(*  Title:      HOL/Tools/SMT/smt_solver.ML

    Author:     Sascha Boehme, TU Muenchen

SMT solvers registry and SMT tactic.

*)

signature SMT_SOLVER =

sig

  (*configuration*)

  datatype outcome = Unsat | Sat | Unknown

  type solver_config = {

    name: string,

    class: Proof.context -> SMT_Utils.class,

    avail: unit -> bool,

    command: unit -> string list,

    options: Proof.context -> string list,

    default_max_relevant: int,

    supports_filter: bool,

    outcome: string -> string list -> outcome * string list,

    cex_parser: (Proof.context -> SMT_Translate.recon -> string list ->

      term list * term list) option,

    reconstruct: (Proof.context -> SMT_Translate.recon -> string list ->

      int list * thm) option }

  (*registry*)

  val add_solver: solver_config -> theory -> theory

  val solver_name_of: Proof.context -> string

  val available_solvers_of: Proof.context -> string list

  val apply_solver: Proof.context -> (int * (int option * thm)) list ->

    int list * thm

  val default_max_relevant: Proof.context -> string -> int

  (*filter*)

  type 'a smt_filter_data =

    ('a * thm) list * ((int * thm) list * Proof.context)

  val smt_filter_preprocess: Proof.state ->

    ('a * (int option * thm)) list -> int -> 'a smt_filter_data

  val smt_filter_apply: Time.time -> 'a smt_filter_data ->

    {outcome: SMT_Failure.failure option, used_facts: ('a * thm) list}

  (*tactic*)

  val smt_tac: Proof.context -> thm list -> int -> tactic

  val smt_tac': Proof.context -> thm list -> int -> tactic

end

structure SMT_Solver: SMT_SOLVER =

struct

(* interface to external solvers *)

local

fun make_cmd command options problem_path proof_path = space_implode " " (

  "(exec 2>&1;" :: map File.shell_quote (command () @ options) @

  [File.shell_path problem_path, ")", ">", File.shell_path proof_path])

fun trace_and ctxt msg f x =

  let val _ = SMT_Config.trace_msg ctxt (fn () => msg) ()

  in f x end

fun run ctxt name mk_cmd input =

  (case SMT_Config.certificates_of ctxt of

    NONE =>

      if not (SMT_Config.is_available ctxt name) then

        error ("The SMT solver " ^ quote name ^ " is not installed.")

      else if Config.get ctxt SMT_Config.debug_files = "" then

        trace_and ctxt ("Invoking SMT solver " ^ quote name ^ " ...")

          (Cache_IO.run mk_cmd) input

      else

        let

          val base_path = Path.explode (Config.get ctxt SMT_Config.debug_files)

          val in_path = Path.ext "smt_in" base_path

          val out_path = Path.ext "smt_out" base_path

        in Cache_IO.raw_run mk_cmd input in_path out_path end

  | SOME certs =>

      (case Cache_IO.lookup certs input of

        (NONE, key) =>

          if Config.get ctxt SMT_Config.read_only_certificates then

            error ("Bad certificate cache: missing certificate")

          else

            Cache_IO.run_and_cache certs key mk_cmd input

      | (SOME output, _) =>

          trace_and ctxt ("Using cached certificate from " ^

            File.shell_path (Cache_IO.cache_path_of certs) ^ " ...")

            I output))

fun run_solver ctxt name mk_cmd input =

  let

    fun pretty tag ls = Pretty.string_of (Pretty.big_list tag

      (map Pretty.str ls))

    val _ = SMT_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input

    val {redirected_output=res, output=err, return_code} =

      SMT_Config.with_timeout ctxt (run ctxt name mk_cmd) input

    val _ = SMT_Config.trace_msg ctxt (pretty "Solver:") err

    val ls = rev (snd (chop_while (equal "") (rev res)))

    val _ = SMT_Config.trace_msg ctxt (pretty "Result:") ls

    val _ = return_code <> 0 andalso

      raise SMT_Failure.SMT (SMT_Failure.Abnormal_Termination return_code)

  in ls end

fun trace_assms ctxt =

  SMT_Config.trace_msg ctxt (Pretty.string_of o

    Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))

fun trace_recon_data ({context=ctxt, typs, terms, ...} : SMT_Translate.recon) =

  let

    fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]

    fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)

    fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)

  in

    SMT_Config.trace_msg ctxt (fn () =>

      Pretty.string_of (Pretty.big_list "Names:" [

        Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)),

        Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) ()

  end

in

fun invoke name command ithms ctxt =

  let

    val options = SMT_Config.solver_options_of ctxt

    val comments = ("solver: " ^ name) ::

      ("timeout: " ^ string_of_real (Config.get ctxt SMT_Config.timeout)) ::

      ("random seed: " ^

        string_of_int (Config.get ctxt SMT_Config.random_seed)) ::

      "arguments:" :: options

    val (str, recon as {context=ctxt', ...}) =

      ithms

      |> tap (trace_assms ctxt)

      |> SMT_Translate.translate ctxt comments

      ||> tap trace_recon_data

  in (run_solver ctxt' name (make_cmd command options) str, recon) end

end

(* configuration *)

datatype outcome = Unsat | Sat | Unknown

type solver_config = {

  name: string,

  class: Proof.context -> SMT_Utils.class,

  avail: unit -> bool,

  command: unit -> string list,

  options: Proof.context -> string list,

  default_max_relevant: int,

  supports_filter: bool,

  outcome: string -> string list -> outcome * string list,

  cex_parser: (Proof.context -> SMT_Translate.recon -> string list ->

    term list * term list) option,

  reconstruct: (Proof.context -> SMT_Translate.recon -> string list ->

    int list * thm) option }

(* registry *)

type solver_info = {

  command: unit -> string list,

  default_max_relevant: int,

  supports_filter: bool,

  reconstruct: Proof.context -> string list * SMT_Translate.recon ->

    int list * thm }

structure Solvers = Generic_Data

(

  type T = solver_info Symtab.table

  val empty = Symtab.empty

  val extend = I

  fun merge data = Symtab.merge (K true) data

)

local

  fun finish outcome cex_parser reconstruct ocl outer_ctxt

      (output, (recon as {context=ctxt, ...} : SMT_Translate.recon)) =

    (case outcome output of

      (Unsat, ls) =>

        if not (Config.get ctxt SMT_Config.oracle) andalso is_some reconstruct

        then the reconstruct outer_ctxt recon ls

        else ([], ocl ())

    | (result, ls) =>

        let

          val (ts, us) =

            (case cex_parser of SOME f => f ctxt recon ls | _ => ([], []))

         in

          raise SMT_Failure.SMT (SMT_Failure.Counterexample {

            is_real_cex = (result = Sat),

            free_constraints = ts,

            const_defs = us})

        end)

  val cfalse = Thm.cterm_of @{theory} (@{const Trueprop} $ @{const False})

in

fun add_solver cfg =

  let

    val {name, class, avail, command, options, default_max_relevant,

      supports_filter, outcome, cex_parser, reconstruct} = cfg

    fun core_oracle () = cfalse

    fun solver ocl = {

      command = command,

      default_max_relevant = default_max_relevant,

      supports_filter = supports_filter,

      reconstruct = finish (outcome name) cex_parser reconstruct ocl }

    val info = {name=name, class=class, avail=avail, options=options}

  in

    Thm.add_oracle (Binding.name name, core_oracle) #-> (fn (_, ocl) =>

    Context.theory_map (Solvers.map (Symtab.update_new (name, solver ocl)))) #>

    Context.theory_map (SMT_Config.add_solver info)

  end

end

fun get_info ctxt name =

  the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)

val solver_name_of = SMT_Config.solver_of

val available_solvers_of = SMT_Config.available_solvers_of

fun name_and_info_of ctxt =

  let val name = solver_name_of ctxt

  in (name, get_info ctxt name) end

fun gen_preprocess ctxt iwthms = SMT_Normalize.normalize iwthms ctxt

fun gen_apply (ithms, ctxt) =

  let val (name, {command, reconstruct, ...}) = name_and_info_of ctxt

  in

    (ithms, ctxt)

    |-> invoke name command

    |> reconstruct ctxt

    |>> distinct (op =)

  end

fun apply_solver ctxt = gen_apply o gen_preprocess ctxt

val default_max_relevant = #default_max_relevant oo get_info

val supports_filter = #supports_filter o snd o name_and_info_of 

(* check well-sortedness *)

val has_topsort = Term.exists_type (Term.exists_subtype (fn

    TFree (_, []) => true

  | TVar (_, []) => true

  | _ => false))

(* without this test, we would run into problems when atomizing the rules: *)

fun check_topsort iwthms =

  if exists (has_topsort o Thm.prop_of o snd o snd) iwthms then

    raise SMT_Failure.SMT (SMT_Failure.Other_Failure ("proof state " ^

      "contains the universal sort {}"))

  else ()

(* filter *)

val cnot = Thm.cterm_of @{theory} @{const Not}

fun mk_result outcome xrules = { outcome = outcome, used_facts = xrules }

type 'a smt_filter_data = ('a * thm) list * ((int * thm) list * Proof.context)

fun smt_filter_preprocess st xwthms i =

  let

    val ctxt =

      Proof.context_of st

      |> Config.put SMT_Config.oracle false

      |> Config.put SMT_Config.drop_bad_facts true

      |> Config.put SMT_Config.filter_only_facts true

    val {facts, goal, ...} = Proof.goal st

    val ({context=ctxt', prems, concl, ...}, _) = Subgoal.focus ctxt i goal

    fun negate ct = Thm.dest_comb ct ||> Thm.apply cnot |-> Thm.apply

    val cprop =

      (case try negate (Thm.rhs_of (SMT_Normalize.atomize_conv ctxt' concl)) of

        SOME ct => ct

      | NONE => raise SMT_Failure.SMT (SMT_Failure.Other_Failure (

          "goal is not a HOL term")))

  in

    map snd xwthms

    |> map_index I

    |> append (map (pair ~1 o pair NONE) (Thm.assume cprop :: prems @ facts))

    |> tap check_topsort

    |> gen_preprocess ctxt'

    |> pair (map (apsnd snd) xwthms)

  end

fun smt_filter_apply time_limit (xthms, (ithms, ctxt)) =

  let

    val ctxt' =

      ctxt

      |> Config.put SMT_Config.timeout (Time.toReal time_limit)

    fun filter_thms false = K xthms

      | filter_thms true = map_filter (try (nth xthms)) o fst

  in

    (ithms, ctxt')

    |> gen_apply

    |> filter_thms (supports_filter ctxt')

    |> mk_result NONE

  end

  handle SMT_Failure.SMT fail => mk_result (SOME fail) []

(* SMT tactic *)

local

  fun trace_assumptions ctxt iwthms idxs =

    let

      val wthms =

        idxs

        |> filter (fn i => i >= 0)

        |> map_filter (AList.lookup (op =) iwthms)

    in

      if Config.get ctxt SMT_Config.trace_used_facts andalso length wthms > 0

      then

        tracing (Pretty.string_of (Pretty.big_list "SMT used facts:"

          (map (Display.pretty_thm ctxt o snd) wthms)))

      else ()

    end

  fun solve ctxt iwthms =

    iwthms

    |> tap check_topsort

    |> apply_solver ctxt

    |>> trace_assumptions ctxt iwthms

    |> snd

  fun str_of ctxt fail =

    SMT_Failure.string_of_failure ctxt fail

    |> prefix ("Solver " ^ SMT_Config.solver_of ctxt ^ ": ")

  fun safe_solve ctxt iwthms = SOME (solve ctxt iwthms)

    handle

      SMT_Failure.SMT (fail as SMT_Failure.Counterexample _) =>

        (SMT_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)

    | SMT_Failure.SMT (fail as SMT_Failure.Time_Out) =>

        error ("SMT: Solver " ^ quote (SMT_Config.solver_of ctxt) ^ ": " ^

          SMT_Failure.string_of_failure ctxt fail ^ " (setting the " ^

          "configuration option " ^ quote (Config.name_of SMT_Config.timeout) ^ " might help)")

    | SMT_Failure.SMT fail => error (str_of ctxt fail)

  fun tag_rules thms = map_index (apsnd (pair NONE)) thms

  fun tag_prems thms = map (pair ~1 o pair NONE) thms

  fun resolve (SOME thm) = Tactic.rtac thm 1

    | resolve NONE = no_tac

  fun tac prove ctxt rules =

    CONVERSION (SMT_Normalize.atomize_conv ctxt)

    THEN' Tactic.rtac @{thm ccontr}

    THEN' SUBPROOF (fn {context, prems, ...} =>

      resolve (prove context (tag_rules rules @ tag_prems prems))) ctxt

in

val smt_tac = tac safe_solve

val smt_tac' = tac (SOME oo solve)

end

end