], tr_context, ctxt), ts)
   548 
   549     val ts1 = map (Envir.beta_eta_contract o Old_SMT_Utils.prop_of o snd) ithms
   550 
   551     val ((funcs, dtyps, tr_context, ctxt1), ts2) =
   552       ((make_tr_context prefixes, ctxt), ts1)
   553       |-> (if with_datatypes then collect_datatypes_and_records else no_dtyps)
   554 
   555     fun is_binder (Const (@{const_name Let}, _) $ _) = true
   556       | is_binder t = Lambda_Lifting.is_quantifier t
   557 
   558     fun mk_trigger ((q as Const (@{const_name All}, _)) $ Abs (n, T, t)) =
   559           q $ Abs (n, T, mk_trigger t)
   560       | mk_trigger (eq as (Const (@{const_name HOL.eq}, T) $ lhs $ _)) =
   561           Term.domain_type T --> @{typ pattern}
   562           |> (fn T => Const (@{const_name pat}, T) $ lhs)
   563           |> HOLogic.mk_list @{typ pattern} o single
   564           |> HOLogic.mk_list @{typ "pattern list"} o single
   565           |> (fn t => @{const trigger} $ t $ eq)
   566       | mk_trigger t = t
   567 
   568     val (ctxt2, ts3) =
   569       ts2
   570       |> eta_expand ctxt1 is_fol funcs
   571       |> rpair ctxt1
   572       |-> Lambda_Lifting.lift_lambdas NONE is_binder
   573       |-> (fn (ts', defs) => fn ctxt' =>
   574           map mk_trigger defs @ ts'
   575           |> intro_explicit_application ctxt' funcs 
   576           |> pair ctxt')
   577 
   578     val ((rewrite_rules, extra_thms, builtin), ts4) =
   579       (if is_fol then folify ctxt2 else pair ([], [], I)) ts3
   580 
   581     val rewrite_rules' = fun_app_eq :: rewrite_rules
   582   in
   583     (ts4, tr_context)
   584     |-> intermediate header dtyps (builtin Old_SMT_Builtin.dest_builtin) ctxt2
   585     |>> uncurry (serialize comments)
   586     ||> recon_of ctxt2 rewrite_rules' extra_thms ithms
   587   end
   588 
   589 end