(*  Title:      Tools/quickcheck.ML

    Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen

Generic counterexample search engine.

*)

signature QUICKCHECK =

sig

  val setup: theory -> theory

  (* configuration *)

  val auto: bool Unsynchronized.ref

  val timing : bool Unsynchronized.ref

  datatype report = Report of

    { iterations : int, raised_match_errors : int,

      satisfied_assms : int list, positive_concl_tests : int }

  datatype test_params = Test_Params of

  { size: int, iterations: int, default_type: typ list, no_assms: bool, report: bool, quiet : bool};

  val test_params_of: theory -> test_params 

  val add_generator:

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

      -> theory -> theory

  (* testing terms and proof states *)

  val gen_test_term: Proof.context -> bool -> bool -> string option -> int -> int -> term ->

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

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

    (string * term) list option

  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

  (setmp_CRITICAL auto true (fn () =>

    Preferences.bool_pref auto

      "auto-quickcheck"

      "Whether to 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}

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

datatype test_params = Test_Params of

  { size: int, iterations: int, default_type: typ list, no_assms: bool, report: bool, quiet : bool};

fun dest_test_params (Test_Params { size, iterations, default_type, no_assms, report, quiet }) =

  ((size, iterations), ((default_type, no_assms), (report, quiet)));

fun make_test_params ((size, iterations), ((default_type, no_assms), (report, quiet))) =

  Test_Params { size = size, iterations = iterations, default_type = default_type,

                no_assms = no_assms, report = report, quiet = quiet };

fun map_test_params f (Test_Params { size, iterations, default_type, no_assms, report, quiet }) =

  make_test_params (f ((size, iterations), ((default_type, no_assms), (report, quiet))));

fun merge_test_params (Test_Params { size = size1, iterations = iterations1, default_type = default_type1,

                                     no_assms = no_assms1, report = report1, quiet = quiet1 },

  Test_Params { size = size2, iterations = iterations2, default_type = default_type2,

                no_assms = no_assms2, report = report2, quiet = quiet2 }) =

  make_test_params ((Int.max (size1, size2), Int.max (iterations1, iterations2)),

    ((merge (op =) (default_type1, default_type2), no_assms1 orelse no_assms2),

    (report1 orelse report2, quiet1 orelse quiet2)));

structure Data = Theory_Data

(

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

    * test_params;

  val empty = ([], Test_Params

    { size = 10, iterations = 100, default_type = [], no_assms = false, report = false, quiet = false});

  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;

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 ProofContext.theory_of) ctxt) name

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

    | SOME generator => generator ctxt;

fun mk_testers ctxt report t =

  (map snd o fst o Data.get o ProofContext.theory_of) ctxt

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

fun mk_testers_strict ctxt report t =

  let

    val generators = ((map snd o fst o Data.get o ProofContext.theory_of) ctxt)

    val testers = map (fn generator => Exn.capture (generator ctxt report) 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 gen_test_term ctxt quiet report generator_name size i t =

  let

    val (names, t') = prep_test_term t;

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

      (fn () => (case generator_name

       of NONE => if quiet then mk_testers ctxt report t' else mk_testers_strict ctxt report t'

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

    fun iterate f 0 report = (NONE, report)

      | iterate f j report =

        let

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

          case iterate (fn () => tester (k - 1)) i empty_report

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

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

    fun with_size k reports = if k > size then (NONE, reports)

      else (if quiet then () else priority ("Test data size: " ^ string_of_int k);

        let

          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) = cpu_time "quickcheck execution"

      (fn () => apfst

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

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

  in

    (result, ([exec_time, comp_time], if report then SOME reports else NONE))

  end;

fun test_term ctxt quiet generator_name size i t =

  fst (gen_test_term ctxt quiet false generator_name size i t)

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 quiet report generator_name size iterations default_T no_assms insts i assms state =

  let

    val ctxt = 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 gi' = Logic.list_implies (if no_assms then [] else assms,

                                  subst_bounds (frees, strip gi))

    val inst_goals = map (fn T =>

      Term (monomorphic_term thy insts T gi |> Object_Logic.atomize_term thy)

        handle WELLSORTED s => Wellsorted_Error s) default_T

    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 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 (gen_test_term ctxt quiet report generator_name size iterations) [] correct_inst_goals end;

(* pretty printing *)

fun pretty_counterex ctxt NONE = Pretty.str "Quickcheck found no counterexample."

  | pretty_counterex ctxt (SOME cex) =

      Pretty.chunks (Pretty.str "Quickcheck 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 (cex, timing_and_reports) =

  Pretty.chunks (pretty_counterex ctxt 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 assms = map term_of (Assumption.all_assms_of ctxt);

      val Test_Params { size, iterations, default_type, no_assms, report, quiet } =

        (snd o Data.get o Proof.theory_of) state;

      val res =

        try (test_goal true false NONE size iterations default_type no_assms [] 1 assms) state;

    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 cex)])) state)

    end

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

(* 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 parse_test_param ctxt ("size", [arg]) =

      (apfst o apfst o K) (read_nat arg)

  | parse_test_param ctxt ("iterations", [arg]) =

      (apfst o apsnd o K) (read_nat arg)

  | parse_test_param ctxt ("default_type", arg) =

      (apsnd o apfst o apfst o K) (map (ProofContext.read_typ ctxt) arg)

  | parse_test_param ctxt ("no_assms", [arg]) =

      (apsnd o apfst o apsnd o K) (read_bool arg)

  | parse_test_param ctxt ("report", [arg]) =

      (apsnd o apsnd o apfst o K) (read_bool arg)

  | parse_test_param ctxt ("quiet", [arg]) =

      (apsnd o apsnd o apsnd o K) (read_bool arg)

  | parse_test_param ctxt (name, _) =

      error ("Unknown test parameter: " ^ name);

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

      (apsnd o apfst o K o SOME) arg

  | parse_test_param_inst ctxt (name, arg) =

      case try (ProofContext.read_typ ctxt) name

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

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

        | _ => (apfst o parse_test_param ctxt) (name, arg);

fun quickcheck_params_cmd args thy =

  let

    val ctxt = ProofContext.init_global thy;

    val f = fold (parse_test_param ctxt) args;

  in

    thy

    |> (Data.map o apsnd o map_test_params) f

  end;

fun gen_quickcheck args i state =

  let

    val thy = Proof.theory_of state;

    val ctxt = Proof.context_of state;

    val assms = map term_of (Assumption.all_assms_of ctxt);

    val default_params = (dest_test_params o snd o Data.get) thy;

    val f = fold (parse_test_param_inst ctxt) args;

    val (((size, iterations), ((default_type, no_assms), (report, quiet))), (generator_name, insts)) =

      f (default_params, (NONE, []));

  in

    test_goal quiet report generator_name size iterations default_type no_assms insts i assms state

  end;

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);

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

  ((Parse.name >> 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;