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@36898:   (* 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@36898:   (* configuration options *)
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@41059:     header: Proof.context -> 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@36898:     typs: typ Symtab.table,
boehmes@36898:     terms: term Symtab.table,
boehmes@36898:     unfolds: thm list,
boehmes@40161:     assms: (int * thm) list }
boehmes@36898: 
boehmes@40161:   val translate: config -> 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@36898: (* configuration options *)
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@41059:   header: Proof.context -> 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@36898:   typs: typ Symtab.table,
boehmes@36898:   terms: term Symtab.table,
boehmes@36898:   unfolds: thm list,
boehmes@40161:   assms: (int * thm) list }
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@36898: (* 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@37124:   | dest_pat t = raise TERM ("dest_pat", [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@37124:       | _ => raise TERM ("dest_pats", 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: fun prop_of thm = HOLogic.dest_Trueprop (Thm.prop_of thm)
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (* map HOL formulas to FOL formulas (i.e., separate formulas froms terms) *)
boehmes@36898: 
boehmes@41059: val tboolT = @{typ SMT.term_bool}
boehmes@41059: val term_true = Const (@{const_name True}, tboolT)
boehmes@41059: val term_false = Const (@{const_name False}, tboolT)
boehmes@36898: 
boehmes@41059: val term_bool = @{lemma "True ~= False" by simp}
boehmes@41059: val term_bool_prop =
boehmes@41059:   let
boehmes@41059:     fun replace @{const HOL.eq (bool)} = @{const HOL.eq (SMT.term_bool)}
boehmes@41059:       | replace @{const True} = term_true
boehmes@41059:       | replace @{const False} = term_false
boehmes@41059:       | replace t = t
boehmes@41059:   in Term.map_aterms replace (prop_of term_bool) end
boehmes@36898: 
boehmes@36898: val needs_rewrite = Thm.prop_of #> Term.exists_subterm (fn
boehmes@36898:     Const (@{const_name Let}, _) => true
boehmes@40579:   | @{const HOL.eq (bool)} $ _ $ @{const True} => true
boehmes@40579:   | Const (@{const_name If}, _) $ _ $ @{const True} $ @{const False} => true
boehmes@36898:   | _ => false)
boehmes@36898: 
boehmes@36898: val rewrite_rules = [
boehmes@36898:   Let_def,
boehmes@36898:   @{lemma "P = True == P" by (rule eq_reflection) simp},
boehmes@36898:   @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
boehmes@36898: 
boehmes@41059: fun rewrite ctxt ct =
boehmes@41059:   Conv.top_sweep_conv (fn ctxt' =>
boehmes@41059:     Conv.rewrs_conv rewrite_rules then_conv rewrite ctxt') ctxt ct
boehmes@36898: 
boehmes@36898: fun normalize ctxt thm =
boehmes@36898:   if needs_rewrite thm then Conv.fconv_rule (rewrite ctxt) thm else thm
boehmes@36898: 
boehmes@41059: fun revert_typ @{typ SMT.term_bool} = @{typ bool}
boehmes@41059:   | revert_typ (Type (n, Ts)) = Type (n, map revert_typ Ts)
boehmes@41059:   | revert_typ T = T
boehmes@36898: 
boehmes@41059: val revert_types = Term.map_types revert_typ
boehmes@36898: 
boehmes@41059: fun folify ctxt =
boehmes@36898:   let
boehmes@41059:     fun is_builtin_conn (@{const_name True}, _) _ = false
boehmes@41059:       | is_builtin_conn (@{const_name False}, _) _ = false
boehmes@41059:       | is_builtin_conn c ts = B.is_builtin_conn ctxt c ts
boehmes@36898: 
boehmes@41059:     fun as_term t = @{const HOL.eq (SMT.term_bool)} $ t $ term_true
boehmes@40681: 
boehmes@41059:     fun as_tbool @{typ bool} = tboolT
boehmes@41059:       | as_tbool (Type (n, Ts)) = Type (n, map as_tbool Ts)
boehmes@41059:       | as_tbool T = T
boehmes@36898:     fun mapTs f g = Term.strip_type #> (fn (Ts, T) => map f Ts ---> g T)
boehmes@41059:     fun predT T = mapTs as_tbool I T
boehmes@41059:     fun funcT T = mapTs as_tbool as_tbool T
boehmes@41059:     fun func (n, T) = Const (n, funcT T)
boehmes@36898: 
boehmes@41059:     fun map_ifT T = T |> Term.dest_funT ||> funcT |> (op -->)
boehmes@41059:     val if_term = @{const If (bool)} |> Term.dest_Const ||> map_ifT |> Const
boehmes@41059:     fun wrap_in_if t = if_term $ t $ term_true $ term_false
boehmes@36898: 
boehmes@36898:     fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
boehmes@36898: 
boehmes@36898:     fun in_term t =
boehmes@36898:       (case Term.strip_comb t of
boehmes@41059:         (Const (c as @{const_name If}, T), [t1, t2, t3]) =>
boehmes@41059:           Const (c, map_ifT T) $ in_form t1 $ in_term t2 $ in_term t3
boehmes@41059:       | (Const c, ts) =>
boehmes@41059:           if is_builtin_conn c ts orelse B.is_builtin_pred ctxt c ts
boehmes@36898:           then wrap_in_if (in_form t)
boehmes@41059:           else Term.list_comb (func c, map in_term ts)
boehmes@41059:       | (Free (n, T), ts) => Term.list_comb (Free (n, funcT T), map in_term ts)
boehmes@36898:       | _ => t)
boehmes@36898: 
boehmes@40664:     and in_weight ((c as @{const SMT.weight}) $ w $ t) = c $ w $ in_form t
boehmes@40664:       | in_weight t = in_form t 
boehmes@40664: 
boehmes@41059:     and in_pat (Const (c as (@{const_name pat}, _)) $ t) = func c $ in_term t
boehmes@41059:       | in_pat (Const (c as (@{const_name nopat}, _)) $ t) = func c $ in_term t
boehmes@36898:       | in_pat t = raise TERM ("in_pat", [t])
boehmes@36898: 
boehmes@37124:     and in_pats ps =
boehmes@37124:       in_list @{typ "pattern list"} (in_list @{typ pattern} in_pat) ps
boehmes@36898: 
boehmes@40664:     and in_trig ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_weight t
boehmes@40664:       | in_trig t = in_weight t
boehmes@36898: 
boehmes@36898:     and in_form t =
boehmes@36898:       (case Term.strip_comb t of
boehmes@36898:         (q as Const (qn, _), [Abs (n, T, t')]) =>
boehmes@41059:           if is_some (quantifier qn) then q $ Abs (n, as_tbool T, in_trig t')
boehmes@36898:           else as_term (in_term t)
boehmes@41059:       | (Const (c as (n as @{const_name distinct}, T)), [t']) =>
boehmes@41059:           if B.is_builtin_fun ctxt c [t'] then
boehmes@41059:             Const (n, predT T) $ in_list T in_term t'
boehmes@36898:           else as_term (in_term t)
boehmes@41059:       | (Const (c as (n, T)), ts) =>
boehmes@41059:           if B.is_builtin_conn ctxt c ts
boehmes@41059:           then Term.list_comb (Const c, map in_form ts)
boehmes@41059:           else if B.is_builtin_pred ctxt c ts
boehmes@41059:           then Term.list_comb (Const (n, predT T), map in_term ts)
boehmes@36898:           else as_term (in_term t)
boehmes@36898:       | _ => as_term (in_term t))
boehmes@36898:   in
boehmes@40161:     map (apsnd (normalize ctxt)) #> (fn irules =>
boehmes@41059:     ((rewrite_rules, (~1, term_bool) :: irules),
boehmes@41059:      term_bool_prop :: map (in_form o prop_of o snd) irules))
boehmes@36898:   end
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@36898: (* translation from Isabelle terms into SMT intermediate terms *)
boehmes@36898: 
boehmes@39298: val empty_context = (1, Typtab.empty, [], 1, Termtab.empty)
boehmes@36898: 
boehmes@39298: fun make_sign header (_, typs, dtyps, _, terms) = {
boehmes@36899:   header = header,
boehmes@39298:   sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
boehmes@39298:   funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms [],
boehmes@39435:   dtyps = rev dtyps }
boehmes@36898: 
boehmes@39298: fun make_recon (unfolds, assms) (_, typs, _, _, terms) = {
boehmes@39298:   typs = Symtab.make (map (apfst fst o swap) (Typtab.dest typs)),
boehmes@39298:     (*FIXME: don't drop the datatype information! *)
boehmes@36898:   terms = Symtab.make (map (fn (t, (n, _)) => (n, t)) (Termtab.dest terms)),
boehmes@36898:   unfolds = unfolds,
boehmes@36899:   assms = assms }
boehmes@36898: 
boehmes@36898: fun string_of_index pre i = pre ^ string_of_int i
boehmes@36898: 
boehmes@39298: fun new_typ sort_prefix proper T (Tidx, typs, dtyps, idx, terms) =
boehmes@41059:   let
boehmes@41059:     val s = string_of_index sort_prefix Tidx
boehmes@41059:     val U = revert_typ T
boehmes@41059:   in (s, (Tidx+1, Typtab.update (U, (s, proper)) typs, dtyps, idx, terms)) end
boehmes@39298: 
boehmes@41059: fun lookup_typ (_, typs, _, _, _) = Typtab.lookup typs o revert_typ
boehmes@36898: 
boehmes@39298: fun fresh_typ T f cx =
boehmes@39298:   (case lookup_typ cx T of
boehmes@39298:     SOME (s, _) => (s, cx)
boehmes@39298:   | NONE => f T cx)
boehmes@39298: 
boehmes@39298: fun new_fun func_prefix t ss (Tidx, typs, dtyps, idx, terms) =
boehmes@39298:   let
boehmes@39298:     val f = string_of_index func_prefix idx
boehmes@39298:     val terms' = Termtab.update (revert_types t, (f, ss)) terms
boehmes@39298:   in (f, (Tidx, typs, dtyps, idx+1, terms')) end
boehmes@39298: 
boehmes@39298: fun fresh_fun func_prefix t ss (cx as (_, _, _, _, terms)) =
boehmes@41059:   (case Termtab.lookup terms (revert_types t) of
boehmes@36898:     SOME (f, _) => (f, cx)
boehmes@39298:   | NONE => new_fun func_prefix t ss cx)
boehmes@39298: 
boehmes@39483: fun mk_type (_, Tfs) (d as Datatype.DtTFree _) = the (AList.lookup (op =) Tfs d)
boehmes@39483:   | mk_type Ts (Datatype.DtType (n, ds)) = Type (n, map (mk_type Ts) ds)
boehmes@39483:   | mk_type (Tds, _) (Datatype.DtRec i) = nth Tds i
boehmes@39298: 
boehmes@39483: fun mk_selector ctxt Ts T n (i, d) =
boehmes@39483:   (case Datatype_Selectors.lookup_selector ctxt (n, i+1) of
boehmes@39483:     NONE => raise Fail ("missing selector for datatype constructor " ^ quote n)
boehmes@39483:   | SOME m => mk_type Ts d |> (fn U => (Const (m, T --> U), U)))
boehmes@39483: 
boehmes@39483: fun mk_constructor ctxt Ts T (n, args) =
boehmes@39483:   let val (sels, Us) = split_list (map_index (mk_selector ctxt Ts T n) args)
boehmes@39483:   in (Const (n, Us ---> T), sels) end
boehmes@39298: 
boehmes@39535: fun lookup_datatype ctxt n Ts =
boehmes@39535:   if member (op =) [@{type_name bool}, @{type_name nat}] n then NONE
boehmes@39535:   else
boehmes@39535:     Datatype.get_info (ProofContext.theory_of ctxt) n
boehmes@39535:     |> Option.map (fn {descr, ...} =>
boehmes@39535:          let
boehmes@39535:            val Tds = map (fn (_, (tn, _, _)) => Type (tn, Ts))
boehmes@39535:              (sort (int_ord o pairself fst) descr)
boehmes@39535:            val Tfs = (case hd descr of (_, (_, tfs, _)) => tfs ~~ Ts)
boehmes@39535:          in
boehmes@39535:            descr |> map (fn (i, (_, _, cs)) =>
boehmes@39535:              (nth Tds i, map (mk_constructor ctxt (Tds, Tfs) (nth Tds i)) cs))
boehmes@39535:          end)
boehmes@36898: 
boehmes@40161: fun relaxed irules = (([], irules), map (prop_of o snd) irules)
boehmes@36898: 
boehmes@36899: fun with_context header f (ths, ts) =
boehmes@36898:   let val (us, context) = fold_map f ts empty_context
boehmes@36899:   in ((make_sign (header ts) context, us), make_recon ths context) end
boehmes@36898: 
boehmes@36898: 
boehmes@41059: fun translate config ctxt comments =
boehmes@36898:   let
boehmes@41059:     val {prefixes, is_fol, header, has_datatypes, serialize} = config
boehmes@36898:     val {sort_prefix, func_prefix} = prefixes
boehmes@39298: 
boehmes@39298:     fun transT (T as TFree _) = fresh_typ T (new_typ sort_prefix true)
boehmes@39298:       | transT (T as TVar _) = (fn _ => raise TYPE ("smt_translate", [T], []))
boehmes@39298:       | transT (T as Type (n, Ts)) =
boehmes@41059:           (case B.builtin_typ ctxt T of
boehmes@39298:             SOME n => pair n
boehmes@39298:           | NONE => fresh_typ T (fn _ => fn cx =>
boehmes@39298:               if not has_datatypes then new_typ sort_prefix true T cx
boehmes@39298:               else
boehmes@39298:                 (case lookup_datatype ctxt n Ts of
boehmes@39298:                   NONE => new_typ sort_prefix true T cx
boehmes@39298:                 | SOME dts =>
boehmes@39298:                     let val cx' = new_dtyps dts cx 
boehmes@39298:                     in (fst (the (lookup_typ cx' T)), cx') end)))
boehmes@36898: 
boehmes@39298:     and new_dtyps dts cx =
boehmes@39298:       let
boehmes@39298:         fun new_decl i t =
boehmes@40663:           let val (Ts, T) = U.dest_funT i (Term.fastype_of t)
boehmes@39298:           in
boehmes@39298:             fold_map transT Ts ##>> transT T ##>>
boehmes@39298:             new_fun func_prefix t NONE #>> swap
boehmes@39298:           end
boehmes@39298:         fun new_dtyp_decl (con, sels) =
boehmes@39298:           new_decl (length sels) con ##>> fold_map (new_decl 1) sels #>>
boehmes@39298:           (fn ((con', _), sels') => (con', map (apsnd snd) sels'))
boehmes@39298:       in
boehmes@39298:         cx
boehmes@39298:         |> fold_map (new_typ sort_prefix false o fst) dts
boehmes@39298:         ||>> fold_map (fold_map new_dtyp_decl o snd) dts
boehmes@39298:         |-> (fn (ss, decls) => fn (Tidx, typs, dtyps, idx, terms) =>
boehmes@39298:               (Tidx, typs, (ss ~~ decls) :: dtyps, idx, terms))
boehmes@39298:       end
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@36898:           | NONE => raise TERM ("intermediate", [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@40681:       | (h as Const (c as (@{const_name distinct}, T)), ts) =>
boehmes@41059:           (case B.builtin_fun ctxt c ts of
boehmes@36899:             SOME (n, ts) => fold_map trans ts #>> app n
boehmes@40681:           | NONE => transs h T ts)
boehmes@36898:       | (h as Const (c as (_, T)), ts) =>
boehmes@41059:           (case B.builtin_num ctxt t of
boehmes@41059:             SOME n => pair (SApp (n, []))
boehmes@36898:           | NONE =>
boehmes@41059:               (case B.builtin_fun ctxt c ts of
boehmes@36899:                 SOME (n, ts') => fold_map trans ts' #>> app n
boehmes@36898:               | NONE => transs h T ts))
boehmes@36898:       | (h as Free (_, T), ts) => transs h T ts
boehmes@36898:       | (Bound i, []) => pair (SVar i)
blanchet@40697:       | (Abs (_, _, t1 $ Bound 0), []) =>
blanchet@40697:         if not (loose_bvar1 (t1, 0)) then trans t1 (* eta-reduce on the fly *)
blanchet@40697:         else raise TERM ("smt_translate", [t])
boehmes@39298:       | _ => raise TERM ("smt_translate", [t]))
boehmes@36898: 
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@39298:         fresh_fun func_prefix t (SOME Up) ##>> fold_map trans ts #>> SApp)
boehmes@36898:       end
boehmes@36898:   in
boehmes@41059:     (if is_fol then folify ctxt else relaxed) #>
boehmes@36899:     with_context (header ctxt) trans #>> uncurry (serialize comments)
boehmes@36898:   end
boehmes@36898: 
boehmes@36898: end