boehmes@36898: (*  Title:      HOL/Tools/SMT/smt_translate.ML
boehmes@36898:     Author:     Sascha Boehme, TU Muenchen
boehmes@36898: 
boehmes@36898: Translate theorems into an SMT intermediate format and serialize them.
boehmes@36898: *)
boehmes@36898: 
boehmes@36898: signature SMT_TRANSLATE =
boehmes@36898: sig
boehmes@41123:   (*intermediate term structure*)
boehmes@36898:   datatype squant = SForall | SExists
boehmes@36898:   datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
boehmes@36898:   datatype sterm =
boehmes@36898:     SVar of int |
boehmes@36898:     SApp of string * sterm list |
boehmes@36898:     SLet of string * sterm * sterm |
boehmes@40664:     SQua of squant * string list * sterm spattern list * int option * sterm
boehmes@36898: 
boehmes@41127:   (*translation configuration*)
boehmes@36898:   type prefixes = {sort_prefix: string, func_prefix: string}
boehmes@36898:   type sign = {
boehmes@36899:     header: string list,
boehmes@36898:     sorts: string list,
boehmes@39298:     dtyps: (string * (string * (string * string) list) list) list list,
boehmes@36898:     funcs: (string * (string list * string)) list }
boehmes@36898:   type config = {
boehmes@36898:     prefixes: prefixes,
boehmes@41127:     header: term list -> string list,
boehmes@41059:     is_fol: bool,
boehmes@41059:     has_datatypes: bool,
boehmes@36898:     serialize: string list -> sign -> sterm list -> string }
boehmes@36898:   type recon = {
boehmes@41127:     context: Proof.context,
boehmes@36898:     typs: typ Symtab.table,
boehmes@36898:     terms: term Symtab.table,
boehmes@41127:     rewrite_rules: thm list,
boehmes@40161:     assms: (int * thm) list }
boehmes@36898: 
boehmes@41127:   (*translation*)
boehmes@41127:   val add_config: SMT_Utils.class * (Proof.context -> config) ->
boehmes@41127:     Context.generic -> Context.generic 
boehmes@41127:   val translate: Proof.context -> string list -> (int * thm) list ->
boehmes@36898:     string * recon
boehmes@36898: end
boehmes@36898: 
boehmes@36898: structure SMT_Translate: SMT_TRANSLATE =
boehmes@36898: struct
boehmes@36898: 
boehmes@40663: structure U = SMT_Utils
boehmes@41059: structure B = SMT_Builtin
boehmes@40663: 
boehmes@40663: 
boehmes@36898: (* intermediate term structure *)
boehmes@36898: 
boehmes@36898: datatype squant = SForall | SExists
boehmes@36898: 
boehmes@36898: datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
boehmes@36898: 
boehmes@36898: datatype sterm =
boehmes@36898:   SVar of int |
boehmes@36898:   SApp of string * sterm list |
boehmes@36898:   SLet of string * sterm * sterm |
boehmes@40664:   SQua of squant * string list * sterm spattern list * int option * sterm
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@41127: (* translation configuration *)
boehmes@36898: 
boehmes@36898: type prefixes = {sort_prefix: string, func_prefix: string}
boehmes@36898: 
boehmes@36898: type sign = {
boehmes@36899:   header: string list,
boehmes@36898:   sorts: string list,
boehmes@39298:   dtyps: (string * (string * (string * string) list) list) list list,
boehmes@36898:   funcs: (string * (string list * string)) list }
boehmes@36898: 
boehmes@36898: type config = {
boehmes@36898:   prefixes: prefixes,
boehmes@41127:   header: term list -> string list,
boehmes@41059:   is_fol: bool,
boehmes@41059:   has_datatypes: bool,
boehmes@36898:   serialize: string list -> sign -> sterm list -> string }
boehmes@36898: 
boehmes@36898: type recon = {
boehmes@41127:   context: Proof.context,
boehmes@36898:   typs: typ Symtab.table,
boehmes@36898:   terms: term Symtab.table,
boehmes@41127:   rewrite_rules: thm list,
boehmes@40161:   assms: (int * thm) list }
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@41127: (* translation context *)
boehmes@41127: 
boehmes@41127: fun make_tr_context {sort_prefix, func_prefix} =
boehmes@41127:   (sort_prefix, 1, Typtab.empty, func_prefix, 1, Termtab.empty)
boehmes@41127: 
boehmes@41127: fun string_of_index pre i = pre ^ string_of_int i
boehmes@41127: 
boehmes@41127: fun add_typ T proper (cx as (sp, Tidx, typs, fp, idx, terms)) =
boehmes@41127:   (case Typtab.lookup typs T of
boehmes@41127:     SOME (n, _) => (n, cx)
boehmes@41127:   | NONE =>
boehmes@41127:       let
boehmes@41127:         val n = string_of_index sp Tidx
boehmes@41127:         val typs' = Typtab.update (T, (n, proper)) typs
boehmes@41127:       in (n, (sp, Tidx+1, typs', fp, idx, terms)) end)
boehmes@41127: 
boehmes@41127: fun add_fun t sort (cx as (sp, Tidx, typs, fp, idx, terms)) =
boehmes@41127:   (case Termtab.lookup terms t of
boehmes@41127:     SOME (n, _) => (n, cx)
boehmes@41127:   | NONE => 
boehmes@41127:       let
boehmes@41127:         val n = string_of_index fp idx
boehmes@41127:         val terms' = Termtab.update (t, (n, sort)) terms
boehmes@41127:       in (n, (sp, Tidx, typs, fp, idx+1, terms')) end)
boehmes@41127: 
boehmes@41127: fun sign_of header dtyps (_, _, typs, _, _, terms) = {
boehmes@41127:   header = header,
boehmes@41127:   sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
boehmes@41127:   dtyps = dtyps,
boehmes@41127:   funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
boehmes@41127: 
boehmes@41127: fun recon_of ctxt rules thms ithms revertT revert (_, _, typs, _, _, terms) =
boehmes@41127:   let
boehmes@41127:     fun add_typ (T, (n, _)) = Symtab.update (n, revertT T)
boehmes@41127:     val typs' = Typtab.fold add_typ typs Symtab.empty
boehmes@41127: 
boehmes@41127:     fun add_fun (t, (n, _)) = Symtab.update (n, revert t)
boehmes@41127:     val terms' = Termtab.fold add_fun terms Symtab.empty
boehmes@41127: 
boehmes@41127:     val assms = map (pair ~1) thms @ ithms
boehmes@41127:   in
boehmes@41127:     {context=ctxt, typs=typs', terms=terms', rewrite_rules=rules, assms=assms}
boehmes@41127:   end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (* preprocessing *)
boehmes@41127: 
boehmes@41127: (** mark built-in constants as Var **)
boehmes@41127: 
boehmes@41127: fun mark_builtins ctxt =
boehmes@41127:   let
boehmes@41127:     (*
boehmes@41127:       Note: schematic terms cannot occur anymore in terms at this stage.
boehmes@41127:     *)
boehmes@41127:     fun mark t =
boehmes@41127:       (case Term.strip_comb t of
boehmes@41127:         (u as Const (@{const_name If}, _), ts) => marks u ts
boehmes@41127:       | (u as Const c, ts) =>
boehmes@41127:           (case B.builtin_num ctxt t of
boehmes@41127:             SOME (n, T) =>
boehmes@41127:               let val v = ((n, 0), T)
boehmes@41127:               in Vartab.update v #> pair (Var v) end
boehmes@41127:           | NONE =>
boehmes@41127:               (case B.builtin_fun ctxt c ts of
boehmes@41127:                 SOME ((ni, T), us, U) =>
boehmes@41127:                   Vartab.update (ni, U) #> marks (Var (ni, T)) us
boehmes@41127:               | NONE => marks u ts))
boehmes@41127:       | (Abs (n, T, u), ts) => mark u #-> (fn u' => marks (Abs (n, T, u')) ts)
boehmes@41127:       | (u, ts) => marks u ts)
boehmes@41127:  
boehmes@41127:     and marks t ts = fold_map mark ts #>> Term.list_comb o pair t
boehmes@41127: 
boehmes@41127:   in (fn ts => swap (fold_map mark ts Vartab.empty)) end
boehmes@41127: 
boehmes@41127: fun mark_builtins' ctxt t = hd (snd (mark_builtins ctxt [t]))
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (** FIXME **)
boehmes@41127: 
boehmes@41127: local
boehmes@41127:   (*
boehmes@41127:     mark constructors and selectors as Vars (forcing eta-expansion),
boehmes@41127:     add missing datatype selectors via hypothetical definitions,
boehmes@41127:     also return necessary datatype and record theorems
boehmes@41127:   *)
boehmes@41127: in
boehmes@41127: 
boehmes@41127: fun collect_datatypes_and_records (tr_context, ctxt) ts =
boehmes@41127:   (([], tr_context, ctxt), ts)
boehmes@41127: 
boehmes@41127: end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (** eta-expand quantifiers, let expressions and built-ins *)
boehmes@41127: 
boehmes@41127: local
boehmes@41127:   fun eta T t = Abs (Name.uu, T, Term.incr_boundvars 1 t $ Bound 0)
boehmes@41127: 
boehmes@41127:   fun exp T = eta (Term.domain_type (Term.domain_type T))
boehmes@41127: 
boehmes@41127:   fun exp2 T q =
boehmes@41127:     let val U = Term.domain_type T
boehmes@41127:     in Abs (Name.uu, U, q $ eta (Term.domain_type U) (Bound 0)) end
boehmes@41127: 
boehmes@41127:   fun exp2' T l =
boehmes@41127:     let val (U1, U2) = Term.dest_funT T ||> Term.domain_type
boehmes@41127:     in Abs (Name.uu, U1, eta U2 (l $ Bound 0)) end
boehmes@41127: 
boehmes@41127:   fun expf t i T ts =
boehmes@41127:     let val Ts = U.dest_funT i T |> fst |> drop (length ts)
boehmes@41127:     in Term.list_comb (t, ts) |> fold_rev eta Ts end
boehmes@41127: 
boehmes@41127:   fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
boehmes@41127:     | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp T t
boehmes@41127:     | expand (q as Const (@{const_name All}, T)) = exp2 T q
boehmes@41127:     | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
boehmes@41127:     | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp T t
boehmes@41127:     | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
boehmes@41127:     | expand ((l as Const (@{const_name Let}, _)) $ t $ Abs a) =
boehmes@41127:         l $ expand t $ abs_expand a
boehmes@41127:     | expand ((l as Const (@{const_name Let}, T)) $ t $ u) =
boehmes@41127:         l $ expand t $ exp (Term.range_type T) u
boehmes@41127:     | expand ((l as Const (@{const_name Let}, T)) $ t) = exp2 T (l $ expand t)
boehmes@41127:     | expand (l as Const (@{const_name Let}, T)) = exp2' T l
boehmes@41127:     | expand (Abs a) = abs_expand a
boehmes@41127:     | expand t =
boehmes@41127:         (case Term.strip_comb t of
boehmes@41127:           (u as Const (@{const_name If}, T), ts) => expf u 3 T (map expand ts)
boehmes@41127:         | (u as Var ((_, i), T), ts) => expf u i T (map expand ts)
boehmes@41127:         | (u, ts) => Term.list_comb (u, map expand ts))
boehmes@41127: 
boehmes@41127:   and abs_expand (n, T, t) = Abs (n, T, expand t)
boehmes@41127: in
boehmes@41127: 
boehmes@41127: val eta_expand = map expand
boehmes@41127: 
boehmes@41127: end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (** lambda-lifting **)
boehmes@41127: 
boehmes@41127: local
boehmes@41127:   fun mk_def Ts T lhs rhs =
boehmes@41127:     let
boehmes@41127:       val eq = HOLogic.eq_const T $ lhs $ rhs
boehmes@41127:       val trigger =
boehmes@41127:         [[Const (@{const_name SMT.pat}, T --> @{typ SMT.pattern}) $ lhs]]
boehmes@41127:         |> map (HOLogic.mk_list @{typ SMT.pattern})
boehmes@41127:         |> HOLogic.mk_list @{typ "SMT.pattern list"}
boehmes@41127:       fun mk_all T t = HOLogic.all_const T $ Abs (Name.uu, T, t)
boehmes@41127:     in fold mk_all Ts (@{const SMT.trigger} $ trigger $ eq) end
boehmes@41127: 
boehmes@41127:   fun replace_lambda Us Ts t (cx as (defs, ctxt)) =
boehmes@41127:     let
boehmes@41127:       val T = Term.fastype_of1 (Us @ Ts, t)
boehmes@41127:       val lev = length Us
boehmes@41127:       val bs = sort int_ord (Term.add_loose_bnos (t, lev, []))
boehmes@41127:       val bss = map_index (fn (i, j) => (j, Integer.add lev i)) bs
boehmes@41127:       val norm = perhaps (AList.lookup (op =) bss)
boehmes@41127:       val t' = Term.map_aterms (fn Bound i => Bound (norm i) | t => t) t
boehmes@41127:       val Ts' = map (nth Ts) bs
boehmes@41127: 
boehmes@41127:       fun mk_abs U u = Abs (Name.uu, U, u)
boehmes@41127:       val abs_rhs = fold mk_abs Ts' (fold mk_abs Us t')
boehmes@41127:     in
boehmes@41127:       (case Termtab.lookup defs abs_rhs of
boehmes@41127:         SOME (f, _) => (Term.list_comb (f, map Bound bs), cx)
boehmes@41127:       | NONE =>
boehmes@41127:           let
boehmes@41127:             val (n, ctxt') =
boehmes@41127:               yield_singleton Variable.variant_fixes Name.uu ctxt
boehmes@41127:             val f = Free (n, rev Ts' ---> (rev Us ---> T))
boehmes@41127:             fun mk_bapp i t = t $ Bound i
boehmes@41127:             val lhs =
boehmes@41127:               f
boehmes@41127:               |> fold_rev (mk_bapp o snd) bss
boehmes@41127:               |> fold_rev mk_bapp (0 upto (length Us - 1))
boehmes@41127:             val def = mk_def (Us @ Ts') T lhs t'
boehmes@41127:           in (f, (Termtab.update (abs_rhs, (f, def)) defs, ctxt')) end)
boehmes@41127:     end
boehmes@41127: 
boehmes@41127:   fun dest_abs Ts (Abs (_, T, t)) = dest_abs (T :: Ts) t
boehmes@41127:     | dest_abs Ts t = (Ts, t)
boehmes@41127: 
boehmes@41127:   fun traverse Ts t =
boehmes@41127:     (case t of
boehmes@41127:       (q as Const (@{const_name All}, _)) $ Abs a =>
boehmes@41127:         abs_traverse Ts a #>> (fn a' => q $ Abs a')
boehmes@41127:     | (q as Const (@{const_name Ex}, _)) $ Abs a =>
boehmes@41127:         abs_traverse Ts a #>> (fn a' => q $ Abs a')
boehmes@41127:     | (l as Const (@{const_name Let}, _)) $ u $ Abs a =>
boehmes@41127:         traverse Ts u ##>> abs_traverse Ts a #>>
boehmes@41127:         (fn (u', a') => l $ u' $ Abs a')
boehmes@41127:     | Abs _ =>
boehmes@41127:         let val (Us, u) = dest_abs [] t
boehmes@41127:         in traverse (Us @ Ts) u #-> replace_lambda Us Ts end
boehmes@41127:     | u1 $ u2 => traverse Ts u1 ##>> traverse Ts u2 #>> (op $)
boehmes@41127:     | _ => pair t)
boehmes@41127: 
boehmes@41127:   and abs_traverse Ts (n, T, t) = traverse (T::Ts) t #>> (fn t' => (n, T, t'))
boehmes@41127: in
boehmes@41127: 
boehmes@41127: fun lift_lambdas ctxt ts =
boehmes@41127:   (Termtab.empty, ctxt)
boehmes@41127:   |> fold_map (traverse []) ts
boehmes@41127:   |> (fn (us, (defs, ctxt')) =>
boehmes@41127:        (ctxt', Termtab.fold (cons o snd o snd) defs us))
boehmes@41127: 
boehmes@41127: end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (** introduce explicit applications **)
boehmes@41127: 
boehmes@41127: local
boehmes@41127:   (*
boehmes@41127:     Make application explicit for functions with varying number of arguments.
boehmes@41127:   *)
boehmes@41127: 
boehmes@41127:   fun add t ts =
boehmes@41127:     Termtab.map_default (t, []) (Ord_List.insert int_ord (length ts))
boehmes@41127: 
boehmes@41127:   fun collect t =
boehmes@41127:     (case Term.strip_comb t of
boehmes@41127:       (u as Const _, ts) => add u ts #> fold collect ts
boehmes@41127:     | (u as Free _, ts) => add u ts #> fold collect ts
boehmes@41127:     | (Abs (_, _, u), ts) => collect u #> fold collect ts
boehmes@41127:     | (_, ts) => fold collect ts)
boehmes@41127: 
boehmes@41127:   fun app ts (t, T) =
boehmes@41127:     let val f = Const (@{const_name SMT.fun_app}, T --> T)
boehmes@41127:     in (Term.list_comb (f $ t, ts), snd (U.dest_funT (length ts) T)) end 
boehmes@41127: 
boehmes@41127:   fun appl _ _ [] = fst
boehmes@41127:     | appl _ [] ts = fst o app ts
boehmes@41127:     | appl i (k :: ks) ts =
boehmes@41127:         let val (ts1, ts2) = chop (k - i) ts
boehmes@41127:         in appl k ks ts2 o app ts1 end
boehmes@41127: 
boehmes@41127:   fun appl0 [_] ts (t, _) = Term.list_comb (t, ts)
boehmes@41127:     | appl0 (0 :: ks) ts tT = appl 0 ks ts tT
boehmes@41127:     | appl0 ks ts tT = appl 0 ks ts tT
boehmes@41127: 
boehmes@41127:   fun apply terms T t ts = appl0 (Termtab.lookup_list terms t) ts (t, T)
boehmes@41127: 
boehmes@41127:   fun get_arities i t =
boehmes@41127:     (case Term.strip_comb t of
boehmes@41127:       (Bound j, ts) =>
boehmes@41127:         (if i = j then Ord_List.insert int_ord (length ts) else I) #>
boehmes@41127:         fold (get_arities i) ts
boehmes@41127:     | (Abs (_, _, u), ts) => get_arities (i+1) u #> fold (get_arities i) ts
boehmes@41127:     | (_, ts) => fold (get_arities i) ts)
boehmes@41127: in
boehmes@41127: 
boehmes@41127: fun intro_explicit_application ts =
boehmes@41127:   let
boehmes@41127:     val terms = fold collect ts Termtab.empty
boehmes@41127: 
boehmes@41127:     fun traverse (env as (arities, Ts)) t =
boehmes@41127:       (case Term.strip_comb t of
boehmes@41127:         (u as Const (_, T), ts) => apply terms T u (map (traverse env) ts)
boehmes@41127:       | (u as Free (_, T), ts) => apply terms T u (map (traverse env) ts)
boehmes@41127:       | (u as Bound i, ts) =>
boehmes@41127:           appl0 (nth arities i) (map (traverse env) ts) (u, nth Ts i)
boehmes@41127:       | (Abs (n, T, u), ts) =>
boehmes@41127:           let val env' = (get_arities 0 u [] :: arities, T :: Ts)
boehmes@41127:           in traverses env (Abs (n, T, traverse env' u)) ts end
boehmes@41127:       | (u, ts) => traverses env u ts)
boehmes@41127:     and traverses env t ts = Term.list_comb (t, map (traverse env) ts)
boehmes@41127:   in map (traverse ([], [])) ts end
boehmes@41127: 
boehmes@41127: val fun_app_eq = mk_meta_eq @{thm SMT.fun_app_def}
boehmes@41127: 
boehmes@41127: end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
boehmes@41127: 
boehmes@41127: val tboolT = @{typ SMT.term_bool}
boehmes@41127: val term_true = Const (@{const_name True}, tboolT)
boehmes@41127: val term_false = Const (@{const_name False}, tboolT)
boehmes@41127: 
boehmes@41127: val term_bool = @{lemma "True ~= False" by simp}
boehmes@41127: val term_bool_prop =
boehmes@41127:   let
boehmes@41127:     fun replace @{const HOL.eq (bool)} = @{const HOL.eq (SMT.term_bool)}
boehmes@41127:       | replace @{const True} = term_true
boehmes@41127:       | replace @{const False} = term_false
boehmes@41127:       | replace t = t
boehmes@41127:   in
boehmes@41127:     Term.map_aterms replace (HOLogic.dest_Trueprop (Thm.prop_of term_bool))
boehmes@41127:   end
boehmes@41127: 
boehmes@41127: val fol_rules = [
boehmes@41127:   Let_def,
boehmes@41127:   @{lemma "P = True == P" by (rule eq_reflection) simp},
boehmes@41127:   @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
boehmes@41127: 
boehmes@41127: fun reduce_let (Const (@{const_name Let}, _) $ t $ u) =
boehmes@41127:       reduce_let (Term.betapply (u, t))
boehmes@41127:   | reduce_let (t $ u) = reduce_let t $ reduce_let u
boehmes@41127:   | reduce_let (Abs (n, T, t)) = Abs (n, T, reduce_let t)
boehmes@41127:   | reduce_let t = t
boehmes@41127: 
boehmes@41127: fun is_pred_type NONE = false
boehmes@41127:   | is_pred_type (SOME T) = (Term.body_type T = @{typ bool})
boehmes@41127: 
boehmes@41127: fun is_conn_type NONE = false
boehmes@41127:   | is_conn_type (SOME T) =
boehmes@41127:       forall (equal @{typ bool}) (Term.body_type T :: Term.binder_types T)
boehmes@41127: 
boehmes@41127: fun revert_typ @{typ SMT.term_bool} = @{typ bool}
boehmes@41127:   | revert_typ (Type (n, Ts)) = Type (n, map revert_typ Ts)
boehmes@41127:   | revert_typ T = T
boehmes@41127: 
boehmes@41127: val revert_types = Term.map_types revert_typ
boehmes@41127: 
boehmes@41127: fun folify ctxt builtins =
boehmes@41127:   let
boehmes@41127:     fun as_term t = @{const HOL.eq (SMT.term_bool)} $ t $ term_true
boehmes@41127: 
boehmes@41127:     fun as_tbool @{typ bool} = tboolT
boehmes@41127:       | as_tbool (Type (n, Ts)) = Type (n, map as_tbool Ts)
boehmes@41127:       | as_tbool T = T
boehmes@41127:     fun mapTs f g i = U.dest_funT i #> (fn (Ts, T) => map f Ts ---> g T)
boehmes@41127:     fun predT i = mapTs as_tbool I i
boehmes@41127:     fun funcT i = mapTs as_tbool as_tbool i
boehmes@41127:     fun func i (n, T) = (n, funcT i T)
boehmes@41127: 
boehmes@41127:     fun map_ifT T = T |> Term.dest_funT ||> funcT 2 |> (op -->)
boehmes@41127:     val if_term = @{const If (bool)} |> Term.dest_Const ||> map_ifT |> Const
boehmes@41127:     fun wrap_in_if t = if_term $ t $ term_true $ term_false
boehmes@41127: 
boehmes@41127:     fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
boehmes@41127: 
boehmes@41127:     fun in_term t =
boehmes@41127:       (case Term.strip_comb t of
boehmes@41127:         (Const (n as @{const_name If}, T), [t1, t2, t3]) =>
boehmes@41127:           Const (n, map_ifT T) $ in_form t1 $ in_term t2 $ in_term t3
boehmes@41127:       | (Const (@{const_name HOL.eq}, _), _) => wrap_in_if (in_form t)
boehmes@41127:       | (Var (ni as (_, i), T), ts) =>
boehmes@41127:           let val U = Vartab.lookup builtins ni
boehmes@41127:           in
boehmes@41127:             if is_conn_type U orelse is_pred_type U then wrap_in_if (in_form t)
boehmes@41127:             else Term.list_comb (Var (ni, funcT i T), map in_term ts)
boehmes@41127:           end
boehmes@41127:       | (Const c, ts) =>
boehmes@41127:           Term.list_comb (Const (func (length ts) c), map in_term ts)
boehmes@41127:       | (Free c, ts) =>
boehmes@41127:           Term.list_comb (Free (func (length ts) c), map in_term ts)
boehmes@41127:       | _ => t)
boehmes@41127: 
boehmes@41127:     and in_weight ((c as @{const SMT.weight}) $ w $ t) = c $ w $ in_form t
boehmes@41127:       | in_weight t = in_form t 
boehmes@41127: 
boehmes@41127:     and in_pat (Const (c as (@{const_name pat}, _)) $ t) =
boehmes@41127:           Const (func 1 c) $ in_term t
boehmes@41127:       | in_pat (Const (c as (@{const_name nopat}, _)) $ t) =
boehmes@41127:           Const (func 1 c) $ in_term t
boehmes@41127:       | in_pat t = raise TERM ("bad pattern", [t])
boehmes@41127: 
boehmes@41127:     and in_pats ps =
boehmes@41127:       in_list @{typ "pattern list"} (in_list @{typ pattern} in_pat) ps
boehmes@41127: 
boehmes@41127:     and in_trig ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_weight t
boehmes@41127:       | in_trig t = in_weight t
boehmes@41127: 
boehmes@41127:     and in_form t =
boehmes@41127:       (case Term.strip_comb t of
boehmes@41127:         (q as Const (qn, _), [Abs (n, T, u)]) =>
boehmes@41127:           if member (op =) [@{const_name All}, @{const_name Ex}] qn then
boehmes@41127:             q $ Abs (n, as_tbool T, in_trig u)
boehmes@41127:           else as_term (in_term t)
boehmes@41127:       | (u as Const (@{const_name If}, _), ts) =>
boehmes@41127:           Term.list_comb (u, map in_form ts)
boehmes@41127:       | (b as @{const HOL.eq (bool)}, ts) => Term.list_comb (b, map in_form ts)
boehmes@41127:       | (Const (n as @{const_name HOL.eq}, T), ts) =>
boehmes@41127:           Term.list_comb (Const (n, predT 2 T), map in_term ts)
boehmes@41127:       | (b as Var (ni as (_, i), T), ts) =>
boehmes@41127:           if is_conn_type (Vartab.lookup builtins ni) then
boehmes@41127:             Term.list_comb (b, map in_form ts)
boehmes@41127:           else if is_pred_type (Vartab.lookup builtins ni) then
boehmes@41127:             Term.list_comb (Var (ni, predT i T), map in_term ts)
boehmes@41127:           else as_term (in_term t)
boehmes@41127:       | _ => as_term (in_term t))
boehmes@41127:   in
boehmes@41127:     map (reduce_let #> in_form) #>
boehmes@41127:     cons (mark_builtins' ctxt term_bool_prop) #>
boehmes@41127:     pair (fol_rules, [term_bool])
boehmes@41127:   end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (* translation into intermediate format *)
boehmes@41127: 
boehmes@41127: (** utility functions **)
boehmes@36898: 
boehmes@36898: val quantifier = (fn
boehmes@36898:     @{const_name All} => SOME SForall
boehmes@36898:   | @{const_name Ex} => SOME SExists
boehmes@36898:   | _ => NONE)
boehmes@36898: 
boehmes@36898: fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
boehmes@36898:       if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
boehmes@36898:   | group_quant _ Ts t = (Ts, t)
boehmes@36898: 
boehmes@40664: fun dest_weight (@{const SMT.weight} $ w $ t) =
boehmes@40664:       (SOME (snd (HOLogic.dest_number w)), t)
boehmes@40664:   | dest_weight t = (NONE, t)
boehmes@40664: 
boehmes@37124: fun dest_pat (Const (@{const_name pat}, _) $ t) = (t, true)
boehmes@37124:   | dest_pat (Const (@{const_name nopat}, _) $ t) = (t, false)
boehmes@41127:   | dest_pat t = raise TERM ("bad pattern", [t])
boehmes@37124: 
boehmes@37124: fun dest_pats [] = I
boehmes@37124:   | dest_pats ts =
boehmes@37124:       (case map dest_pat ts |> split_list ||> distinct (op =) of
boehmes@37124:         (ps, [true]) => cons (SPat ps)
boehmes@37124:       | (ps, [false]) => cons (SNoPat ps)
boehmes@41127:       | _ => raise TERM ("bad multi-pattern", ts))
boehmes@36898: 
boehmes@40579: fun dest_trigger (@{const trigger} $ tl $ t) =
boehmes@37124:       (rev (fold (dest_pats o HOLogic.dest_list) (HOLogic.dest_list tl) []), t)
boehmes@36898:   | dest_trigger t = ([], t)
boehmes@36898: 
boehmes@36898: fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
boehmes@36898:   let
boehmes@36898:     val (Ts, u) = group_quant qn [T] t
boehmes@40664:     val (ps, p) = dest_trigger u
boehmes@40664:     val (w, b) = dest_weight p
boehmes@40664:   in (q, rev Ts, ps, w, b) end)
boehmes@36898: 
boehmes@36898: fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
boehmes@36898:   | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
boehmes@36898: 
boehmes@36898: 
boehmes@41127: (** translation from Isabelle terms into SMT intermediate terms **)
boehmes@36898: 
boehmes@41127: fun intermediate header dtyps ctxt ts trx =
boehmes@41059:   let
boehmes@41127:     fun transT (T as TFree _) = add_typ T true
boehmes@41127:       | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
boehmes@41127:       | transT (T as Type _) =
boehmes@41059:           (case B.builtin_typ ctxt T of
boehmes@39298:             SOME n => pair n
boehmes@41127:           | NONE => add_typ T true)
boehmes@36898: 
boehmes@41127:     val unmarked_builtins = [@{const_name If}, @{const_name HOL.eq}]
boehmes@36898: 
boehmes@36898:     fun app n ts = SApp (n, ts)
boehmes@36898: 
boehmes@36898:     fun trans t =
boehmes@36898:       (case Term.strip_comb t of
boehmes@36898:         (Const (qn, _), [Abs (_, T, t1)]) =>
boehmes@36898:           (case dest_quant qn T t1 of
boehmes@40664:             SOME (q, Ts, ps, w, b) =>
boehmes@36898:               fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
boehmes@40664:               trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', w, b'))
boehmes@41127:           | NONE => raise TERM ("unsupported quantifier", [t]))
boehmes@36898:       | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
boehmes@36898:           transT T ##>> trans t1 ##>> trans t2 #>>
boehmes@36898:           (fn ((U, u1), u2) => SLet (U, u1, u2))
boehmes@41127:       | (Var ((n, _), _), ts) => fold_map trans ts #>> app n
boehmes@41127:       | (u as Const (c as (n, T)), ts) =>
boehmes@41127:           if member (op =) unmarked_builtins n then
boehmes@41127:             (case B.builtin_fun ctxt c ts of
boehmes@41127:               SOME (((m, _), _), us, _) => fold_map trans us #>> app m
boehmes@41127:             | NONE => raise TERM ("not a built-in symbol", [t]))
boehmes@41127:           else transs u T ts
boehmes@41127:       | (u as Free (_, T), ts) => transs u T ts
boehmes@36898:       | (Bound i, []) => pair (SVar i)
boehmes@41127:       | _ => raise TERM ("bad SMT term", [t]))
boehmes@41127:  
boehmes@36898:     and transs t T ts =
boehmes@40663:       let val (Us, U) = U.dest_funT (length ts) T
boehmes@36898:       in
boehmes@36898:         fold_map transT Us ##>> transT U #-> (fn Up =>
boehmes@41127:         add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
boehmes@36898:       end
boehmes@41127: 
boehmes@41127:     val (us, trx') = fold_map trans ts trx
boehmes@41127:   in ((sign_of (header ts) dtyps trx', us), trx') end
boehmes@41127: 
boehmes@41127: 
boehmes@41127: 
boehmes@41127: (* translation *)
boehmes@41127: 
boehmes@41127: structure Configs = Generic_Data
boehmes@41127: (
boehmes@41127:   type T = (Proof.context -> config) U.dict
boehmes@41127:   val empty = []
boehmes@41127:   val extend = I
boehmes@41127:   val merge = U.dict_merge fst
boehmes@41127: )
boehmes@41127: 
boehmes@41127: fun add_config (cs, cfg) = Configs.map (U.dict_update (cs, cfg))
boehmes@41127: 
boehmes@41127: fun translate ctxt comments ithms =
boehmes@41127:   let
boehmes@41127:     val cs = SMT_Config.solver_class_of ctxt
boehmes@41127:     val {prefixes, is_fol, header, has_datatypes, serialize} =
boehmes@41127:       (case U.dict_get (Configs.get (Context.Proof ctxt)) cs of
boehmes@41127:         SOME cfg => cfg ctxt
boehmes@41127:       | NONE => error ("SMT: no translation configuration found " ^
boehmes@41127:           "for solver class " ^ quote (U.string_of_class cs)))
boehmes@41127:       
boehmes@41127:     val with_datatypes =
boehmes@41127:       has_datatypes andalso Config.get ctxt SMT_Config.datatypes
boehmes@41127: 
boehmes@41127:     fun no_dtyps (tr_context, ctxt) ts = (([], tr_context, ctxt), ts)
boehmes@41127: 
boehmes@41127:     val (builtins, ts1) =
boehmes@41127:       ithms
boehmes@41127:       |> map (HOLogic.dest_Trueprop o Thm.prop_of o snd)
boehmes@41127:       |> map (Envir.eta_contract o Envir.beta_norm)
boehmes@41127:       |> mark_builtins ctxt
boehmes@41127: 
boehmes@41127:     val ((dtyps, tr_context, ctxt1), ts2) =
boehmes@41127:       ((make_tr_context prefixes, ctxt), ts1)
boehmes@41127:       |-> (if with_datatypes then collect_datatypes_and_records else no_dtyps)
boehmes@41127: 
boehmes@41127:     val (ctxt2, ts3) =
boehmes@41127:       ts2
boehmes@41127:       |> eta_expand
boehmes@41127:       |> lift_lambdas ctxt1
boehmes@41127:       ||> intro_explicit_application
boehmes@41127: 
boehmes@41127:     val ((rewrite_rules, extra_thms), ts4) =
boehmes@41127:       (if is_fol then folify ctxt2 builtins else pair ([], [])) ts3
boehmes@41127: 
boehmes@41127:     val rewrite_rules' = fun_app_eq :: rewrite_rules
boehmes@36898:   in
boehmes@41127:     (ts4, tr_context)
boehmes@41127:     |-> intermediate header dtyps ctxt2
boehmes@41127:     |>> uncurry (serialize comments)
boehmes@41127:     ||> recon_of ctxt2 rewrite_rules' extra_thms ithms revert_typ revert_types
boehmes@36898:   end
boehmes@36898: 
boehmes@36898: end