(*  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 tester : string Config.T

  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 * report option)

      -> Context.generic -> Context.generic

  val add_batch_generator:

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

      -> Context.generic -> Context.generic

  (* testing terms and proof states *)

  val test_term: Proof.context -> bool * bool -> term ->

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

  val test_goal_terms:

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

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

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

  (* testing a batch of terms *)

  val test_terms: Proof.context -> term list -> (string * term) list option 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 report = Report of

  { iterations : int, raised_match_errors : int,

    satisfied_assms : int list, positive_concl_tests : int }

(* 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 (tester, setup_tester) = Attrib.config_string "quickcheck_tester" (K "")

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_tester #> 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 * report option)) list

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

      * test_params;

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

  val extend = I;

  fun merge (((generators1, batch_generators1), params1), ((generators2, batch_generators2), params2)) : T =

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

    AList.merge (op =) (K true) (batch_generators1, batch_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 apfst o AList.update (op =);

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

(* generating tests *)

fun gen_mk_tester lookup ctxt v =

  let

    val name = Config.get ctxt tester

    val tester = case lookup ctxt name

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

      | SOME tester => tester ctxt;

  in

    if Config.get ctxt quiet then

      try tester v

    else

      let

        val tester = Exn.interruptible_capture tester v

      in case Exn.get_result tester of

          NONE => SOME (Exn.release tester)

        | SOME tester => SOME tester

      end

  end

val mk_tester = gen_mk_tester (fn ctxt =>

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

val mk_batch_tester = gen_mk_tester (fn ctxt => AList.lookup (op =) ((snd o fst o Data.get o Context.Proof) ctxt))

(* 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 (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 limit ctxt (limit_time, is_interactive) f exc () =

  if limit_time then

      TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f ()

    handle TimeLimit.TimeOut =>

      if is_interactive then exc () else raise TimeLimit.TimeOut

  else

    f ()

fun test_term ctxt (limit_time, is_interactive) t =

  let

    val (names, t') = apfst (map fst) (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 (test_fun, comp_time) = cpu_time "quickcheck compilation" (fn () => mk_tester ctxt t');

    fun with_size test_fun k reports =

      if k > Config.get ctxt size then

        (NONE, reports)

      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, new_report), timing) =

            cpu_time ("size " ^ string_of_int k) (fn () => test_fun (k - 1))

          val reports = case new_report of NONE => reports | SOME rep => (k, rep) :: reports

        in

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

        end;

  in

    case test_fun of NONE => (NONE, ([comp_time], NONE))

      | SOME test_fun =>

        limit ctxt (limit_time, is_interactive) (fn () =>

          let

            val ((result, reports), exec_time) =

              cpu_time "quickcheck execution" (fn () => with_size test_fun 1 [])

          in

            (case result of NONE => NONE | SOME ts => SOME (names ~~ ts),

              ([exec_time, comp_time],

               if Config.get ctxt report andalso not (null reports) then SOME reports else NONE))

          end) (fn () => error (excipit "ran out of time")) ()

  end;

fun test_terms ctxt ts =

  let

    val (namess, ts') = split_list (map (fn t => apfst (map fst) (prep_test_term t)) ts)

    val test_funs = mk_batch_tester ctxt ts'

    fun with_size tester k =

      if k > Config.get ctxt size then NONE

      else case tester k of SOME ts => SOME ts | NONE => with_size tester (k + 1)

    val results =

      Option.map (map (fn test_fun => TimeLimit.timeLimit (seconds (Config.get ctxt timeout))

            (fn () => with_size test_fun 1)  ()

           handle TimeLimit.TimeOut => NONE)) test_funs

  in

    Option.map (map2 (fn names => Option.map (fn ts => names ~~ ts)) namess) results

  end

(* FIXME: this function shows that many assumptions are made upon the generation *)

(* In the end there is probably no generic quickcheck interface left... *)

fun test_term_with_increasing_cardinality ctxt (limit_time, is_interactive) ts =

  let

    val thy = ProofContext.theory_of ctxt

    val (freess, ts') = split_list (map prep_test_term ts)

    val Ts = map snd (hd freess)

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

      (fn () => map (mk_tester ctxt) ts')

    fun test_card_size (card, size) =

      (* FIXME: why decrement size by one? *)

      case fst (the (nth test_funs (card - 1)) (size - 1)) of

        SOME ts => SOME (map fst (nth freess (card - 1)) ~~ ts)

      | NONE => NONE

    val enumeration_card_size =

      if forall (fn T => Sign.of_sort thy (T,  ["Enum.enum"])) Ts then

        (* size does not matter *)

        map (rpair 0) (1 upto (length ts))

      else

        (* size does matter *)

        map_product pair (1 upto (length ts)) (1 upto (Config.get ctxt size))

        |> sort (fn ((c1, s1), (c2, s2)) => int_ord ((c1 + s1), (c2 + s2)))

    in

      if (forall is_none test_funs) then

        (NONE, ([comp_time], NONE))

      else if (forall is_some test_funs) then

        limit ctxt (limit_time, is_interactive) (fn () =>

          (get_first test_card_size enumeration_card_size, ([comp_time], NONE)))

          (fn () => error "Quickcheck ran out of time") ()

      else

        error "Unexpectedly, testers of some cardinalities are executable but others are not"

    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 (limit_time, is_interactive) insts check_goals =

  let

    val thy = ProofContext.theory_of lthy

    val default_insts =

      if Config.get lthy finite_types then (get_finite_types lthy) else (default_type lthy)

    val inst_goals =

      map (fn check_goal =>

        if not (null (Term.add_tfree_names check_goal [])) then

          map (fn T =>

            (pair (SOME T) o Term o Object_Logic.atomize_term thy o monomorphic_term thy insts T)

              check_goal

              handle WELLSORTED s => (SOME T, Wellsorted_Error s)) default_insts

        else

          [(NONE, Term (Object_Logic.atomize_term thy check_goal))]) check_goals

    val error_msg =

      cat_lines

        (maps (map_filter (fn (_, Term t) => NONE | (_, Wellsorted_Error s) => SOME s)) inst_goals)

    fun is_wellsorted_term (T, Term t) = SOME (T, t)

      | is_wellsorted_term (_, Wellsorted_Error s) = NONE

    val correct_inst_goals =

      case map (map_filter is_wellsorted_term) 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

    fun test_term' goal =

      case goal of

        [(NONE, t)] => test_term lthy (limit_time, is_interactive) t

      | ts => test_term_with_increasing_cardinality lthy (limit_time, is_interactive) (map snd ts)

  in

    if Config.get lthy finite_types then

      collect_results test_term' [] correct_inst_goals

    else

      collect_results (test_term lthy (limit_time, is_interactive)) [] (maps (map snd) correct_inst_goals)

  end;

fun test_goal (time_limit, is_interactive) 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 (time_limit, is_interactive) 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]) (rev 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 ctxt (SOME reports) =

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

    maps (fn (size, report) =>

      Pretty.str ("size " ^ string_of_int size ^ ":") :: pretty_report report @ [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 =

  let

    val ctxt = Proof.context_of state;

    val res =

      state

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

      |> try (test_goal (false, false) [] 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 (auto, 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 valid_tester_name genctxt = AList.defined (op =) (fst (fst (Data.get genctxt)))

fun parse_tester name genctxt =

  if valid_tester_name genctxt name then

    Config.put_generic tester name genctxt

  else

    error ("Unknown tester: " ^ name)

fun parse_test_param ("tester", [arg]) = parse_tester arg

  | 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, _) = fn genctxt =>

    if valid_tester_name genctxt name then

      Config.put_generic tester name genctxt

    else error ("Unknown tester or test parameter: " ^ name);

fun parse_test_param_inst (name, arg) (insts, ctxt) =

      case try (ProofContext.read_typ ctxt) name

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

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

        | _ => (apsnd o Context.proof_map o parse_test_param) (name, arg) (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 ([], ctxt))

  |> (fn (insts, state') => test_goal (true, true) 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;