(*  Title:      Tools/quickcheck.ML

     Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen

 Generic counterexample search engine.

 *)

 signature QUICKCHECK =

 sig

   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 }

   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 add_generator:

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

       -> theory -> theory

   val setup: theory -> theory

   val quickcheck: (string * string) 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 option, 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)),

     ((case default_type1 of NONE => default_type2 | _ => default_type1, 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 = NONE, 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 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)

 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 (the_default T default_T)

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

             else error ("Type " ^ Syntax.string_of_typ_global thy T ^

               " to be substituted for variable " ^

               Syntax.string_of_typ_global thy T ^ "\ndoes not have sort " ^

               Syntax.string_of_sort_global thy S)

           end

       | subst T = T;

   in (map_types o map_atyps) subst end;

 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))

       |> monomorphic_term thy insts default_T

       |> Object_Logic.atomize_term thy;

   in gen_test_term ctxt quiet report generator_name size iterations gi' end;

 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, reports)) =

   Pretty.chunks [pretty_counterex ctxt cex, pretty_reports ctxt 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 o SOME) (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 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) "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;