(*  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

   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

   { size: int, iterations: int, default_type: typ list, no_assms: bool,

     expect : expectation, report: bool, quiet : bool, timeout : real};

   val test_params_of : Proof.context -> test_params

   val report : Proof.context -> bool

   val map_test_params :

     ((int * int) * ((typ list * bool) * ((expectation * bool) * (bool * real)))

       -> (int * int) * ((typ list * bool) * ((expectation * bool) * (bool * real))))

     -> 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 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 *)

 datatype test_params = Test_Params of

   { size: int, iterations: int, default_type: typ list, no_assms: bool,

     expect : expectation, report: bool, quiet : bool, timeout : real};

 fun dest_test_params

     (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =

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

 fun make_test_params

     ((size, iterations), ((default_type, no_assms), ((expect, report), (quiet, timeout)))) =

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

     no_assms = no_assms, expect = expect, report = report, quiet = quiet, timeout = timeout };

 fun map_test_params' f

     (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =

   make_test_params

     (f ((size, iterations), ((default_type, no_assms), ((expect, report), (quiet, timeout)))));

 fun merge_test_params

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

     no_assms = no_assms1, expect = expect1, report = report1, quiet = quiet1, timeout = timeout1 },

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

     no_assms = no_assms2, expect = expect2, report = report2, quiet = quiet2, timeout = timeout2}) =

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

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

     ((merge_expectation (expect1, expect2), report1 orelse report2),

     (quiet1 orelse quiet2, Real.min (timeout1, timeout2)))));

 structure Data = Generic_Data

 (

   type T =

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

       * test_params;

   val empty = ([], Test_Params

     { size = 10, iterations = 100, default_type = [], no_assms = false,

       expect = No_Expectation, report = false, quiet = false, timeout = 30.0});

   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 size = fst o fst o dest_test_params o test_params_of

 val iterations = snd o fst o dest_test_params o test_params_of

 val default_type = fst o fst o snd o dest_test_params o test_params_of

 val no_assms = snd o fst o snd o dest_test_params o test_params_of

 val expect = fst o fst o snd o snd o dest_test_params o test_params_of

 val report = snd o fst o snd o snd o dest_test_params o test_params_of

 val quiet = fst o snd o snd o snd o dest_test_params o test_params_of

 val timeout = snd o snd o snd o snd o dest_test_params o test_params_of

 fun map_report f

   (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =

     make_test_params

       ((size, iterations), ((default_type, no_assms), ((expect, f report), (quiet, timeout))));

 fun map_quiet f

   (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =

     make_test_params

       ((size, iterations), ((default_type, no_assms), ((expect, report), (f quiet, timeout))));

 fun set_report report = Data.map (apsnd (map_report (K report)))

 fun set_quiet quiet = Data.map (apsnd (map_quiet (K quiet)))

 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 > size ctxt then (NONE, timings)

       else

          let

            val _ = if quiet ctxt 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 quiet ctxt 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

 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 quiet ctxt 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 quiet ctxt 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)) (iterations ctxt) 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 ctxt then (NONE, reports)

       else

        (if quiet ctxt 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 (timeout ctxt)) (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 report ctxt then SOME reports else NONE))

   end;

 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 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 no_assms lthy 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);

     val inst_goals = 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 quiet lthy 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;

 (* 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 (Context.proof_map (set_report false #> set_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)

 (* 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 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 ("expect", [arg]) =

       (apsnd o apsnd o apfst o apfst o K) (read_expectation arg)

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

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

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

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

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

       (apsnd o apsnd o apsnd o apsnd o K) (read_real 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

     |> (Context.theory_map o map_test_params) f

   end;

 fun gen_quickcheck args i state =

   let

     val ctxt = Proof.context_of state;

     val default_params = (dest_test_params o snd o Data.get o Context.Proof) ctxt;

     val f = fold (parse_test_param_inst ctxt) args;

     val (test_params, (generator_name, insts)) = f (default_params, (NONE, []));

   in

     state

     |> Proof.map_context (Context.proof_map (map_test_params (K test_params)))

     |> (fn state' => test_goal generator_name 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 ()))

   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) 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;