(*  Title:      Tools/quickcheck.ML

     Author:     Stefan Berghofer, Florian Haftmann, Lukas Bulwahn, TU Muenchen

 Generic counterexample search engine.

 *)

 signature QUICKCHECK =

 sig

   val quickcheckN: string

   val genuineN: string

   val noneN: string

   val unknownN: string

   val setup: theory -> theory

   (* configuration *)

   val auto: bool Unsynchronized.ref

   val batch_tester : string Config.T

   val size : int Config.T

   val iterations : int Config.T

   val depth : int Config.T

   val no_assms : bool Config.T

   val report : bool Config.T

   val timeout : real Config.T

   val timing : bool Config.T

   val genuine_only : bool Config.T

   val abort_potential : bool Config.T  

   val quiet : bool Config.T

   val verbose : bool Config.T

   val use_subtype : bool Config.T

   val allow_function_inversion : bool Config.T

   val finite_types : bool Config.T

   val finite_type_size : int Config.T

   val tag : string Config.T

   val locale : string Config.T

   val set_active_testers: string list -> Context.generic -> Context.generic

   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 default_type : Proof.context -> typ list

   datatype report = Report of

     { iterations : int, raised_match_errors : int,

       satisfied_assms : int list, positive_concl_tests : int }

   (* quickcheck's result *)

   datatype result =

     Result of

      {counterexample : (bool * (string * term) list) option,

       evaluation_terms : (term * term) list option,

       timings : (string * int) list,

       reports : (int * report) list}

   val empty_result : result

   val found_counterexample : result -> bool

   val add_timing : (string * int) -> result Unsynchronized.ref -> unit

   val add_response : string list -> term list -> (bool * term list) option -> result Unsynchronized.ref -> unit

   val add_report : int -> report option -> result Unsynchronized.ref -> unit

   val counterexample_of : result -> (bool * (string * term) list) option

   val timings_of : result -> (string * int) list

   (* registering testers & generators *) 

   type tester =

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

   val add_tester : string * (bool Config.T * tester) -> Context.generic -> Context.generic

   val add_batch_generator :

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

       -> Context.generic -> Context.generic

   val add_batch_validator :

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

       -> Context.generic -> Context.generic

   (* basic operations *)

   val message : Proof.context -> string -> unit

   val verbose_message : Proof.context -> string -> unit

   val limit : Time.time -> (bool * bool) -> (unit -> 'a) -> (unit -> 'a) -> unit -> 'a

   val pretty_counterex : Proof.context -> bool ->

     ((bool * (string * term) list) * (term * term) list) option -> Pretty.T

   (* testing terms and proof states *)

   val mk_batch_validator : Proof.context -> term list -> (int -> bool) list option

   val mk_batch_tester : Proof.context -> term list -> (int -> term list option) list option

   val active_testers : Proof.context -> tester list

   val test_terms :

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

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

 end;

 structure Quickcheck : QUICKCHECK =

 struct

 val quickcheckN = "quickcheck"

 val genuineN = "genuine"

 val noneN = "none"

 val unknownN = "unknown"

 (* preferences *)

 val auto = 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 }

 (* Quickcheck Result *)

 datatype result = Result of

   { counterexample : (bool * (string * term) list) option, evaluation_terms : (term * term) list option,

     timings : (string * int) list, reports : (int * report) list}

 val empty_result =

   Result {counterexample = NONE, evaluation_terms = NONE, timings = [], reports = []}

 fun counterexample_of (Result r) = #counterexample r

 fun found_counterexample (Result r) = is_some (#counterexample r)

 fun response_of (Result r) = case (#counterexample r, #evaluation_terms r) of

     (SOME ts, SOME evals) => SOME (ts, evals)

   | (NONE, NONE) => NONE

 fun timings_of (Result r) = #timings r

 fun set_response names eval_terms (SOME (genuine, ts)) (Result r) =

   let

     val (ts1, ts2) = chop (length names) ts

     val (eval_terms', _) = chop (length ts2) eval_terms

   in

     Result {counterexample = SOME (genuine, (names ~~ ts1)),

       evaluation_terms = SOME (eval_terms' ~~ ts2),

       timings = #timings r, reports = #reports r}

   end

   | set_response _ _ NONE result = result

 fun cons_timing timing (Result r) =

   Result {counterexample = #counterexample r, evaluation_terms = #evaluation_terms r,

     timings = cons timing (#timings r), reports = #reports r}

 fun cons_report size (SOME report) (Result r) =

   Result {counterexample = #counterexample r, evaluation_terms = #evaluation_terms r,

     timings = #timings r, reports = cons (size, report) (#reports r)}

   | cons_report _ NONE result = result

 fun add_timing timing result_ref =

   Unsynchronized.change result_ref (cons_timing timing)

 fun add_report size report result_ref =

   Unsynchronized.change result_ref (cons_report size report)

 fun add_response names eval_terms response result_ref =

   Unsynchronized.change result_ref (set_response names eval_terms response)

 (* 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 batch_tester = Attrib.setup_config_string @{binding quickcheck_batch_tester} (K "")

 val size = Attrib.setup_config_int @{binding quickcheck_size} (K 10)

 val iterations = Attrib.setup_config_int @{binding quickcheck_iterations} (K 100)

 val depth = Attrib.setup_config_int @{binding quickcheck_depth} (K 10)

 val no_assms = Attrib.setup_config_bool @{binding quickcheck_no_assms} (K false)

 val locale = Attrib.setup_config_string @{binding quickcheck_locale} (K "interpret expand")

 val report = Attrib.setup_config_bool @{binding quickcheck_report} (K true)

 val timing = Attrib.setup_config_bool @{binding quickcheck_timing} (K false)

 val timeout = Attrib.setup_config_real @{binding quickcheck_timeout} (K 30.0)

 val genuine_only = Attrib.setup_config_bool @{binding quickcheck_genuine_only} (K false)

 val abort_potential = Attrib.setup_config_bool @{binding quickcheck_abort_potential} (K false)

 val quiet = Attrib.setup_config_bool @{binding quickcheck_quiet} (K false)

 val verbose = Attrib.setup_config_bool @{binding quickcheck_verbose} (K false)

 val tag = Attrib.setup_config_string @{binding quickcheck_tag} (K "")

 val use_subtype = Attrib.setup_config_bool @{binding quickcheck_use_subtype} (K false)

 val allow_function_inversion =

   Attrib.setup_config_bool @{binding quickcheck_allow_function_inversion} (K false)

 val finite_types = Attrib.setup_config_bool @{binding quickcheck_finite_types} (K true)

 val finite_type_size = Attrib.setup_config_int @{binding quickcheck_finite_type_size} (K 3)

 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));

 type tester =

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

 structure Data = Generic_Data

 (

   type T =

     ((string * (bool Config.T * tester)) list

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

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

       * test_params;

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

   val extend = I;

   fun merge (((testers1, (batch_generators1, batch_validators1)), params1),

     ((testers2, (batch_generators2, batch_validators2)), params2)) : T =

     ((AList.merge (op =) (K true) (testers1, testers2),

       (AList.merge (op =) (K true) (batch_generators1, batch_generators2),

        AList.merge (op =) (K true) (batch_validators1, batch_validators2))),

       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_tester = Data.map o apfst o apfst o AList.update (op =);

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

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

 fun active_testers ctxt =

   let

     val testers = (map snd o fst o fst o Data.get o Context.Proof) ctxt

   in

     map snd (filter (fn (active, _) => Config.get ctxt active) testers)

   end

 fun set_active_testers [] gen_ctxt = gen_ctxt

   | set_active_testers testers gen_ctxt =

   let

     val registered_testers = (fst o fst o Data.get) gen_ctxt

   in

     fold (fn (name, (config, _)) => Config.put_generic config (member (op =) testers name))

       registered_testers gen_ctxt

   end

 (* generating tests *)

 fun gen_mk_tester lookup ctxt v =

   let

     val name = Config.get ctxt batch_tester

     val tester = case lookup ctxt name

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

       | SOME tester => tester ctxt;

   in

     if Config.get ctxt quiet then

       try tester v

     else

       let (* FIXME !?!? *)

         val tester = Exn.interruptible_capture tester v

       in case Exn.get_res tester of

           NONE => SOME (Exn.release tester)

         | SOME tester => SOME tester

       end

   end

 val mk_batch_tester =

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

 val mk_batch_validator =

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

 (* testing propositions *)

 type compile_generator =

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

 fun limit timeout (limit_time, is_interactive) f exc () =

   if limit_time then

       TimeLimit.timeLimit timeout f ()

     handle TimeLimit.TimeOut =>

       if is_interactive then exc () else raise TimeLimit.TimeOut

   else

     f ()

 fun message ctxt s = if Config.get ctxt quiet then () else Output.urgent_message s

 fun verbose_message ctxt s = if not (Config.get ctxt quiet) andalso Config.get ctxt verbose

   then Output.urgent_message s else ()

 fun test_terms ctxt (limit_time, is_interactive) insts goals =

   case active_testers ctxt of

     [] => error "No active testers for quickcheck"

   | testers =>

     limit (seconds (Config.get ctxt timeout)) (limit_time, is_interactive)

       (fn () => Par_List.get_some (fn tester =>

       tester ctxt (length testers > 1) insts goals |>

       (fn result => if exists found_counterexample result then SOME result else NONE)) testers)

       (fn () => (message ctxt "Quickcheck ran out of time"; NONE)) ();

 fun all_axioms_of ctxt t =

   let

     val intros = Locale.get_intros ctxt

     val unfolds = Locale.get_unfolds ctxt

     fun retrieve_prems thms t = 

        case filter (fn th => Term.could_unify (Thm.concl_of th, t)) thms of

          [] => NONE 

        | [th] =>

          let

            val (tyenv, tenv) =

              Pattern.match (Proof_Context.theory_of ctxt) (Thm.concl_of th, t) (Vartab.empty, Vartab.empty)

          in SOME (map (Envir.subst_term (tyenv, tenv)) (Thm.prems_of th)) end

     fun all t =

       case retrieve_prems intros t of

         NONE => retrieve_prems unfolds t

       | SOME ts => SOME (maps (fn t => the_default [t] (all t)) ts)

   in

     all t

   end

 fun locale_config_of s =

   let

     val cs = space_explode " " s

   in

     if forall (fn c => c = "expand" orelse c = "interpret") cs then cs

     else (warning ("Invalid quickcheck_locale setting: falling back to the default setting.");

       ["interpret", "expand"])

   end

 fun test_goal (time_limit, is_interactive) (insts, eval_terms) i state =

   let

     val lthy = Proof.context_of state;

     val thy = Proof.theory_of state;

     val _ = message lthy "Quickchecking..."

     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));

     fun axioms_of locale = case fst (Locale.specification_of thy locale) of

         NONE => []

       | SOME t => the_default [] (all_axioms_of lthy t)

    val config = locale_config_of (Config.get lthy locale) 

    val goals = case some_locale

      of NONE => [(proto_goal, eval_terms)]

       | SOME locale => fold (fn c =>

           if c = "expand" then cons (Logic.list_implies (axioms_of locale, proto_goal), eval_terms) else

           if c = "interpret" then

             append (map (fn (_, phi) => (Morphism.term phi proto_goal, map (Morphism.term phi) eval_terms))

           (Locale.registrations_of (Context.Theory thy) (*FIXME*) locale)) else I) config [];

     val _ = verbose_message lthy (Pretty.string_of

       (Pretty.big_list ("Checking goals: ") (map (Syntax.pretty_term lthy o fst) goals)))

   in

     test_terms lthy (time_limit, is_interactive) insts 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." ^ Config.get ctxt tag)

   | pretty_counterex ctxt auto (SOME ((genuine, cex), eval_terms)) =

       Pretty.chunks ((Pretty.str (tool_name auto ^ " found a " ^

         (if genuine then "counterexample:"

           else "potentially spurious counterexample due to underspecified functions:")

           ^ Config.get ctxt tag ^ "\n") ::

         map (fn (s, t) =>

           Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) (rev cex))

         @ (if null eval_terms then []

            else (Pretty.fbrk :: Pretty.str ("Evaluated terms:") ::

              map (fn (t, u) =>

                Pretty.block [Syntax.pretty_term ctxt t, Pretty.str " =", Pretty.brk 1,

                  Syntax.pretty_term ctxt u]) (rev eval_terms))));

 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_timings timings =

   Pretty.chunks (Pretty.fbrk :: Pretty.str "timings:" ::

     maps (fn (label, time) =>

       Pretty.str (label ^ ": " ^ string_of_int time ^ " ms") :: Pretty.brk 1 :: []) (rev timings))

 (* 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 name = AList.defined (op =) (fst (fst (Data.get genctxt))) name

 fun parse_tester name (testers, genctxt) =

   if valid_tester_name genctxt name then

     (insert (op =) name testers, genctxt)  

   else

     error ("Unknown tester: " ^ name)

 fun parse_test_param ("tester", args) = fold parse_tester args

   | parse_test_param ("size", [arg]) = apsnd (Config.put_generic size (read_nat arg))

   | parse_test_param ("iterations", [arg]) = apsnd (Config.put_generic iterations (read_nat arg))

   | parse_test_param ("depth", [arg]) = apsnd (Config.put_generic depth (read_nat arg))  

   | parse_test_param ("default_type", arg) = (fn (testers, gen_ctxt) =>

     (testers, map_test_params

       ((apfst o K) (map (Proof_Context.read_typ (Context.proof_of gen_ctxt)) arg)) gen_ctxt))

   | parse_test_param ("no_assms", [arg]) = apsnd (Config.put_generic no_assms (read_bool arg))

   | parse_test_param ("expect", [arg]) = apsnd (map_test_params ((apsnd o K) (read_expectation arg)))

   | parse_test_param ("report", [arg]) = apsnd (Config.put_generic report (read_bool arg))

   | parse_test_param ("genuine_only", [arg]) = apsnd (Config.put_generic genuine_only (read_bool arg))

   | parse_test_param ("abort_potential", [arg]) = apsnd (Config.put_generic abort_potential (read_bool arg))

   | parse_test_param ("quiet", [arg]) = apsnd (Config.put_generic quiet (read_bool arg))

   | parse_test_param ("verbose", [arg]) = apsnd (Config.put_generic verbose (read_bool arg))

   | parse_test_param ("tag", [arg]) = apsnd (Config.put_generic tag arg)

   | parse_test_param ("use_subtype", [arg]) = apsnd (Config.put_generic use_subtype (read_bool arg))  

   | parse_test_param ("timeout", [arg]) = apsnd (Config.put_generic timeout (read_real arg))

   | parse_test_param ("finite_types", [arg]) = apsnd (Config.put_generic finite_types (read_bool arg))

   | parse_test_param ("allow_function_inversion", [arg]) =

       apsnd (Config.put_generic allow_function_inversion (read_bool arg))

   | parse_test_param ("finite_type_size", [arg]) =

     apsnd (Config.put_generic finite_type_size (read_nat arg))

   | parse_test_param (name, _) = (fn (testers, genctxt) =>

     if valid_tester_name genctxt name then

       (insert (op =) name testers, genctxt)  

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

 fun proof_map_result f = apsnd Context.the_proof o f o Context.Proof;

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

       case try (Proof_Context.read_typ ctxt) name

        of SOME (TFree (v, _)) =>

          ((AList.update (op =) (v, Proof_Context.read_typ ctxt (the_single arg)) insts, eval_terms),

            (testers, ctxt))

         | NONE => (case name of

             "eval" => ((insts, eval_terms @ map (Syntax.read_term ctxt) arg), (testers, ctxt))

           | _ => ((insts, eval_terms),

             proof_map_result (fn gen_ctxt => parse_test_param (name, arg) (testers, gen_ctxt)) ctxt));

 fun quickcheck_params_cmd args = Context.theory_map

   (fn gen_ctxt => uncurry set_active_testers (fold parse_test_param args ([], gen_ctxt)));

 fun check_expectation state results =

   (if is_some results andalso expect (Proof.context_of state) = No_Counterexample

   then

     error ("quickcheck expected to find no counterexample but found one")

   else

     (if is_none results andalso expect (Proof.context_of state) = Counterexample

     then

       error ("quickcheck expected to find a counterexample but did not find one")

     else ()))

 fun gen_quickcheck args i state =

   state

   |> Proof.map_context_result (fn ctxt =>

     apsnd (fn (testers, ctxt) => Context.proof_map (set_active_testers testers) ctxt)

       (fold parse_test_param_inst args (([], []), ([], ctxt))))

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

   |> tap (check_expectation state') |> rpair state')

 fun quickcheck args i state =

   Option.map (the o get_first counterexample_of) (fst (gen_quickcheck args i state))

 fun quickcheck_cmd args i state =

   gen_quickcheck args i (Toplevel.proof_of state)

   |> apfst (Option.map (the o get_first response_of))

   |> (fn (r, state) => Output.urgent_message (Pretty.string_of

        (pretty_counterex (Proof.context_of state) false r)));

 val parse_arg =

   Parse.name --

     (Scan.optional (@{keyword "="} |--

       (((Parse.name || Parse.float_number) >> single) ||

         (@{keyword "["} |-- Parse.list1 Parse.name --| @{keyword "]"}))) ["true"]);

 val parse_args =

   @{keyword "["} |-- Parse.list1 parse_arg --| @{keyword "]"} || Scan.succeed [];

 val _ =

   Outer_Syntax.command @{command_spec "quickcheck_params"} "set parameters for random testing"

     (parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));

 val _ =

   Outer_Syntax.improper_command @{command_spec "quickcheck"}

     "try to find counterexample for subgoal"

     (parse_args -- Scan.optional Parse.nat 1

       >> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));

 (* automatic testing *)

 fun try_quickcheck auto state =

   let

     val ctxt = Proof.context_of state;

     val i = 1;

     val res =

       state

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

       |> try (test_goal (false, false) ([], []) i);

   in

     case res of

       NONE => (unknownN, state)

     | SOME results =>

         let

           val msg = pretty_counterex ctxt auto (Option.map (the o get_first response_of) results)

         in

           if is_some results then

             (genuineN,

              state

              |> (if auto then

                    Proof.goal_message (K (Pretty.chunks [Pretty.str "",

                        Pretty.mark Isabelle_Markup.hilite msg]))

                  else

                    tap (fn _ => Output.urgent_message (Pretty.string_of msg))))

           else

             (noneN, state)

         end

   end

   |> `(fn (outcome_code, _) => outcome_code = genuineN)

 val setup = Try.register_tool (quickcheckN, (20, auto, try_quickcheck))

 end;

 val auto_quickcheck = Quickcheck.auto;