(*  Title:      Tools/quickcheck.ML

    Author:     Stefan Berghofer, Florian Haftmann, Lukas Bulwahn, TU Muenchen

Generic counterexample search engine.

*)

signature QUICKCHECK =

sig

  val setup: theory -> theory

  (* configuration *)

  val auto: bool Unsynchronized.ref

  val timing : bool Unsynchronized.ref

  val size : int Config.T

  val iterations : int Config.T

  val no_assms : bool Config.T

  val report : bool Config.T

  val quiet : bool Config.T

  val timeout : real Config.T

  val finite_types : bool Config.T

  val finite_type_size : int Config.T

  datatype report = Report of

    { iterations : int, raised_match_errors : int,

      satisfied_assms : int list, positive_concl_tests : int }

  datatype expectation = No_Expectation | No_Counterexample | Counterexample;  

  datatype test_params = Test_Params of {default_type: typ list, expect : expectation};

  val test_params_of : Proof.context -> test_params

  val map_test_params : (typ list * expectation -> typ list * expectation)

    -> Context.generic -> Context.generic

  val add_generator:

    string * (Proof.context -> term -> int -> term list option * (bool list * bool))

      -> Context.generic -> Context.generic

  (* testing terms and proof states *)

  val test_term_small: Proof.context -> term ->

    (string * term) list option * ((string * int) list * ((int * report list) list) option)

  val test_term: Proof.context -> string option -> term ->

    (string * term) list option * ((string * int) list * ((int * report list) list) option)

  val test_goal_terms:

    Proof.context -> string option * (string * typ) list -> term list

      -> (string * term) list option * ((string * int) list * ((int * report list) list) option) list

  val quickcheck: (string * string list) list -> int -> Proof.state -> (string * term) list option

end;

structure Quickcheck : QUICKCHECK =

struct

(* preferences *)

val auto = Unsynchronized.ref false;

val timing = Unsynchronized.ref false;

val _ =

  ProofGeneralPgip.add_preference Preferences.category_tracing

  (Unsynchronized.setmp auto true (fn () =>

    Preferences.bool_pref auto

      "auto-quickcheck"

      "Run Quickcheck automatically.") ());

(* quickcheck report *)

datatype single_report = Run of bool list * bool | MatchExc

datatype report = Report of

  { iterations : int, raised_match_errors : int,

    satisfied_assms : int list, positive_concl_tests : int }

fun collect_single_report single_report

    (Report {iterations = iterations, raised_match_errors = raised_match_errors,

    satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =

  case single_report

  of MatchExc =>

    Report {iterations = iterations + 1, raised_match_errors = raised_match_errors + 1,

      satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}

   | Run (assms, concl) =>

    Report {iterations = iterations + 1, raised_match_errors = raised_match_errors,

      satisfied_assms =

        map2 (fn b => fn s => if b then s + 1 else s) assms

         (if null satisfied_assms then replicate (length assms) 0 else satisfied_assms),

      positive_concl_tests = if concl then positive_concl_tests + 1 else positive_concl_tests}

(* expectation *)

datatype expectation = No_Expectation | No_Counterexample | Counterexample; 

fun merge_expectation (expect1, expect2) =

  if expect1 = expect2 then expect1 else No_Expectation

(* quickcheck configuration -- default parameters, test generators *)

val (size, setup_size) = Attrib.config_int "quickcheck_size" (K 10)

val (iterations, setup_iterations) = Attrib.config_int "quickcheck_iterations" (K 100)

val (no_assms, setup_no_assms) = Attrib.config_bool "quickcheck_no_assms" (K false)

val (report, setup_report) = Attrib.config_bool "quickcheck_report" (K true)

val (quiet, setup_quiet) = Attrib.config_bool "quickcheck_quiet" (K false)

val (timeout, setup_timeout) = Attrib.config_real "quickcheck_timeout" (K 30.0)

val (finite_types, setup_finite_types) = Attrib.config_bool "quickcheck_finite_types" (K true)

val (finite_type_size, setup_finite_type_size) = Attrib.config_int "quickcheck_finite_type_size" (K 3)

val setup_config =

  setup_size #> setup_iterations #> setup_no_assms #> setup_report #> setup_quiet #> setup_timeout

    #> setup_finite_types #> setup_finite_type_size

datatype test_params = Test_Params of

  {default_type: typ list, expect : expectation};

fun dest_test_params (Test_Params {default_type, expect}) = (default_type, expect);

fun make_test_params (default_type, expect) = Test_Params {default_type = default_type, expect = expect};

fun map_test_params' f (Test_Params {default_type, expect}) = make_test_params (f (default_type, expect));

fun merge_test_params

 (Test_Params {default_type = default_type1, expect = expect1},

  Test_Params {default_type = default_type2, expect = expect2}) =

  make_test_params (merge (op =) (default_type1, default_type2), merge_expectation (expect1, expect2));

structure Data = Generic_Data

(

  type T =

    (string * (Proof.context -> term -> int -> term list option * (bool list * bool))) list

      * test_params;

  val empty = ([], Test_Params {default_type = [], expect = No_Expectation});

  val extend = I;

  fun merge ((generators1, params1), (generators2, params2)) : T =

    (AList.merge (op =) (K true) (generators1, generators2),

      merge_test_params (params1, params2));

);

val test_params_of = snd o Data.get o Context.Proof;

val default_type = fst o dest_test_params o test_params_of

val expect = snd o dest_test_params o test_params_of

val map_test_params = Data.map o apsnd o map_test_params'

val add_generator = Data.map o apfst o AList.update (op =);

(* generating tests *)

fun mk_tester_select name ctxt =

  case AList.lookup (op =) ((fst o Data.get o Context.Proof) ctxt) name

   of NONE => error ("No such quickcheck generator: " ^ name)

    | SOME generator => generator ctxt;

fun mk_testers ctxt t =

  (map snd o fst o Data.get o Context.Proof) ctxt

  |> map_filter (fn generator => try (generator ctxt) t);

fun mk_testers_strict ctxt t =

  let

    val generators = ((map snd o fst o Data.get o Context.Proof) ctxt)

    val testers = map (fn generator => Exn.interruptible_capture (generator ctxt) t) generators;

  in

    if forall (is_none o Exn.get_result) testers

    then [(Exn.release o snd o split_last) testers]

    else map_filter Exn.get_result testers

  end;

(* testing propositions *)

fun prep_test_term t =

  let

    val _ = (null (Term.add_tvars t []) andalso null (Term.add_tfrees t [])) orelse

      error "Term to be tested contains type variables";

    val _ = null (Term.add_vars t []) orelse

      error "Term to be tested contains schematic variables";

    val frees = Term.add_frees t [];

  in (map fst frees, list_abs_free (frees, t)) end

fun cpu_time description f =

  let

    val start = start_timing ()

    val result = Exn.capture f ()

    val time = Time.toMilliseconds (#cpu (end_timing start))

  in (Exn.release result, (description, time)) end

fun test_term_small ctxt t =

  let

    val (names, t') = prep_test_term t;

    val current_size = Unsynchronized.ref 0

    fun excipit s =

      "Quickcheck " ^ s ^ " while testing at size " ^ string_of_int (!current_size)

    val (tester, comp_time) = cpu_time "compilation"

      (fn () => the (AList.lookup (op =) ((fst o Data.get o Context.Proof) ctxt) "small") ctxt t');

    val empty_report = Report { iterations = 0, raised_match_errors = 0,

      satisfied_assms = [], positive_concl_tests = 0 }

    fun with_size k timings =

      if k > Config.get ctxt size then (NONE, timings)

      else

        let

          val _ = if Config.get ctxt quiet then () else Output.urgent_message ("Test data size: " ^ string_of_int k);

          val _ = current_size := k

          val (result, timing) = cpu_time ("size " ^ string_of_int k)

            (fn () => (fst (tester k)) handle Match => (if Config.get ctxt quiet then ()

              else warning "Exception Match raised during quickcheck"; NONE))

        in

          case result of

            NONE => with_size (k + 1) (timing :: timings)

          | SOME q => (SOME q, (timing :: timings))

        end;

     val result = with_size 1 [comp_time]

   in

     apsnd (rpair NONE) (apfst (Option.map (curry (op ~~) names)) result)

   end

(* we actually assume we know the generators and its behaviour *)

fun is_iteratable "SML" = true

  | is_iteratable "random" = true

  | is_iteratable _ = false

fun test_term ctxt generator_name t =

  let

    val (names, t') = prep_test_term t;

    val current_size = Unsynchronized.ref 0

    fun excipit s =

      "Quickcheck " ^ s ^ " while testing at size " ^ string_of_int (!current_size)

    val (testers, comp_time) = cpu_time "quickcheck compilation"

      (fn () => (case generator_name

       of NONE => if Config.get ctxt quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'

        | SOME name => [mk_tester_select name ctxt t']));

    fun iterate f 0 report = (NONE, report)

      | iterate f j report =

        let

          val (test_result, single_report) = apsnd Run (f ()) handle Match => 

            (if Config.get ctxt quiet then ()

             else warning "Exception Match raised during quickcheck"; (NONE, MatchExc))

          val report = collect_single_report single_report report

        in

          case test_result of NONE => iterate f (j - 1) report | SOME q => (SOME q, report)

        end

    val empty_report = Report { iterations = 0, raised_match_errors = 0,

      satisfied_assms = [], positive_concl_tests = 0 }

    fun with_testers k [] = (NONE, [])

      | with_testers k (tester :: testers) =

        let

          val niterations = case generator_name of

            SOME generator_name =>

              if is_iteratable generator_name then Config.get ctxt iterations else 1

          | NONE => Config.get ctxt iterations

          val (result, timing) = cpu_time ("size " ^ string_of_int k)

            (fn () => iterate (fn () => tester (k - 1)) niterations empty_report)

        in

          case result

           of (NONE, report) => apsnd (cons report) (with_testers k testers)

            | (SOME q, report) => (SOME q, [report])

        end

    fun with_size k reports =

      if k > Config.get ctxt size then (NONE, reports)

      else

       (if Config.get ctxt quiet then () else Output.urgent_message ("Test data size: " ^ string_of_int k);

        let

          val _ = current_size := k

          val (result, new_report) = with_testers k testers

          val reports = ((k, new_report) :: reports)

        in case result of NONE => with_size (k + 1) reports | SOME q => (SOME q, reports) end);

    val ((result, reports), exec_time) =

      TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) (fn () => cpu_time "quickcheck execution"

      (fn () => apfst

         (fn result => case result of NONE => NONE

        | SOME ts => SOME (names ~~ ts)) (with_size 1 []))) ()

      handle TimeLimit.TimeOut =>

        error (excipit "ran out of time")

     | Exn.Interrupt => error (excipit "was interrupted")  (* FIXME violates Isabelle/ML exception model *)

  in

    (result, ([exec_time, comp_time], if Config.get ctxt report then SOME reports else NONE))

  end;

fun get_finite_types ctxt =

  fst (chop (Config.get ctxt finite_type_size)

    (map (Type o rpair []) ["Enum.finite_1", "Enum.finite_2", "Enum.finite_3",

     "Enum.finite_4", "Enum.finite_5"]))  

exception WELLSORTED of string

fun monomorphic_term thy insts default_T = 

  let

    fun subst (T as TFree (v, S)) =

      let

        val T' = AList.lookup (op =) insts v

          |> the_default default_T

      in if Sign.of_sort thy (T', S) then T'

        else raise (WELLSORTED ("For instantiation with default_type " ^ Syntax.string_of_typ_global thy default_T ^

          ":\n" ^ Syntax.string_of_typ_global thy T' ^

          " to be substituted for variable " ^

          Syntax.string_of_typ_global thy T ^ " does not have sort " ^

          Syntax.string_of_sort_global thy S))

      end

      | subst T = T;

  in (map_types o map_atyps) subst end;

datatype wellsorted_error = Wellsorted_Error of string | Term of term

fun test_goal_terms lthy (generator_name, insts) check_goals =

  let

    val thy = ProofContext.theory_of lthy 

    val inst_goals =

      if Config.get lthy finite_types then 

        maps (fn check_goal => map (fn T =>

          Term ((Object_Logic.atomize_term thy o monomorphic_term thy insts T) check_goal)

            handle WELLSORTED s => Wellsorted_Error s) (get_finite_types lthy)) check_goals

      else

        maps (fn check_goal => map (fn T =>

          Term ((Object_Logic.atomize_term thy o monomorphic_term thy insts T) check_goal)

            handle WELLSORTED s => Wellsorted_Error s) (default_type lthy)) check_goals

    val error_msg = cat_lines (map_filter (fn Term t => NONE | Wellsorted_Error s => SOME s) inst_goals)

    val correct_inst_goals =

      case map_filter (fn Term t => SOME t | Wellsorted_Error s => NONE) inst_goals of

        [] => error error_msg

      | xs => xs

    val _ = if Config.get lthy quiet then () else warning error_msg

    fun collect_results f reports [] = (NONE, rev reports)

      | collect_results f reports (t :: ts) =

        case f t of

          (SOME res, report) => (SOME res, rev (report :: reports))

        | (NONE, report) => collect_results f (report :: reports) ts

  in collect_results (test_term lthy generator_name) [] correct_inst_goals end;

fun test_goal (generator_name, insts) i state =

  let

    val lthy = Proof.context_of state;

    val thy = Proof.theory_of state;

    fun strip (Const ("all", _) $ Abs (_, _, t)) = strip t

      | strip t = t;

    val {goal = st, ...} = Proof.raw_goal state;

    val (gi, frees) = Logic.goal_params (prop_of st) i;

    val some_locale = case (Option.map #target o Named_Target.peek) lthy

     of NONE => NONE

      | SOME "" => NONE

      | SOME locale => SOME locale;

    val assms = if Config.get lthy no_assms then [] else case some_locale

     of NONE => Assumption.all_assms_of lthy

      | SOME locale => Assumption.local_assms_of lthy (Locale.init locale thy);

    val proto_goal = Logic.list_implies (map Thm.term_of assms, subst_bounds (frees, strip gi));

    val check_goals = case some_locale

     of NONE => [proto_goal]

      | SOME locale => map (fn (_, phi) => Morphism.term phi proto_goal)

        (Locale.registrations_of (Context.Theory thy) (*FIXME*) locale);

  in

    test_goal_terms lthy (generator_name, insts) check_goals

  end

(* pretty printing *)

fun tool_name auto = (if auto then "Auto " else "") ^ "Quickcheck"

fun pretty_counterex ctxt auto NONE = Pretty.str (tool_name auto ^ " found no counterexample.")

  | pretty_counterex ctxt auto (SOME cex) =

      Pretty.chunks (Pretty.str (tool_name auto ^ " found a counterexample:\n") ::

        map (fn (s, t) =>

          Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) cex);

fun pretty_report (Report {iterations = iterations, raised_match_errors = raised_match_errors,

    satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =

  let

    fun pretty_stat s i = Pretty.block ([Pretty.str (s ^ ": " ^ string_of_int i)])

  in

     ([pretty_stat "iterations" iterations,

     pretty_stat "match exceptions" raised_match_errors]

     @ map_index (fn (i, n) => pretty_stat ("satisfied " ^ string_of_int (i + 1) ^ ". assumption") n)

       satisfied_assms

     @ [pretty_stat "positive conclusion tests" positive_concl_tests])

  end

fun pretty_reports' [report] = [Pretty.chunks (pretty_report report)]

  | pretty_reports' reports =

  map_index (fn (i, report) =>

    Pretty.chunks (Pretty.str (string_of_int (i + 1) ^ ". generator:\n") :: pretty_report report))

    reports

fun pretty_reports ctxt (SOME reports) =

  Pretty.chunks (Pretty.str "Quickcheck report:" ::

    maps (fn (size, reports) =>

      Pretty.str ("size " ^ string_of_int size ^ ":") :: pretty_reports' reports @ [Pretty.brk 1])

      (rev reports))

  | pretty_reports ctxt NONE = Pretty.str ""

fun pretty_counterex_and_reports ctxt auto (cex, timing_and_reports) =

  Pretty.chunks (pretty_counterex ctxt auto cex ::

    map (pretty_reports ctxt) (map snd timing_and_reports))

(* automatic testing *)

fun auto_quickcheck state =

  if not (!auto) then

    (false, state)

  else

    let

      val ctxt = Proof.context_of state;

      val res =

        state

        |> Proof.map_context (Config.put report false #> Config.put quiet true)

        |> try (test_goal (NONE, []) 1);

    in

      case res of

        NONE => (false, state)

      | SOME (NONE, report) => (false, state)

      | SOME (cex, report) => (true, Proof.goal_message (K (Pretty.chunks [Pretty.str "",

          Pretty.mark Markup.hilite (pretty_counterex ctxt true cex)])) state)

    end

val setup = Auto_Tools.register_tool ("quickcheck", auto_quickcheck)

  #> setup_config

(* Isar commands *)

fun read_nat s = case (Library.read_int o Symbol.explode) s

 of (k, []) => if k >= 0 then k

      else error ("Not a natural number: " ^ s)

  | (_, _ :: _) => error ("Not a natural number: " ^ s);

fun read_bool "false" = false

  | read_bool "true" = true

  | read_bool s = error ("Not a Boolean value: " ^ s)

fun read_real s =

  case (Real.fromString s) of

    SOME s => s

  | NONE => error ("Not a real number: " ^ s)

fun read_expectation "no_expectation" = No_Expectation

  | read_expectation "no_counterexample" = No_Counterexample 

  | read_expectation "counterexample" = Counterexample

  | read_expectation s = error ("Not an expectation value: " ^ s)  

fun parse_test_param ("size", [arg]) = Config.put_generic size (read_nat arg)

  | parse_test_param ("iterations", [arg]) = Config.put_generic iterations (read_nat arg)

  | parse_test_param ("default_type", arg) = (fn gen_ctxt =>

    map_test_params ((apfst o K) (map (ProofContext.read_typ (Context.proof_of gen_ctxt)) arg)) gen_ctxt)

  | parse_test_param ("no_assms", [arg]) = Config.put_generic no_assms (read_bool arg)

  | parse_test_param ("expect", [arg]) = map_test_params ((apsnd o K) (read_expectation arg))

  | parse_test_param ("report", [arg]) = Config.put_generic report (read_bool arg)

  | parse_test_param ("quiet", [arg]) = Config.put_generic quiet (read_bool arg)

  | parse_test_param ("timeout", [arg]) = Config.put_generic timeout (read_real arg)

  | parse_test_param ("finite_types", [arg]) = Config.put_generic finite_types (read_bool arg)

  | parse_test_param ("finite_type_size", [arg]) = Config.put_generic finite_type_size (read_nat arg)

  | parse_test_param (name, _) = error ("Unknown test parameter: " ^ name);

fun parse_test_param_inst ("generator", [arg]) ((generator, insts), ctxt) =

      (apfst o apfst o K o SOME) arg ((generator, insts), ctxt)

  | parse_test_param_inst (name, arg) ((generator, insts), ctxt) =

      case try (ProofContext.read_typ ctxt) name

       of SOME (TFree (v, _)) => (apfst o apsnd o AList.update (op =))

              (v, ProofContext.read_typ ctxt (the_single arg)) ((generator, insts), ctxt)

        | _ => (apsnd o Context.proof_map o parse_test_param) (name, arg) ((generator, insts), ctxt);

fun quickcheck_params_cmd args = Context.theory_map (fold parse_test_param args);

fun gen_quickcheck args i state =

  state

  |> Proof.map_context_result (fn ctxt => fold parse_test_param_inst args ((NONE, []), ctxt))

  |> (fn ((generator, insts), state') => test_goal (generator, insts) i state'

  |> tap (fn (SOME x, _) => if expect (Proof.context_of state') = No_Counterexample then

               error ("quickcheck expected to find no counterexample but found one") else ()

           | (NONE, _) => if expect (Proof.context_of state') = Counterexample then

               error ("quickcheck expected to find a counterexample but did not find one") else ()))

fun quickcheck args i state = fst (gen_quickcheck args i state);

fun quickcheck_cmd args i state =

  gen_quickcheck args i (Toplevel.proof_of state)

  |> Pretty.writeln o pretty_counterex_and_reports (Toplevel.context_of state) false;

val parse_arg = Parse.name -- (Scan.optional (Parse.$$$ "=" |-- 

  (((Parse.name || Parse.float_number) >> single) || (Parse.$$$ "[" |-- Parse.list1 Parse.name --| Parse.$$$ "]"))) ["true"]);

val parse_args = Parse.$$$ "[" |-- Parse.list1 parse_arg --| Parse.$$$ "]"

  || Scan.succeed [];

val _ =

  Outer_Syntax.command "quickcheck_params" "set parameters for random testing" Keyword.thy_decl

    (parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));

val _ =

  Outer_Syntax.improper_command "quickcheck" "try to find counterexample for subgoal" Keyword.diag

    (parse_args -- Scan.optional Parse.nat 1

      >> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));

end;

val auto_quickcheck = Quickcheck.auto;