(*  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;