src/Tools/quickcheck.ML

improving function is_iterable in quickcheck

(*  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;