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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;
