src/HOL/Tools/SMT/smtlib_interface.ML
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(*  Title:      HOL/Tools/SMT/smtlib_interface.ML
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    Author:     Sascha Boehme, TU Muenchen
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Interface to SMT solvers based on the SMT-LIB format.
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*)
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signature SMTLIB_INTERFACE =
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sig
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  type builtins = {
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    builtin_typ: typ -> string option,
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    builtin_num: typ -> int -> string option,
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    builtin_func: string * typ -> term list -> (string * term list) option,
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    builtin_pred: string * typ -> term list -> (string * term list) option,
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    is_builtin_pred: string -> typ -> bool }
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  val add_builtins: builtins -> Context.generic -> Context.generic
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  val add_logic: (term list -> string option) -> Context.generic ->
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    Context.generic
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  val interface: SMT_Solver.interface
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end
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structure SMTLIB_Interface: SMTLIB_INTERFACE =
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struct
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structure N = SMT_Normalize
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structure T = SMT_Translate
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(** facts about uninterpreted constants **)
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infix 2 ??
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fun (ex ?? f) thms = if exists (ex o Thm.prop_of) thms then f thms else thms
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(* pairs *)
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val pair_rules = [@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}]
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val pair_type = (fn Type (@{type_name "*"}, _) => true | _ => false)
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val exists_pair_type = Term.exists_type (Term.exists_subtype pair_type)
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val add_pair_rules = exists_pair_type ?? append pair_rules
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(* function update *)
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val fun_upd_rules = [@{thm fun_upd_same}, @{thm fun_upd_apply}]
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val is_fun_upd = (fn Const (@{const_name fun_upd}, _) => true | _ => false)
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val exists_fun_upd = Term.exists_subterm is_fun_upd
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val add_fun_upd_rules = exists_fun_upd ?? append fun_upd_rules
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(* abs/min/max *)
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val exists_abs_min_max = Term.exists_subterm (fn
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    Const (@{const_name abs}, _) => true
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  | Const (@{const_name min}, _) => true
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  | Const (@{const_name max}, _) => true
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  | _ => false)
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val unfold_abs_conv = Conv.rewr_conv @{thm abs_if[THEN eq_reflection]}
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val unfold_min_conv = Conv.rewr_conv @{thm min_def[THEN eq_reflection]}
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val unfold_max_conv = Conv.rewr_conv @{thm max_def[THEN eq_reflection]}
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fun expand_conv cv = N.eta_expand_conv (K cv)
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fun expand2_conv cv = N.eta_expand_conv (N.eta_expand_conv (K cv))
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fun unfold_def_conv ctxt ct =
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  (case Thm.term_of ct of
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    Const (@{const_name abs}, _) $ _ => unfold_abs_conv
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  | Const (@{const_name abs}, _) => expand_conv unfold_abs_conv ctxt
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  | Const (@{const_name min}, _) $ _ $ _ => unfold_min_conv
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  | Const (@{const_name min}, _) $ _ => expand_conv unfold_min_conv ctxt
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  | Const (@{const_name min}, _) => expand2_conv unfold_min_conv ctxt
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  | Const (@{const_name max}, _) $ _ $ _ => unfold_max_conv
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  | Const (@{const_name max}, _) $ _ => expand_conv unfold_max_conv ctxt
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  | Const (@{const_name max}, _) => expand2_conv unfold_max_conv ctxt
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  | _ => Conv.all_conv) ct
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fun unfold_abs_min_max_defs ctxt thm =
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  if exists_abs_min_max (Thm.prop_of thm)
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  then Conv.fconv_rule (More_Conv.top_conv unfold_def_conv ctxt) thm
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  else thm
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(* include additional facts *)
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fun extra_norm thms ctxt =
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  thms
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  |> add_pair_rules
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  |> add_fun_upd_rules
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  |> map (unfold_abs_min_max_defs ctxt)
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  |> rpair ctxt
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(** builtins **)
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(* additional builtins *)
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type builtins = {
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  builtin_typ: typ -> string option,
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  builtin_num: typ -> int -> string option,
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  builtin_func: string * typ -> term list -> (string * term list) option,
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  builtin_pred: string * typ -> term list -> (string * term list) option,
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  is_builtin_pred: string -> typ -> bool }
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fun chained _ [] = NONE
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  | chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs)
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fun chained' _ [] = false
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  | chained' f (b :: bs) = f b orelse chained' f bs
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fun chained_builtin_typ bs T =
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  chained (fn {builtin_typ, ...} : builtins => builtin_typ T) bs
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fun chained_builtin_num bs T i =
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  chained (fn {builtin_num, ...} : builtins => builtin_num T i) bs
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fun chained_builtin_func bs c ts =
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  chained (fn {builtin_func, ...} : builtins => builtin_func c ts) bs
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fun chained_builtin_pred bs c ts =
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  chained (fn {builtin_pred, ...} : builtins => builtin_pred c ts) bs
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fun chained_is_builtin_pred bs n T =
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  chained' (fn {is_builtin_pred, ...} : builtins => is_builtin_pred n T) bs
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fun fst_int_ord ((s1, _), (s2, _)) = int_ord (s1, s2)
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structure Builtins = Generic_Data
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(
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  type T = (int * builtins) list
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  val empty = []
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  val extend = I
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  fun merge (bs1, bs2) = OrdList.union fst_int_ord bs2 bs1
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)
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fun add_builtins bs = Builtins.map (OrdList.insert fst_int_ord (serial (), bs))
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fun get_builtins ctxt = map snd (Builtins.get (Context.Proof ctxt))
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(* basic builtins combined with additional builtins *)
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fun builtin_typ _ @{typ int} = SOME "Int"
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  | builtin_typ ctxt T = chained_builtin_typ (get_builtins ctxt) T
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fun builtin_num _ @{typ int} i = SOME (string_of_int i)
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  | builtin_num ctxt T i = chained_builtin_num (get_builtins ctxt) T i
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fun if_int_type T n =
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  (case try Term.domain_type T of
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    SOME @{typ int} => SOME n
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  | _ => NONE)
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fun conn @{const_name True} = SOME "true"
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  | conn @{const_name False} = SOME "false"
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  | conn @{const_name Not} = SOME "not"
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  | conn @{const_name "op &"} = SOME "and"
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  | conn @{const_name "op |"} = SOME "or"
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  | conn @{const_name "op -->"} = SOME "implies"
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  | conn @{const_name "op ="} = SOME "iff"
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  | conn @{const_name If} = SOME "if_then_else"
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  | conn _ = NONE
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fun pred @{const_name distinct} _ = SOME "distinct"
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  | pred @{const_name "op ="} _ = SOME "="
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  | pred @{const_name term_eq} _ = SOME "="
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  | pred @{const_name less} T = if_int_type T "<"
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  | pred @{const_name less_eq} T = if_int_type T "<="
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  | pred _ _ = NONE
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fun func @{const_name If} _ = SOME "ite"
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  | func @{const_name uminus} T = if_int_type T "~"
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  | func @{const_name plus} T = if_int_type T "+"
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  | func @{const_name minus} T = if_int_type T "-"
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  | func @{const_name times} T = if_int_type T "*"
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  | func _ _ = NONE
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val is_propT = (fn @{typ prop} => true | _ => false)
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fun is_connT T = Term.strip_type T |> (fn (Us, U) => forall is_propT (U :: Us))
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fun is_predT T = is_propT (Term.body_type T)
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fun is_builtin_conn (n, T) = is_connT T andalso is_some (conn n)
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fun is_builtin_pred ctxt (n, T) = is_predT T andalso
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  (is_some (pred n T) orelse chained_is_builtin_pred (get_builtins ctxt) n T)
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fun builtin_fun ctxt (c as (n, T)) ts =
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  let
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    val builtin_func' = chained_builtin_func (get_builtins ctxt)
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    val builtin_pred' = chained_builtin_pred (get_builtins ctxt)
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  in
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    if is_connT T then conn n |> Option.map (rpair ts)
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    else if is_predT T then
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      (case pred n T of SOME c' => SOME (c', ts) | NONE => builtin_pred' c ts)
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    else 
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      (case func n T of SOME c' => SOME (c', ts) | NONE => builtin_func' c ts)
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  end
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(** serialization **)
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(* header *)
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structure Logics = Generic_Data
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(
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  type T = (int * (term list -> string option)) list
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  val empty = []
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  val extend = I
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  fun merge (bs1, bs2) = OrdList.union fst_int_ord bs2 bs1
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)
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fun add_logic l = Logics.map (OrdList.insert fst_int_ord (serial (), l))
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fun choose_logic ctxt ts =
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  let
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    fun choose [] = "AUFLIA"
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      | choose ((_, l) :: ls) = (case l ts of SOME s => s | NONE => choose ls)
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  in [":logic " ^ choose (rev (Logics.get (Context.Proof ctxt)))] end
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(* serialization *)
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val add = Buffer.add
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fun sep f = add " " #> f
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fun enclose l r f = sep (add l #> f #> add r)
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val par = enclose "(" ")"
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fun app n f = (fn [] => sep (add n) | xs => par (add n #> fold f xs))
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fun line f = f #> add "\n"
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fun var i = add "?v" #> add (string_of_int i)
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fun sterm l (T.SVar i) = sep (var (l - i - 1))
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  | sterm l (T.SApp (n, ts)) = app n (sterm l) ts
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  | sterm _ (T.SLet _) = raise Fail "SMT-LIB: unsupported let expression"
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  | sterm l (T.SQua (q, ss, ps, t)) =
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      let
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        val quant = add o (fn T.SForall => "forall" | T.SExists => "exists")
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        val vs = map_index (apfst (Integer.add l)) ss
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        fun var_decl (i, s) = par (var i #> sep (add s))
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        val sub = sterm (l + length ss)
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        fun pat kind ts = sep (add kind #> enclose "{" " }" (fold sub ts))
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        fun pats (T.SPat ts) = pat ":pat" ts
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          | pats (T.SNoPat ts) = pat ":nopat" ts
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      in par (quant q #> fold var_decl vs #> sub t #> fold pats ps) end
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fun serialize comments {header, sorts, funcs} ts =
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  Buffer.empty
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  |> line (add "(benchmark Isabelle")
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  |> line (add ":status unknown")
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  |> fold (line o add) header
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  |> length sorts > 0 ?
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       line (add ":extrasorts" #> par (fold (sep o add) sorts))
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  |> length funcs > 0 ? (
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       line (add ":extrafuns" #> add " (") #>
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       fold (fn (f, (ss, s)) =>
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         line (sep (app f (sep o add) (ss @ [s])))) funcs #>
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       line (add ")"))
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  |> fold (fn t => line (add ":assumption" #> sterm 0 t)) ts
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  |> line (add ":formula true)")
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  |> fold (fn str => line (add "; " #> add str)) comments
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  |> Buffer.content
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(** interfaces **)
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val interface = {
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  extra_norm = extra_norm,
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  translate = {
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    prefixes = {
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      sort_prefix = "S",
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      func_prefix = "f"},
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    header = choose_logic,
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    strict = SOME {
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      is_builtin_conn = is_builtin_conn,
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      is_builtin_pred = is_builtin_pred,
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      is_builtin_distinct = true},
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    builtins = {
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      builtin_typ = builtin_typ,
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      builtin_num = builtin_num,
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      builtin_fun = builtin_fun},
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    serialize = serialize}}
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end