(*  Title:      HOL/Tools/SMT2/smt2_solver.ML

    Author:     Sascha Boehme, TU Muenchen

SMT solvers registry and SMT tactic.

*)

signature SMT2_SOLVER =

sig

  (*configuration*)

  datatype outcome = Unsat | Sat | Unknown

  type solver_config = {

    name: string,

    class: Proof.context -> SMT2_Util.class,

    avail: unit -> bool,

    command: unit -> string list,

    options: Proof.context -> string list,

    default_max_relevant: int,

    can_filter: bool,

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

    cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list ->

      term list * term list) option,

    replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->

      ((int * (int * thm)) list * Z3_New_Proof.z3_step 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 option * thm) list ->

    ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm

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

  (*filter*)

  val smt2_filter: Proof.context -> thm -> ('a * (int option * thm)) list -> int -> Time.time ->

    {outcome: SMT2_Failure.failure option, conjecture_id: int, helper_ids: (int * thm) list,

     fact_ids: (int * ('a * thm)) list, z3_proof: Z3_New_Proof.z3_step list}

  (*tactic*)

  val smt2_tac: Proof.context -> thm list -> int -> tactic

  val smt2_tac': Proof.context -> thm list -> int -> tactic

end

structure SMT2_Solver: SMT2_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 _ = SMT2_Config.trace_msg ctxt (fn () => msg) ()

  in f x end

fun run ctxt name mk_cmd input =

  (case SMT2_Config.certificates_of ctxt of

    NONE =>

      if not (SMT2_Config.is_available ctxt name) then

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

      else if Config.get ctxt SMT2_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 SMT2_Config.debug_files)

          val in_path = Path.ext "smt2_in" base_path

          val out_path = Path.ext "smt2_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 SMT2_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))

(* Z3 returns 1 if "get-model" or "get-model" fails *)

val normal_return_codes = [0, 1]

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 _ = SMT2_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input

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

      SMT2_Config.with_timeout ctxt (run ctxt name mk_cmd) input

    val _ = SMT2_Config.trace_msg ctxt (pretty "Solver:") err

    val output = fst (take_suffix (equal "") res)

    val _ = SMT2_Config.trace_msg ctxt (pretty "Result:") output

    val _ = member (op =) normal_return_codes return_code orelse

      raise SMT2_Failure.SMT (SMT2_Failure.Abnormal_Termination return_code)

  in output end

fun trace_assms ctxt =

  SMT2_Config.trace_msg ctxt (Pretty.string_of o

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

fun trace_replay_data ({context=ctxt, typs, terms, ...} : SMT2_Translate.replay_data) =

  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

    SMT2_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 = SMT2_Config.solver_options_of ctxt

    val cmd = command ()

    val comments = [space_implode " " options]

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

      ithms

      |> tap (trace_assms ctxt)

      |> SMT2_Translate.translate ctxt comments

      ||> tap trace_replay_data

  in (run_solver ctxt' name (make_cmd cmd options) str, replay_data) end

end

(* configuration *)

datatype outcome = Unsat | Sat | Unknown

type solver_config = {

  name: string,

  class: Proof.context -> SMT2_Util.class,

  avail: unit -> bool,

  command: unit -> string list,

  options: Proof.context -> string list,

  default_max_relevant: int,

  can_filter: bool,

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

  cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list ->

    term list * term list) option,

  replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->

    ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm) option}

(* check well-sortedness *)

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

    TFree (_, []) => true

  | TVar (_, []) => true

  | _ => false))

(* top sorts cause problems with atomization *)

fun check_topsort ctxt thm =

  if has_topsort (Thm.prop_of thm) then (SMT2_Normalize.drop_fact_warning ctxt thm; TrueI) else thm

(* registry *)

type solver_info = {

  command: unit -> string list,

  default_max_relevant: int,

  can_filter: bool,

  finish: Proof.context -> SMT2_Translate.replay_data -> string list ->

    ((int * (int * thm)) list * Z3_New_Proof.z3_step 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 replay ocl outer_ctxt

      (replay_data as {context=ctxt, ...} : SMT2_Translate.replay_data) output =

    (case outcome output of

      (Unsat, ls) =>

        if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay

        then the replay outer_ctxt replay_data ls

        else (([], []), ocl ())

    | (result, ls) =>

        let

          val (ts, us) =

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

        in

          raise SMT2_Failure.SMT (SMT2_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 ({name, class, avail, command, options, default_max_relevant, can_filter,

    outcome, cex_parser, replay} : solver_config) =

  let

    fun solver ocl = {

      command = command,

      default_max_relevant = default_max_relevant,

      can_filter = can_filter,

      finish = finish (outcome name) cex_parser replay ocl}

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

  in

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

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

    Context.theory_map (SMT2_Config.add_solver info)

  end

end

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

val solver_name_of = SMT2_Config.solver_of

val available_solvers_of = SMT2_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 apply_solver ctxt wthms0 =

  let

    val wthms = map (apsnd (check_topsort ctxt)) wthms0

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

    val (output, replay_data) = invoke name command (SMT2_Normalize.normalize ctxt wthms) ctxt

  in finish ctxt replay_data output end

val default_max_relevant = #default_max_relevant oo get_info

val can_filter = #can_filter o snd o name_and_info_of 

(* filter *)

val no_id = ~1

fun smt2_filter ctxt goal xwfacts i time_limit =

  let

    val ctxt =

      ctxt

      |> Config.put SMT2_Config.oracle false

      |> Config.put SMT2_Config.filter_only_facts true

      |> Config.put SMT2_Config.timeout (Time.toReal time_limit)

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

    fun negate ct = Thm.dest_comb ct ||> Thm.apply @{cterm Not} |-> Thm.apply

    val cprop =

      (case try negate (Thm.rhs_of (SMT2_Normalize.atomize_conv ctxt concl)) of

        SOME ct => ct

      | NONE => raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure "goal is not a HOL term"))

    val wconjecture = (NONE, Thm.assume cprop)

    val wprems = map (pair NONE) prems

    val wfacts = map snd xwfacts

    val wthms = wconjecture :: wprems @ wfacts

    val iwthms = map_index I wthms

    val conjecture_i = 0

    val facts_i = 1 + length wprems

  in

    wthms

    |> apply_solver ctxt

    |> fst

    |> (fn (iidths0, z3_proof) =>

      let

        val iidths = if can_filter ctxt then iidths0 else map (apsnd (apfst (K no_id))) iwthms

      in

        {outcome = NONE, 

         conjecture_id =

           the_default no_id (Option.map fst (AList.lookup (op =) iidths conjecture_i)),

         helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths,

         fact_ids = map_filter (fn (i, (id, _)) =>

           try (apsnd (apsnd snd o nth xwfacts)) (id, i - facts_i)) iidths,

         z3_proof = z3_proof}

      end)

  end

  handle SMT2_Failure.SMT fail => {outcome = SOME fail, conjecture_id = no_id, helper_ids = [],

    fact_ids = [], z3_proof = []}

(* SMT tactic *)

local

  fun trace_assumptions ctxt wfacts iidths =

    let val used = map_filter (try (snd o nth wfacts) o fst) iidths in

      if Config.get ctxt SMT2_Config.trace_used_facts andalso length wfacts > 0 then

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

          (map (Display.pretty_thm ctxt) used)))

      else ()

    end

  fun solve ctxt wfacts =

    wfacts

    |> apply_solver ctxt

    |>> apfst (trace_assumptions ctxt wfacts)

    |> snd

  fun str_of ctxt fail =

    SMT2_Failure.string_of_failure ctxt fail

    |> prefix ("Solver " ^ SMT2_Config.solver_of ctxt ^ ": ")

  fun safe_solve ctxt wfacts = SOME (solve ctxt wfacts)

    handle

      SMT2_Failure.SMT (fail as SMT2_Failure.Counterexample _) =>

        (SMT2_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)

    | SMT2_Failure.SMT (fail as SMT2_Failure.Time_Out) =>

        error ("SMT: Solver " ^ quote (SMT2_Config.solver_of ctxt) ^ ": " ^

          SMT2_Failure.string_of_failure ctxt fail ^ " (setting the " ^

          "configuration option " ^ quote (Config.name_of SMT2_Config.timeout) ^ " might help)")

    | SMT2_Failure.SMT fail => error (str_of ctxt fail)

  fun resolve (SOME thm) = rtac thm 1

    | resolve NONE = no_tac

  fun tac prove ctxt rules =

    CONVERSION (SMT2_Normalize.atomize_conv ctxt)

    THEN' rtac @{thm ccontr}

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

      resolve (prove ctxt (map (pair NONE) (rules @ prems)))) ctxt

in

val smt2_tac = tac safe_solve

val smt2_tac' = tac (SOME oo solve)

end

end