(* Title: Tools/quickcheck.ML
Author: Stefan Berghofer, Florian Haftmann, TU Muenchen
Generic counterexample search engine.
*)
signature QUICKCHECK =
sig
val setup: theory -> theory
(* configuration *)
val auto: bool Unsynchronized.ref
val timing : bool Unsynchronized.ref
datatype report = Report of
{ iterations : int, raised_match_errors : int,
satisfied_assms : int list, positive_concl_tests : int }
datatype expectation = No_Expectation | No_Counterexample | Counterexample;
datatype test_params = Test_Params of
{ size: int, iterations: int, default_type: typ list, no_assms: bool,
expect : expectation, report: bool, quiet : bool};
val test_params_of: theory -> test_params
val add_generator:
string * (Proof.context -> bool -> term -> int -> term list option * (bool list * bool))
-> theory -> theory
(* testing terms and proof states *)
val gen_test_term: Proof.context -> bool -> bool -> string option -> int -> int -> term ->
(string * term) list option * ((string * int) list * ((int * report list) list) option)
val test_term: Proof.context -> bool -> string option -> int -> int -> term ->
(string * term) list option
val quickcheck: (string * string list) list -> int -> Proof.state -> (string * term) list option
end;
structure Quickcheck : QUICKCHECK =
struct
(* preferences *)
val auto = Unsynchronized.ref false;
val timing = Unsynchronized.ref false;
val _ =
ProofGeneralPgip.add_preference Preferences.category_tracing
(setmp_CRITICAL auto true (fn () =>
Preferences.bool_pref auto
"auto-quickcheck"
"Whether to run Quickcheck automatically.") ());
(* quickcheck report *)
datatype single_report = Run of bool list * bool | MatchExc
datatype report = Report of
{ iterations : int, raised_match_errors : int,
satisfied_assms : int list, positive_concl_tests : int }
fun collect_single_report single_report
(Report {iterations = iterations, raised_match_errors = raised_match_errors,
satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =
case single_report
of MatchExc =>
Report {iterations = iterations + 1, raised_match_errors = raised_match_errors + 1,
satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}
| Run (assms, concl) =>
Report {iterations = iterations + 1, raised_match_errors = raised_match_errors,
satisfied_assms =
map2 (fn b => fn s => if b then s + 1 else s) assms
(if null satisfied_assms then replicate (length assms) 0 else satisfied_assms),
positive_concl_tests = if concl then positive_concl_tests + 1 else positive_concl_tests}
(* 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 *)
datatype test_params = Test_Params of
{ size: int, iterations: int, default_type: typ list, no_assms: bool,
expect : expectation, report: bool, quiet : bool};
fun dest_test_params (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet }) =
((size, iterations), ((default_type, no_assms), ((expect, report), quiet)));
fun make_test_params ((size, iterations), ((default_type, no_assms), ((expect, report), quiet))) =
Test_Params { size = size, iterations = iterations, default_type = default_type,
no_assms = no_assms, expect = expect, report = report, quiet = quiet };
fun map_test_params f (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet }) =
make_test_params (f ((size, iterations), ((default_type, no_assms), ((expect, report), quiet))));
fun merge_test_params (Test_Params { size = size1, iterations = iterations1, default_type = default_type1,
no_assms = no_assms1, expect = expect1, report = report1, quiet = quiet1 },
Test_Params { size = size2, iterations = iterations2, default_type = default_type2,
no_assms = no_assms2, expect = expect2, report = report2, quiet = quiet2 }) =
make_test_params ((Int.max (size1, size2), Int.max (iterations1, iterations2)),
((merge (op =) (default_type1, default_type2), no_assms1 orelse no_assms2),
((merge_expectation (expect1, expect2), report1 orelse report2), quiet1 orelse quiet2)));
structure Data = Theory_Data
(
type T = (string * (Proof.context -> bool -> term -> int -> term list option * (bool list * bool))) list
* test_params;
val empty = ([], Test_Params
{ size = 10, iterations = 100, default_type = [], no_assms = false,
expect = No_Expectation, report = false, quiet = false});
val extend = I;
fun merge ((generators1, params1), (generators2, params2)) : T =
(AList.merge (op =) (K true) (generators1, generators2),
merge_test_params (params1, params2));
);
val test_params_of = snd o Data.get;
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 report t =
(map snd o fst o Data.get o ProofContext.theory_of) ctxt
|> map_filter (fn generator => try (generator ctxt report) t);
fun mk_testers_strict ctxt report 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 report) 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 = Term.add_frees t [];
in (map fst frees, list_abs_free (frees, t)) end
fun cpu_time description f =
let
val start = start_timing ()
val result = Exn.capture f ()
val time = Time.toMilliseconds (#cpu (end_timing start))
in (Exn.release result, (description, time)) end
fun gen_test_term ctxt quiet report generator_name size i t =
let
val (names, t') = prep_test_term t;
val (testers, comp_time) = cpu_time "quickcheck compilation"
(fn () => (case generator_name
of NONE => if quiet then mk_testers ctxt report t' else mk_testers_strict ctxt report t'
| SOME name => [mk_tester_select name ctxt report t']));
fun iterate f 0 report = (NONE, report)
| iterate f j report =
let
val (test_result, single_report) = apsnd Run (f ()) handle Match => (if quiet then ()
else warning "Exception Match raised during quickcheck"; (NONE, MatchExc))
val report = collect_single_report single_report report
in
case test_result of NONE => iterate f (j - 1) report | SOME q => (SOME q, report)
end
val empty_report = Report { iterations = 0, raised_match_errors = 0,
satisfied_assms = [], positive_concl_tests = 0 }
fun with_testers k [] = (NONE, [])
| with_testers k (tester :: testers) =
case iterate (fn () => tester (k - 1)) i empty_report
of (NONE, report) => apsnd (cons report) (with_testers k testers)
| (SOME q, report) => (SOME q, [report]);
fun with_size k reports = if k > size then (NONE, reports)
else (if quiet then () else priority ("Test data size: " ^ string_of_int k);
let
val (result, new_report) = with_testers k testers
val reports = ((k, new_report) :: reports)
in case result of NONE => with_size (k + 1) reports | SOME q => (SOME q, reports) end);
val ((result, reports), exec_time) = cpu_time "quickcheck execution"
(fn () => apfst
(fn result => case result of NONE => NONE
| SOME ts => SOME (names ~~ ts)) (with_size 1 []))
in
(result, ([exec_time, comp_time], if report then SOME reports else NONE))
end;
fun test_term ctxt quiet generator_name size i t =
fst (gen_test_term ctxt quiet false generator_name size i t)
exception WELLSORTED of string
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 default_T
in if Sign.of_sort thy (T', S) then T'
else raise (WELLSORTED ("For instantiation with default_type " ^ Syntax.string_of_typ_global thy default_T ^
":\n" ^ Syntax.string_of_typ_global thy T' ^
" to be substituted for variable " ^
Syntax.string_of_typ_global thy T ^ " does not have sort " ^
Syntax.string_of_sort_global thy S))
end
| subst T = T;
in (map_types o map_atyps) subst end;
datatype wellsorted_error = Wellsorted_Error of string | Term of term
fun test_goal quiet report generator_name size iterations default_Ts no_assms insts i state =
let
val lthy = Proof.context_of state;
val thy = Proof.theory_of state;
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 (#target o Named_Target.peek) lthy
of "" => NONE
| locale => SOME locale;
val assms = if 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));
val check_goals = case some_locale
of NONE => [proto_goal]
| SOME locale => map (fn (_, phi) => Morphism.term phi proto_goal) (Locale.registrations_of (Context.Theory thy) (*FIXME*) locale);
val inst_goals = maps (fn check_goal => map (fn T =>
Term ((Object_Logic.atomize_term thy o monomorphic_term thy insts T) check_goal)
handle WELLSORTED s => Wellsorted_Error s) default_Ts) check_goals
val error_msg = cat_lines (map_filter (fn Term t => NONE | Wellsorted_Error s => SOME s) inst_goals)
val correct_inst_goals =
case map_filter (fn Term t => SOME t | Wellsorted_Error s => NONE) inst_goals of
[] => error error_msg
| xs => xs
val _ = if quiet then () else warning error_msg
fun collect_results f reports [] = (NONE, rev reports)
| collect_results f reports (t :: ts) =
case f t of
(SOME res, report) => (SOME res, rev (report :: reports))
| (NONE, report) => collect_results f (report :: reports) ts
in collect_results (gen_test_term lthy quiet report generator_name size iterations) [] correct_inst_goals end;
(* pretty printing *)
fun pretty_counterex ctxt NONE = Pretty.str "Quickcheck found no counterexample."
| pretty_counterex ctxt (SOME cex) =
Pretty.chunks (Pretty.str "Quickcheck found a counterexample:\n" ::
map (fn (s, t) =>
Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) cex);
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_reports' [report] = [Pretty.chunks (pretty_report report)]
| pretty_reports' reports =
map_index (fn (i, report) =>
Pretty.chunks (Pretty.str (string_of_int (i + 1) ^ ". generator:\n") :: pretty_report report))
reports
fun pretty_reports ctxt (SOME reports) =
Pretty.chunks (Pretty.str "Quickcheck report:" ::
maps (fn (size, reports) =>
Pretty.str ("size " ^ string_of_int size ^ ":") :: pretty_reports' reports @ [Pretty.brk 1])
(rev reports))
| pretty_reports ctxt NONE = Pretty.str ""
fun pretty_counterex_and_reports ctxt (cex, timing_and_reports) =
Pretty.chunks (pretty_counterex ctxt cex :: map (pretty_reports ctxt) (map snd timing_and_reports))
(* automatic testing *)
fun auto_quickcheck state =
if not (!auto) then
(false, state)
else
let
val ctxt = Proof.context_of state;
val Test_Params {size, iterations, default_type, no_assms, ...} =
(snd o Data.get o Proof.theory_of) state;
val res =
try (test_goal true false NONE size iterations default_type no_assms [] 1) state;
in
case res of
NONE => (false, state)
| SOME (NONE, report) => (false, state)
| SOME (cex, report) => (true, Proof.goal_message (K (Pretty.chunks [Pretty.str "",
Pretty.mark Markup.hilite (pretty_counterex ctxt cex)])) state)
end
val setup = Auto_Counterexample.register_tool ("quickcheck", auto_quickcheck)
(* 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_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 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 apfst o apfst o K) (map (ProofContext.read_typ ctxt) arg)
| parse_test_param ctxt ("no_assms", [arg]) =
(apsnd o apfst o apsnd o K) (read_bool arg)
| parse_test_param ctxt ("expect", [arg]) =
(apsnd o apsnd o apfst o apfst o K) (read_expectation arg)
| parse_test_param ctxt ("report", [arg]) =
(apsnd o apsnd o apfst o apsnd o K) (read_bool arg)
| parse_test_param ctxt ("quiet", [arg]) =
(apsnd o apsnd o apsnd o K) (read_bool arg)
| parse_test_param ctxt (name, _) =
error ("Unknown 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 (the_single arg))
| _ => (apfst o parse_test_param ctxt) (name, arg);
fun quickcheck_params_cmd args thy =
let
val ctxt = ProofContext.init_global thy;
val f = fold (parse_test_param ctxt) args;
in
thy
|> (Data.map o apsnd o map_test_params) f
end;
fun gen_quickcheck args i state =
let
val thy = Proof.theory_of state;
val ctxt = Proof.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, no_assms), ((expect, report), quiet))), (generator_name, insts)) =
f (default_params, (NONE, []));
in
test_goal quiet report generator_name size iterations default_type no_assms insts i state
|> tap (fn (SOME x, _) => if expect = No_Counterexample then
error ("quickcheck expected to find no counterexample but found one") else ()
| (NONE, _) => if expect = Counterexample then
error ("quickcheck expected to find a counterexample but did not find one") else ())
end;
fun quickcheck args i state = fst (gen_quickcheck args i state);
fun quickcheck_cmd args i state =
gen_quickcheck args i (Toplevel.proof_of state)
|> Pretty.writeln o pretty_counterex_and_reports (Toplevel.context_of state);
val parse_arg = Parse.name -- (Scan.optional (Parse.$$$ "=" |--
((Parse.name >> single) || (Parse.$$$ "[" |-- Parse.list1 Parse.name --| Parse.$$$ "]"))) ["true"]);
val parse_args = Parse.$$$ "[" |-- Parse.list1 parse_arg --| Parse.$$$ "]"
|| Scan.succeed [];
val _ =
Outer_Syntax.command "quickcheck_params" "set parameters for random testing" Keyword.thy_decl
(parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));
val _ =
Outer_Syntax.improper_command "quickcheck" "try to find counterexample for subgoal" Keyword.diag
(parse_args -- Scan.optional Parse.nat 1
>> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));
end;
val auto_quickcheck = Quickcheck.auto;