boehmes@36898: (*  Title:      HOL/Tools/SMT/smtlib_interface.ML
boehmes@36898:     Author:     Sascha Boehme, TU Muenchen
boehmes@36898: 
boehmes@36898: Interface to SMT solvers based on the SMT-LIB format.
boehmes@36898: *)
boehmes@36898: 
boehmes@36898: signature SMTLIB_INTERFACE =
boehmes@36898: sig
boehmes@41059:   val smtlibC: SMT_Config.class
boehmes@41059:   val add_logic: int * (term list -> string option) -> Context.generic ->
boehmes@36899:     Context.generic
boehmes@41059:   val setup: theory -> theory
boehmes@36898:   val interface: SMT_Solver.interface
boehmes@36898: end
boehmes@36898: 
boehmes@36898: structure SMTLIB_Interface: SMTLIB_INTERFACE =
boehmes@36898: struct
boehmes@36898: 
boehmes@41059: structure B = SMT_Builtin
boehmes@36898: structure N = SMT_Normalize
boehmes@36898: structure T = SMT_Translate
boehmes@36898: 
boehmes@41059: val smtlibC = ["smtlib"]
boehmes@36898: 
boehmes@36898: 
boehmes@41059: 
boehmes@41059: (* facts about uninterpreted constants *)
boehmes@36898: 
boehmes@36898: infix 2 ??
boehmes@40161: fun (ex ?? f) irules = irules |> exists (ex o Thm.prop_of o snd) irules ? f
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (** pairs **)
boehmes@36898: 
boehmes@36898: val pair_rules = [@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}]
boehmes@36898: 
haftmann@37678: val pair_type = (fn Type (@{type_name Product_Type.prod}, _) => true | _ => false)
boehmes@36898: val exists_pair_type = Term.exists_type (Term.exists_subtype pair_type)
boehmes@36898: 
boehmes@40161: val add_pair_rules = exists_pair_type ?? append (map (pair ~1) pair_rules)
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (** function update **)
boehmes@36898: 
boehmes@36898: val fun_upd_rules = [@{thm fun_upd_same}, @{thm fun_upd_apply}]
boehmes@36898: 
boehmes@36898: val is_fun_upd = (fn Const (@{const_name fun_upd}, _) => true | _ => false)
boehmes@36898: val exists_fun_upd = Term.exists_subterm is_fun_upd
boehmes@36898: 
boehmes@40161: val add_fun_upd_rules = exists_fun_upd ?? append (map (pair ~1) fun_upd_rules)
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (** abs/min/max **)
boehmes@36898: 
boehmes@36898: val exists_abs_min_max = Term.exists_subterm (fn
boehmes@36898:     Const (@{const_name abs}, _) => true
boehmes@36898:   | Const (@{const_name min}, _) => true
boehmes@36898:   | Const (@{const_name max}, _) => true
boehmes@36898:   | _ => false)
boehmes@36898: 
boehmes@37786: val unfold_abs_conv = Conv.rewr_conv (mk_meta_eq @{thm abs_if})
boehmes@37786: val unfold_min_conv = Conv.rewr_conv (mk_meta_eq @{thm min_def})
boehmes@37786: val unfold_max_conv = Conv.rewr_conv (mk_meta_eq @{thm max_def})
boehmes@36898: 
boehmes@36898: fun expand_conv cv = N.eta_expand_conv (K cv)
boehmes@36898: fun expand2_conv cv = N.eta_expand_conv (N.eta_expand_conv (K cv))
boehmes@36898: 
boehmes@36898: fun unfold_def_conv ctxt ct =
boehmes@36898:   (case Thm.term_of ct of
boehmes@36898:     Const (@{const_name abs}, _) $ _ => unfold_abs_conv
boehmes@36898:   | Const (@{const_name abs}, _) => expand_conv unfold_abs_conv ctxt
boehmes@36898:   | Const (@{const_name min}, _) $ _ $ _ => unfold_min_conv
boehmes@36898:   | Const (@{const_name min}, _) $ _ => expand_conv unfold_min_conv ctxt
boehmes@36898:   | Const (@{const_name min}, _) => expand2_conv unfold_min_conv ctxt
boehmes@36898:   | Const (@{const_name max}, _) $ _ $ _ => unfold_max_conv
boehmes@36898:   | Const (@{const_name max}, _) $ _ => expand_conv unfold_max_conv ctxt
boehmes@36898:   | Const (@{const_name max}, _) => expand2_conv unfold_max_conv ctxt
boehmes@36898:   | _ => Conv.all_conv) ct
boehmes@36898: 
boehmes@36898: fun unfold_abs_min_max_defs ctxt thm =
boehmes@36898:   if exists_abs_min_max (Thm.prop_of thm)
wenzelm@36936:   then Conv.fconv_rule (Conv.top_conv unfold_def_conv ctxt) thm
boehmes@36898:   else thm
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (** include additional facts **)
boehmes@36898: 
boehmes@40161: fun extra_norm has_datatypes irules ctxt =
boehmes@40161:   irules
boehmes@39298:   |> not has_datatypes ? add_pair_rules
boehmes@36898:   |> add_fun_upd_rules
boehmes@40161:   |> map (apsnd (unfold_abs_min_max_defs ctxt))
boehmes@36898:   |> rpair ctxt
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (* builtins *)
boehmes@36898: 
boehmes@41059: local
boehmes@41059:   fun int_num _ i = SOME (string_of_int i)
boehmes@36899: 
boehmes@41059:   fun distinct _ _ [t] =
boehmes@41059:         (case try HOLogic.dest_list t of
boehmes@41059:           SOME (ts as _ :: _) => SOME ("distinct", ts)
boehmes@41059:         | _ => NONE)
boehmes@41059:     | distinct _ _ _ = NONE
boehmes@41059: in
boehmes@36898: 
boehmes@41059: val setup =
boehmes@41059:   B.add_builtin_typ smtlibC (@{typ int}, K (SOME "Int"), int_num) #>
boehmes@41059:   fold (B.add_builtin_fun' smtlibC) [
boehmes@41059:     (@{const True}, "true"),
boehmes@41059:     (@{const False}, "false"),
boehmes@41059:  (* FIXME: we do not test if these constants are fully applied! *)
boehmes@41059:     (@{const Not}, "not"),
boehmes@41059:     (@{const HOL.conj}, "and"),
boehmes@41059:     (@{const HOL.disj}, "or"),
boehmes@41059:     (@{const HOL.implies}, "implies"),
boehmes@41059:     (@{const HOL.eq (bool)}, "iff"),
boehmes@41059:     (@{const HOL.eq ('a)}, "="),
boehmes@41059:     (@{const If (bool)}, "if_then_else"),
boehmes@41059:     (@{const If ('a)}, "ite"),
boehmes@41059:     (@{const less (int)}, "<"),
boehmes@41059:     (@{const less_eq (int)}, "<="),
boehmes@41059:     (@{const uminus (int)}, "~"),
boehmes@41059:     (@{const plus (int)}, "+"),
boehmes@41059:     (@{const minus (int)}, "-"),
boehmes@41059:     (@{const times (int)}, "*") ] #>
boehmes@41059:   B.add_builtin_fun smtlibC (Term.dest_Const @{const distinct ('a)}, distinct)
boehmes@36898: 
boehmes@41059: end
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@41059: (* serialization *)
boehmes@36898: 
boehmes@41059: (** header **)
boehmes@41059: 
boehmes@41059: fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
boehmes@36899: 
boehmes@36899: structure Logics = Generic_Data
boehmes@36899: (
boehmes@36899:   type T = (int * (term list -> string option)) list
boehmes@36899:   val empty = []
boehmes@36899:   val extend = I
wenzelm@39687:   fun merge (bs1, bs2) = Ord_List.union fst_int_ord bs2 bs1
boehmes@36899: )
boehmes@36899: 
boehmes@41059: fun add_logic pf = Logics.map (Ord_List.insert fst_int_ord pf)
boehmes@36899: 
boehmes@36899: fun choose_logic ctxt ts =
boehmes@36899:   let
boehmes@36899:     fun choose [] = "AUFLIA"
boehmes@41059:       | choose ((_, f) :: fs) = (case f ts of SOME s => s | NONE => choose fs)
boehmes@41059:   in [":logic " ^ choose (Logics.get (Context.Proof ctxt))] end
boehmes@36899: 
boehmes@36899: 
boehmes@36899: (* serialization *)
boehmes@36899: 
boehmes@36898: val add = Buffer.add
boehmes@36898: fun sep f = add " " #> f
boehmes@36898: fun enclose l r f = sep (add l #> f #> add r)
boehmes@36898: val par = enclose "(" ")"
boehmes@36898: fun app n f = (fn [] => sep (add n) | xs => par (add n #> fold f xs))
boehmes@36898: fun line f = f #> add "\n"
boehmes@36898: 
boehmes@36898: fun var i = add "?v" #> add (string_of_int i)
boehmes@36898: 
boehmes@36898: fun sterm l (T.SVar i) = sep (var (l - i - 1))
boehmes@36898:   | sterm l (T.SApp (n, ts)) = app n (sterm l) ts
boehmes@36898:   | sterm _ (T.SLet _) = raise Fail "SMT-LIB: unsupported let expression"
boehmes@40664:   | sterm l (T.SQua (q, ss, ps, w, t)) =
boehmes@36898:       let
boehmes@36898:         val quant = add o (fn T.SForall => "forall" | T.SExists => "exists")
boehmes@36898:         val vs = map_index (apfst (Integer.add l)) ss
boehmes@36898:         fun var_decl (i, s) = par (var i #> sep (add s))
boehmes@36898:         val sub = sterm (l + length ss)
boehmes@36898:         fun pat kind ts = sep (add kind #> enclose "{" " }" (fold sub ts))
boehmes@36898:         fun pats (T.SPat ts) = pat ":pat" ts
boehmes@36898:           | pats (T.SNoPat ts) = pat ":nopat" ts
boehmes@40664:         fun weight NONE = I
boehmes@40664:           | weight (SOME i) =
boehmes@40664:               sep (add ":weight { " #> add (string_of_int i) #> add " }")
boehmes@40664:       in
boehmes@40664:         par (quant q #> fold var_decl vs #> sub t #> fold pats ps #> weight w)
boehmes@40664:       end
boehmes@36898: 
boehmes@37155: fun ssort sorts = sort fast_string_ord sorts
boehmes@37155: fun fsort funcs = sort (prod_ord fast_string_ord (K EQUAL)) funcs
boehmes@37155: 
boehmes@39298: fun sdatatypes decls =
boehmes@39298:   let
boehmes@39298:     fun con (n, []) = add n
boehmes@39298:       | con (n, sels) = par (add n #>
boehmes@39298:           fold (fn (n, s) => sep (par (add n #> sep (add s)))) sels)
boehmes@39298:     fun dtyp (n, decl) = add n #> fold (sep o con) decl
boehmes@39298:   in line (add ":datatypes " #> par (fold (par o dtyp) decls)) end
boehmes@39298: 
boehmes@39298: fun serialize comments {header, sorts, dtyps, funcs} ts =
boehmes@36898:   Buffer.empty
boehmes@36898:   |> line (add "(benchmark Isabelle")
boehmes@36898:   |> line (add ":status unknown")
boehmes@36899:   |> fold (line o add) header
boehmes@36898:   |> length sorts > 0 ?
boehmes@37155:        line (add ":extrasorts" #> par (fold (sep o add) (ssort sorts)))
boehmes@39298:   |> fold sdatatypes dtyps
boehmes@36898:   |> length funcs > 0 ? (
boehmes@36898:        line (add ":extrafuns" #> add " (") #>
boehmes@36898:        fold (fn (f, (ss, s)) =>
boehmes@37155:          line (sep (app f (sep o add) (ss @ [s])))) (fsort funcs) #>
boehmes@36898:        line (add ")"))
boehmes@36898:   |> fold (fn t => line (add ":assumption" #> sterm 0 t)) ts
boehmes@36898:   |> line (add ":formula true)")
boehmes@36898:   |> fold (fn str => line (add "; " #> add str)) comments
boehmes@36898:   |> Buffer.content
boehmes@36898: 
boehmes@36898: 
boehmes@36898: 
boehmes@36899: (** interfaces **)
boehmes@36898: 
boehmes@36898: val interface = {
boehmes@41059:   class = smtlibC,
boehmes@40162:   extra_norm = extra_norm,
boehmes@36898:   translate = {
boehmes@36898:     prefixes = {
boehmes@36898:       sort_prefix = "S",
boehmes@36898:       func_prefix = "f"},
boehmes@36899:     header = choose_logic,
boehmes@41059:     is_fol = true,
boehmes@41059:     has_datatypes = false,
boehmes@36898:     serialize = serialize}}
boehmes@36898: 
boehmes@36898: end