src/Tools/quickcheck.ML
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(*  Title:      Pure/Tools/quickcheck.ML
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    Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen
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Generic counterexample search engine.
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*)
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signature QUICKCHECK =
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sig
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  val test_term: Proof.context -> bool -> string option -> int -> int -> term -> (string * term) list option;
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  val add_generator: string * (Proof.context -> term -> int -> term list option) -> theory -> theory
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  val auto: bool ref
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  val auto_time_limit: int ref
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end;
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structure Quickcheck : QUICKCHECK =
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struct
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(* quickcheck configuration -- default parameters, test generators *)
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datatype test_params = Test_Params of
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  { size: int, iterations: int, default_type: typ option };
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fun dest_test_params (Test_Params { size, iterations, default_type}) =
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  ((size, iterations), default_type);
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fun mk_test_params ((size, iterations), default_type) =
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  Test_Params { size = size, iterations = iterations, default_type = default_type };
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fun map_test_params f (Test_Params { size, iterations, default_type}) =
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  mk_test_params (f ((size, iterations), default_type));
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fun merge_test_params (Test_Params {size = size1, iterations = iterations1, default_type = default_type1},
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  Test_Params {size = size2, iterations = iterations2, default_type = default_type2}) =
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  mk_test_params ((Int.max (size1, size2), Int.max (iterations1, iterations2)),
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    case default_type1 of NONE => default_type2 | _ => default_type1);
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structure Data = TheoryDataFun(
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  type T = (string * (Proof.context -> term -> int -> term list option)) list
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    * test_params;
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  val empty = ([], Test_Params { size = 10, iterations = 100, default_type = NONE });
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  val copy = I;
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  val extend = I;
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  fun merge pp ((generators1, params1), (generators2, params2)) =
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    (AList.merge (op = : string * string -> bool) (K true) (generators1, generators2),
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      merge_test_params (params1, params2));
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)
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val add_generator = Data.map o apfst o AList.update (op =);
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(* generating tests *)
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fun mk_tester_select name ctxt =
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  case AList.lookup (op =) ((fst o Data.get o ProofContext.theory_of) ctxt) name
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   of NONE => error ("No such quickcheck generator: " ^ name)
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    | SOME generator => generator ctxt;
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fun mk_testers ctxt t =
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  (map snd o fst o Data.get o ProofContext.theory_of) ctxt
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  |> map_filter (fn generator => try (generator ctxt) t);
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fun mk_testers_strict ctxt t =
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  let
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    val generators = ((map snd o fst o Data.get o ProofContext.theory_of) ctxt)
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    val testers = map (fn generator => Exn.capture (generator ctxt) t) generators;
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  in if forall (is_none o Exn.get_result) testers
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    then [(Exn.release o snd o split_last) testers]
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    else map_filter Exn.get_result testers
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  end;
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(* testing propositions *)
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fun prep_test_term t =
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  let
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    val _ = (null (Term.add_tvars t []) andalso null (Term.add_tfrees t [])) orelse
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      error "Term to be tested contains type variables";
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    val _ = null (Term.add_vars t []) orelse
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      error "Term to be tested contains schematic variables";
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    val frees = map dest_Free (OldTerm.term_frees t);
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  in (map fst frees, list_abs_free (frees, t)) end
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fun test_term ctxt quiet generator_name size i t =
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  let
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    val (names, t') = prep_test_term t;
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    val testers = case generator_name
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     of NONE => if quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'
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      | SOME name => [mk_tester_select name ctxt t'];
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    fun iterate f 0 = NONE
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      | iterate f k = case f () handle Match => (if quiet then ()
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             else warning "Exception Match raised during quickcheck"; NONE)
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          of NONE => iterate f (k - 1) | SOME q => SOME q;
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    fun with_testers k [] = NONE
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      | with_testers k (tester :: testers) =
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          case iterate (fn () => tester k) i
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           of NONE => with_testers k testers
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            | SOME q => SOME q;
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    fun with_size k = if k > size then NONE
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      else (if quiet then () else priority ("Test data size: " ^ string_of_int k);
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        case with_testers k testers
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         of NONE => with_size (k + 1) | SOME q => SOME q);
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  in case with_size 1
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   of NONE => NONE
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    | SOME ts => SOME (names ~~ ts)
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  end;
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fun monomorphic_term thy insts default_T = 
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  let
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    fun subst (T as TFree (v, S)) =
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          let
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            val T' = AList.lookup (op =) insts v
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              |> the_default (the_default T default_T)
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          in if Sign.of_sort thy (T, S) then T'
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            else error ("Type " ^ Syntax.string_of_typ_global thy T ^
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              " to be substituted for variable " ^
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              Syntax.string_of_typ_global thy T ^ "\ndoes not have sort " ^
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              Syntax.string_of_sort_global thy S)
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          end
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      | subst T = T;
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  in (map_types o map_atyps) subst end;
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fun test_goal quiet generator_name size iterations default_T insts i assms state =
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  let
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    val ctxt = Proof.context_of state;
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    val thy = Proof.theory_of state;
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    fun strip (Const ("all", _) $ Abs (_, _, t)) = strip t
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      | strip t = t;
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    val (_, (_, st)) = Proof.get_goal state;
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    val (gi, frees) = Logic.goal_params (prop_of st) i;
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    val gi' = Logic.list_implies (assms, subst_bounds (frees, strip gi))
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      |> monomorphic_term thy insts default_T
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      |> ObjectLogic.atomize_term thy;
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  in test_term ctxt quiet generator_name size iterations gi' end;
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fun pretty_counterex ctxt NONE = Pretty.str "No counterexamples found."
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  | pretty_counterex ctxt (SOME cex) =
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      Pretty.chunks (Pretty.str "Counterexample found:\n" ::
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        map (fn (s, t) =>
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          Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) cex);
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(* automatic testing *)
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val auto = ref false;
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val auto_time_limit = ref 5000;
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fun test_goal_auto int state =
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  let
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    val ctxt = Proof.context_of state;
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    val assms = map term_of (Assumption.assms_of ctxt);
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    val Test_Params { size, iterations, default_type } =
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      (snd o Data.get o Proof.theory_of) state;
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    fun test () =
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      let
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        val res = TimeLimit.timeLimit (Time.fromMilliseconds (!auto_time_limit))
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          (try (test_goal true NONE size iterations default_type [] 1 assms)) state;
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      in
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        case res of
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          NONE => state
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        | SOME NONE => state
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        | SOME cex => Proof.goal_message (fn () => Pretty.chunks [Pretty.str "",
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            Pretty.mark Markup.hilite (pretty_counterex ctxt cex)]) state
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      end handle TimeLimit.TimeOut => (warning "Auto quickcheck: timeout."; state);
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  in
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    if int andalso !auto andalso not (!Toplevel.quiet)
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    then test ()
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    else state
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  end;
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val _ = Context.>> (Specification.add_theorem_hook test_goal_auto);
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(* Isar interfaces *)
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fun read_nat s = case (Library.read_int o Symbol.explode) s
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 of (k, []) => if k >= 0 then k
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      else error ("Not a natural number: " ^ s)
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  | (_, _ :: _) => error ("Not a natural number: " ^ s);
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fun parse_test_param ctxt ("size", arg) =
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      (apfst o apfst o K) (read_nat arg)
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  | parse_test_param ctxt ("iterations", arg) =
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      (apfst o apsnd o K) (read_nat arg)
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  | parse_test_param ctxt ("default_type", arg) =
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      (apsnd o K o SOME) (ProofContext.read_typ ctxt arg)
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  | parse_test_param ctxt (name, _) =
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      error ("Bad test parameter: " ^ name);
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fun parse_test_param_inst ctxt ("generator", arg) =
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      (apsnd o apfst o K o SOME) arg
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  | parse_test_param_inst ctxt (name, arg) =
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      case try (ProofContext.read_typ ctxt) name
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       of SOME (TFree (v, _)) => (apsnd o apsnd o AList.update (op =))
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              (v, ProofContext.read_typ ctxt arg)
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        | _ => (apfst o parse_test_param ctxt) (name, arg);
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fun quickcheck_params_cmd args thy =
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  let
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    val ctxt = ProofContext.init thy;
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    val f = fold (parse_test_param ctxt) args;
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  in
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    thy
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    |> (Data.map o apsnd o map_test_params) f
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  end;
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fun quickcheck_cmd args i state =
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  let
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    val prf = Toplevel.proof_of state;
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    val thy = Toplevel.theory_of state;
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    val ctxt = Toplevel.context_of state;
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    val default_params = (dest_test_params o snd o Data.get) thy;
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    val f = fold (parse_test_param_inst ctxt) args;
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    val (((size, iterations), default_type), (generator_name, insts)) =
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      f (default_params, (NONE, []));
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    val counterex = test_goal false generator_name size iterations
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      default_type insts i [] prf;
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  in (Pretty.writeln o pretty_counterex ctxt) counterex end;
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local structure P = OuterParse and K = OuterKeyword in
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val parse_arg = P.name --| P.$$$ "=" -- P.name;
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val parse_args = P.$$$ "[" |-- P.list1 parse_arg --| P.$$$ "]"
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  || Scan.succeed [];
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val _ = OuterSyntax.command "quickcheck_params" "set parameters for random testing" K.thy_decl
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  (parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));
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val _ = OuterSyntax.improper_command "quickcheck" "try to find counterexample for subgoal" K.diag
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  (parse_args -- Scan.optional P.nat 1
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    >> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));
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end; (*local*)
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end;
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val auto_quickcheck = Quickcheck.auto;
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val auto_quickcheck_time_limit = Quickcheck.auto_time_limit;