(*  Title:      Pure/Tools/quickcheck.ML

    Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen

Generic counterexample search engine.

*)

signature QUICKCHECK =

sig

  val test_term: Proof.context -> bool -> string option -> int -> int -> term -> (string * term) list option;

  val add_generator: string * (Proof.context -> term -> int -> term list option) -> theory -> theory

  val auto: bool ref

  val auto_time_limit: int ref

end;

structure Quickcheck : QUICKCHECK =

struct

(* quickcheck configuration -- default parameters, test generators *)

datatype test_params = Test_Params of

  { size: int, iterations: int, default_type: typ option };

fun dest_test_params (Test_Params { size, iterations, default_type}) =

  ((size, iterations), default_type);

fun mk_test_params ((size, iterations), default_type) =

  Test_Params { size = size, iterations = iterations, default_type = default_type };

fun map_test_params f (Test_Params { size, iterations, default_type}) =

  mk_test_params (f ((size, iterations), default_type));

fun merge_test_params (Test_Params {size = size1, iterations = iterations1, default_type = default_type1},

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

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

    case default_type1 of NONE => default_type2 | _ => default_type1);

structure Data = TheoryDataFun(

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

    * test_params;

  val empty = ([], Test_Params { size = 10, iterations = 100, default_type = NONE });

  val copy = I;

  val extend = I;

  fun merge pp ((generators1, params1), (generators2, params2)) =

    (AList.merge (op = : string * string -> bool) (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 t =

  (map snd o fst o Data.get o ProofContext.theory_of) 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 ProofContext.theory_of) ctxt)

    val testers = map (fn generator => Exn.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 = map dest_Free (OldTerm.term_frees t);

  in (map fst frees, list_abs_free (frees, t)) end

fun test_term ctxt quiet generator_name size i t =

  let

    val (names, t') = prep_test_term t;

    val testers = case generator_name

     of NONE => if quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'

      | SOME name => [mk_tester_select name ctxt t'];

    fun iterate f 0 = NONE

      | iterate f k = case f () handle Match => (if quiet then ()

             else warning "Exception Match raised during quickcheck"; NONE)

          of NONE => iterate f (k - 1) | SOME q => SOME q;

    fun with_testers k [] = NONE

      | with_testers k (tester :: testers) =

          case iterate (fn () => tester k) i

           of NONE => with_testers k testers

            | SOME q => SOME q;

    fun with_size k = if k > size then NONE

      else (if quiet then () else priority ("Test data size: " ^ string_of_int k);

        case with_testers k testers

         of NONE => with_size (k + 1) | SOME q => SOME q);

  in case with_size 1

   of NONE => NONE

    | SOME ts => SOME (names ~~ ts)

  end;

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 generator_name size iterations default_T 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 (_, (_, st)) = Proof.get_goal state;

    val (gi, frees) = Logic.goal_params (prop_of st) i;

    val gi' = Logic.list_implies (assms, subst_bounds (frees, strip gi))

      |> monomorphic_term thy insts default_T

      |> ObjectLogic.atomize_term thy;

  in test_term ctxt quiet generator_name size iterations gi' end;

fun pretty_counterex ctxt NONE = Pretty.str "No counterexamples found."

  | pretty_counterex ctxt (SOME cex) =

      Pretty.chunks (Pretty.str "Counterexample found:\n" ::

        map (fn (s, t) =>

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

(* automatic testing *)

val auto = ref false;

val auto_time_limit = ref 5000;

fun test_goal_auto int state =

  let

    val ctxt = Proof.context_of state;

    val assms = map term_of (Assumption.assms_of ctxt);

    val Test_Params { size, iterations, default_type } =

      (snd o Data.get o Proof.theory_of) state;

    fun test () =

      let

        val res = TimeLimit.timeLimit (Time.fromMilliseconds (!auto_time_limit))

          (try (test_goal true NONE size iterations default_type [] 1 assms)) state;

      in

        case res of

          NONE => state

        | SOME NONE => state

        | SOME cex => Proof.goal_message (fn () => Pretty.chunks [Pretty.str "",

            Pretty.mark Markup.hilite (pretty_counterex ctxt cex)]) state

      end handle TimeLimit.TimeOut => (warning "Auto quickcheck: timeout."; state);

  in

    if int andalso !auto andalso not (!Toplevel.quiet)

    then test ()

    else state

  end;

val _ = Context.>> (Specification.add_theorem_hook test_goal_auto);

(* Isar interfaces *)

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 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 K o SOME) (ProofContext.read_typ ctxt arg)

  | parse_test_param ctxt (name, _) =

      error ("Bad 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 thy;

    val f = fold (parse_test_param ctxt) args;

  in

    thy

    |> (Data.map o apsnd o map_test_params) f

  end;

fun quickcheck_cmd args i state =

  let

    val prf = Toplevel.proof_of state;

    val thy = Toplevel.theory_of state;

    val ctxt = Toplevel.context_of state;

    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), (generator_name, insts)) =

      f (default_params, (NONE, []));

    val counterex = test_goal false generator_name size iterations

      default_type insts i [] prf;

  in (Pretty.writeln o pretty_counterex ctxt) counterex end;

local structure P = OuterParse and K = OuterKeyword in

val parse_arg = P.name --| P.$$$ "=" -- P.name;

val parse_args = P.$$$ "[" |-- P.list1 parse_arg --| P.$$$ "]"

  || Scan.succeed [];

val _ = OuterSyntax.command "quickcheck_params" "set parameters for random testing" K.thy_decl

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

val _ = OuterSyntax.improper_command "quickcheck" "try to find counterexample for subgoal" K.diag

  (parse_args -- Scan.optional P.nat 1

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

end; (*local*)

end;

val auto_quickcheck = Quickcheck.auto;

val auto_quickcheck_time_limit = Quickcheck.auto_time_limit;