1 (* Title: Tools/quickcheck.ML
2 Author: Stefan Berghofer, Florian Haftmann, Lukas Bulwahn, TU Muenchen
4 Generic counterexample search engine.
9 val setup: theory -> theory
11 val auto: bool Unsynchronized.ref
12 val timing : bool Unsynchronized.ref
13 datatype report = Report of
14 { iterations : int, raised_match_errors : int,
15 satisfied_assms : int list, positive_concl_tests : int }
16 datatype expectation = No_Expectation | No_Counterexample | Counterexample;
17 datatype test_params = Test_Params of
18 { size: int, iterations: int, default_type: typ list, no_assms: bool,
19 expect : expectation, report: bool, quiet : bool, timeout : int};
20 val test_params_of : Proof.context -> test_params
21 val report : Proof.context -> bool
23 ((int * int) * ((typ list * bool) * ((expectation * bool) * (bool * int)))
24 -> (int * int) * ((typ list * bool) * ((expectation * bool) * (bool * int))))
25 -> Context.generic -> Context.generic
27 string * (Proof.context -> term -> int -> term list option * (bool list * bool))
28 -> Context.generic -> Context.generic
29 (* testing terms and proof states *)
30 val test_term: Proof.context -> string option -> term ->
31 (string * term) list option * ((string * int) list * ((int * report list) list) option)
32 val quickcheck: (string * string list) list -> int -> Proof.state -> (string * term) list option
35 structure Quickcheck : QUICKCHECK =
40 val auto = Unsynchronized.ref false;
42 val timing = Unsynchronized.ref false;
45 ProofGeneralPgip.add_preference Preferences.category_tracing
46 (Unsynchronized.setmp auto true (fn () =>
47 Preferences.bool_pref auto
49 "Run Quickcheck automatically.") ());
51 (* quickcheck report *)
53 datatype single_report = Run of bool list * bool | MatchExc
55 datatype report = Report of
56 { iterations : int, raised_match_errors : int,
57 satisfied_assms : int list, positive_concl_tests : int }
59 fun collect_single_report single_report
60 (Report {iterations = iterations, raised_match_errors = raised_match_errors,
61 satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =
64 Report {iterations = iterations + 1, raised_match_errors = raised_match_errors + 1,
65 satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}
66 | Run (assms, concl) =>
67 Report {iterations = iterations + 1, raised_match_errors = raised_match_errors,
69 map2 (fn b => fn s => if b then s + 1 else s) assms
70 (if null satisfied_assms then replicate (length assms) 0 else satisfied_assms),
71 positive_concl_tests = if concl then positive_concl_tests + 1 else positive_concl_tests}
75 datatype expectation = No_Expectation | No_Counterexample | Counterexample;
77 fun merge_expectation (expect1, expect2) =
78 if expect1 = expect2 then expect1 else No_Expectation
80 (* quickcheck configuration -- default parameters, test generators *)
82 datatype test_params = Test_Params of
83 { size: int, iterations: int, default_type: typ list, no_assms: bool,
84 expect : expectation, report: bool, quiet : bool, timeout : int};
87 (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =
88 ((size, iterations), ((default_type, no_assms), ((expect, report), (quiet, timeout))));
91 ((size, iterations), ((default_type, no_assms), ((expect, report), (quiet, timeout)))) =
92 Test_Params { size = size, iterations = iterations, default_type = default_type,
93 no_assms = no_assms, expect = expect, report = report, quiet = quiet, timeout = timeout };
95 fun map_test_params' f
96 (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =
98 (f ((size, iterations), ((default_type, no_assms), ((expect, report), (quiet, timeout)))));
100 fun merge_test_params
101 (Test_Params { size = size1, iterations = iterations1, default_type = default_type1,
102 no_assms = no_assms1, expect = expect1, report = report1, quiet = quiet1, timeout = timeout1 },
103 Test_Params { size = size2, iterations = iterations2, default_type = default_type2,
104 no_assms = no_assms2, expect = expect2, report = report2, quiet = quiet2, timeout = timeout2}) =
105 make_test_params ((Int.max (size1, size2), Int.max (iterations1, iterations2)),
106 ((merge (op =) (default_type1, default_type2), no_assms1 orelse no_assms2),
107 ((merge_expectation (expect1, expect2), report1 orelse report2),
108 (quiet1 orelse quiet2, Int.min (timeout1, timeout2)))));
110 structure Data = Generic_Data
113 (string * (Proof.context -> term -> int -> term list option * (bool list * bool))) list
115 val empty = ([], Test_Params
116 { size = 10, iterations = 100, default_type = [], no_assms = false,
117 expect = No_Expectation, report = false, quiet = false, timeout = 30});
119 fun merge ((generators1, params1), (generators2, params2)) : T =
120 (AList.merge (op =) (K true) (generators1, generators2),
121 merge_test_params (params1, params2));
124 val test_params_of = snd o Data.get o Context.Proof;
126 val size = fst o fst o dest_test_params o test_params_of
128 val iterations = snd o fst o dest_test_params o test_params_of
130 val default_type = fst o fst o snd o dest_test_params o test_params_of
132 val no_assms = snd o fst o snd o dest_test_params o test_params_of
134 val expect = fst o fst o snd o snd o dest_test_params o test_params_of
136 val report = snd o fst o snd o snd o dest_test_params o test_params_of
138 val quiet = fst o snd o snd o snd o dest_test_params o test_params_of
140 val timeout = snd o snd o snd o snd o dest_test_params o test_params_of
143 (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =
145 ((size, iterations), ((default_type, no_assms), ((expect, f report), (quiet, timeout))));
148 (Test_Params { size, iterations, default_type, no_assms, expect, report, quiet, timeout }) =
150 ((size, iterations), ((default_type, no_assms), ((expect, report), (f quiet, timeout))));
152 fun set_report report = Data.map (apsnd (map_report (K report)))
154 fun set_quiet quiet = Data.map (apsnd (map_quiet (K quiet)))
156 val map_test_params = Data.map o apsnd o map_test_params'
158 val add_generator = Data.map o apfst o AList.update (op =);
160 (* generating tests *)
162 fun mk_tester_select name ctxt =
163 case AList.lookup (op =) ((fst o Data.get o Context.Proof) ctxt) name
164 of NONE => error ("No such quickcheck generator: " ^ name)
165 | SOME generator => generator ctxt;
167 fun mk_testers ctxt t =
168 (map snd o fst o Data.get o Context.Proof) ctxt
169 |> map_filter (fn generator => try (generator ctxt) t);
171 fun mk_testers_strict ctxt t =
173 val generators = ((map snd o fst o Data.get o Context.Proof) ctxt)
174 val testers = map (fn generator => Exn.interruptible_capture (generator ctxt) t) generators;
176 if forall (is_none o Exn.get_result) testers
177 then [(Exn.release o snd o split_last) testers]
178 else map_filter Exn.get_result testers
182 (* testing propositions *)
184 fun prep_test_term t =
186 val _ = (null (Term.add_tvars t []) andalso null (Term.add_tfrees t [])) orelse
187 error "Term to be tested contains type variables";
188 val _ = null (Term.add_vars t []) orelse
189 error "Term to be tested contains schematic variables";
190 val frees = Term.add_frees t [];
191 in (map fst frees, list_abs_free (frees, t)) end
193 fun cpu_time description f =
195 val start = start_timing ()
196 val result = Exn.capture f ()
197 val time = Time.toMilliseconds (#cpu (end_timing start))
198 in (Exn.release result, (description, time)) end
200 fun test_term ctxt generator_name t =
202 val (names, t') = prep_test_term t;
203 val (testers, comp_time) = cpu_time "quickcheck compilation"
204 (fn () => (case generator_name
205 of NONE => if quiet ctxt then mk_testers ctxt t' else mk_testers_strict ctxt t'
206 | SOME name => [mk_tester_select name ctxt t']));
207 fun iterate f 0 report = (NONE, report)
208 | iterate f j report =
210 val (test_result, single_report) = apsnd Run (f ()) handle Match => (if quiet ctxt then ()
211 else warning "Exception Match raised during quickcheck"; (NONE, MatchExc))
212 val report = collect_single_report single_report report
214 case test_result of NONE => iterate f (j - 1) report | SOME q => (SOME q, report)
216 val empty_report = Report { iterations = 0, raised_match_errors = 0,
217 satisfied_assms = [], positive_concl_tests = 0 }
218 fun with_testers k [] = (NONE, [])
219 | with_testers k (tester :: testers) =
220 case iterate (fn () => tester (k - 1)) (iterations ctxt) empty_report
221 of (NONE, report) => apsnd (cons report) (with_testers k testers)
222 | (SOME q, report) => (SOME q, [report]);
223 fun with_size k reports =
224 if k > size ctxt then (NONE, reports)
226 (if quiet ctxt then () else Output.urgent_message ("Test data size: " ^ string_of_int k);
228 val (result, new_report) = with_testers k testers
229 val reports = ((k, new_report) :: reports)
230 in case result of NONE => with_size (k + 1) reports | SOME q => (SOME q, reports) end);
231 val ((result, reports), exec_time) =
232 TimeLimit.timeLimit (Time.fromSeconds (timeout ctxt)) (fn () => cpu_time "quickcheck execution"
234 (fn result => case result of NONE => NONE
235 | SOME ts => SOME (names ~~ ts)) (with_size 1 []))) ()
236 handle TimeLimit.TimeOut => error "Reached timeout during Quickcheck"
238 (result, ([exec_time, comp_time], if report ctxt then SOME reports else NONE))
241 exception WELLSORTED of string
243 fun monomorphic_term thy insts default_T =
245 fun subst (T as TFree (v, S)) =
247 val T' = AList.lookup (op =) insts v
248 |> the_default default_T
249 in if Sign.of_sort thy (T', S) then T'
250 else raise (WELLSORTED ("For instantiation with default_type " ^ Syntax.string_of_typ_global thy default_T ^
251 ":\n" ^ Syntax.string_of_typ_global thy T' ^
252 " to be substituted for variable " ^
253 Syntax.string_of_typ_global thy T ^ " does not have sort " ^
254 Syntax.string_of_sort_global thy S))
257 in (map_types o map_atyps) subst end;
259 datatype wellsorted_error = Wellsorted_Error of string | Term of term
261 fun test_goal generator_name insts i state =
263 val lthy = Proof.context_of state;
264 val thy = Proof.theory_of state;
265 fun strip (Const ("all", _) $ Abs (_, _, t)) = strip t
267 val {goal = st, ...} = Proof.raw_goal state;
268 val (gi, frees) = Logic.goal_params (prop_of st) i;
269 val some_locale = case (Option.map #target o Named_Target.peek) lthy
272 | SOME locale => SOME locale;
273 val assms = if no_assms lthy then [] else case some_locale
274 of NONE => Assumption.all_assms_of lthy
275 | SOME locale => Assumption.local_assms_of lthy (Locale.init locale thy);
276 val proto_goal = Logic.list_implies (map Thm.term_of assms, subst_bounds (frees, strip gi));
277 val check_goals = case some_locale
278 of NONE => [proto_goal]
279 | SOME locale => map (fn (_, phi) => Morphism.term phi proto_goal)
280 (Locale.registrations_of (Context.Theory thy) (*FIXME*) locale);
281 val inst_goals = maps (fn check_goal => map (fn T =>
282 Term ((Object_Logic.atomize_term thy o monomorphic_term thy insts T) check_goal)
283 handle WELLSORTED s => Wellsorted_Error s) (default_type lthy)) check_goals
284 val error_msg = cat_lines (map_filter (fn Term t => NONE | Wellsorted_Error s => SOME s) inst_goals)
285 val correct_inst_goals =
286 case map_filter (fn Term t => SOME t | Wellsorted_Error s => NONE) inst_goals of
287 [] => error error_msg
289 val _ = if quiet lthy then () else warning error_msg
290 fun collect_results f reports [] = (NONE, rev reports)
291 | collect_results f reports (t :: ts) =
293 (SOME res, report) => (SOME res, rev (report :: reports))
294 | (NONE, report) => collect_results f (report :: reports) ts
295 in collect_results (test_term lthy generator_name) [] correct_inst_goals end;
297 (* pretty printing *)
299 fun tool_name auto = (if auto then "Auto " else "") ^ "Quickcheck"
301 fun pretty_counterex ctxt auto NONE = Pretty.str (tool_name auto ^ " found no counterexample.")
302 | pretty_counterex ctxt auto (SOME cex) =
303 Pretty.chunks (Pretty.str (tool_name auto ^ " found a counterexample:\n") ::
305 Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) cex);
307 fun pretty_report (Report {iterations = iterations, raised_match_errors = raised_match_errors,
308 satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =
310 fun pretty_stat s i = Pretty.block ([Pretty.str (s ^ ": " ^ string_of_int i)])
312 ([pretty_stat "iterations" iterations,
313 pretty_stat "match exceptions" raised_match_errors]
314 @ map_index (fn (i, n) => pretty_stat ("satisfied " ^ string_of_int (i + 1) ^ ". assumption") n)
316 @ [pretty_stat "positive conclusion tests" positive_concl_tests])
319 fun pretty_reports' [report] = [Pretty.chunks (pretty_report report)]
320 | pretty_reports' reports =
321 map_index (fn (i, report) =>
322 Pretty.chunks (Pretty.str (string_of_int (i + 1) ^ ". generator:\n") :: pretty_report report))
325 fun pretty_reports ctxt (SOME reports) =
326 Pretty.chunks (Pretty.str "Quickcheck report:" ::
327 maps (fn (size, reports) =>
328 Pretty.str ("size " ^ string_of_int size ^ ":") :: pretty_reports' reports @ [Pretty.brk 1])
330 | pretty_reports ctxt NONE = Pretty.str ""
332 fun pretty_counterex_and_reports ctxt auto (cex, timing_and_reports) =
333 Pretty.chunks (pretty_counterex ctxt auto cex ::
334 map (pretty_reports ctxt) (map snd timing_and_reports))
336 (* automatic testing *)
338 fun auto_quickcheck state =
343 val ctxt = Proof.context_of state;
346 |> Proof.map_context (Context.proof_map (set_report false #> set_quiet true))
347 |> try (test_goal NONE [] 1);
350 NONE => (false, state)
351 | SOME (NONE, report) => (false, state)
352 | SOME (cex, report) => (true, Proof.goal_message (K (Pretty.chunks [Pretty.str "",
353 Pretty.mark Markup.hilite (pretty_counterex ctxt true cex)])) state)
356 val setup = Auto_Tools.register_tool ("quickcheck", auto_quickcheck)
361 fun read_nat s = case (Library.read_int o Symbol.explode) s
362 of (k, []) => if k >= 0 then k
363 else error ("Not a natural number: " ^ s)
364 | (_, _ :: _) => error ("Not a natural number: " ^ s);
366 fun read_bool "false" = false
367 | read_bool "true" = true
368 | read_bool s = error ("Not a Boolean value: " ^ s)
370 fun read_expectation "no_expectation" = No_Expectation
371 | read_expectation "no_counterexample" = No_Counterexample
372 | read_expectation "counterexample" = Counterexample
373 | read_expectation s = error ("Not an expectation value: " ^ s)
375 fun parse_test_param ctxt ("size", [arg]) =
376 (apfst o apfst o K) (read_nat arg)
377 | parse_test_param ctxt ("iterations", [arg]) =
378 (apfst o apsnd o K) (read_nat arg)
379 | parse_test_param ctxt ("default_type", arg) =
380 (apsnd o apfst o apfst o K) (map (ProofContext.read_typ ctxt) arg)
381 | parse_test_param ctxt ("no_assms", [arg]) =
382 (apsnd o apfst o apsnd o K) (read_bool arg)
383 | parse_test_param ctxt ("expect", [arg]) =
384 (apsnd o apsnd o apfst o apfst o K) (read_expectation arg)
385 | parse_test_param ctxt ("report", [arg]) =
386 (apsnd o apsnd o apfst o apsnd o K) (read_bool arg)
387 | parse_test_param ctxt ("quiet", [arg]) =
388 (apsnd o apsnd o apsnd o apfst o K) (read_bool arg)
389 | parse_test_param ctxt ("timeout", [arg]) =
390 (apsnd o apsnd o apsnd o apsnd o K) (read_nat arg)
391 | parse_test_param ctxt (name, _) =
392 error ("Unknown test parameter: " ^ name);
394 fun parse_test_param_inst ctxt ("generator", [arg]) =
395 (apsnd o apfst o K o SOME) arg
396 | parse_test_param_inst ctxt (name, arg) =
397 case try (ProofContext.read_typ ctxt) name
398 of SOME (TFree (v, _)) => (apsnd o apsnd o AList.update (op =))
399 (v, ProofContext.read_typ ctxt (the_single arg))
400 | _ => (apfst o parse_test_param ctxt) (name, arg);
402 fun quickcheck_params_cmd args thy =
404 val ctxt = ProofContext.init_global thy
405 val f = fold (parse_test_param ctxt) args;
408 |> (Context.theory_map o map_test_params) f
411 fun gen_quickcheck args i state =
413 val ctxt = Proof.context_of state;
414 val default_params = (dest_test_params o snd o Data.get o Context.Proof) ctxt;
415 val f = fold (parse_test_param_inst ctxt) args;
416 val (test_params, (generator_name, insts)) = f (default_params, (NONE, []));
419 |> Proof.map_context (Context.proof_map (map_test_params (K test_params)))
420 |> (fn state' => test_goal generator_name insts i state'
421 |> tap (fn (SOME x, _) => if expect (Proof.context_of state') = No_Counterexample then
422 error ("quickcheck expected to find no counterexample but found one") else ()
423 | (NONE, _) => if expect (Proof.context_of state') = Counterexample then
424 error ("quickcheck expected to find a counterexample but did not find one") else ()))
427 fun quickcheck args i state = fst (gen_quickcheck args i state);
429 fun quickcheck_cmd args i state =
430 gen_quickcheck args i (Toplevel.proof_of state)
431 |> Pretty.writeln o pretty_counterex_and_reports (Toplevel.context_of state) false;
433 val parse_arg = Parse.name -- (Scan.optional (Parse.$$$ "=" |--
434 ((Parse.name >> single) || (Parse.$$$ "[" |-- Parse.list1 Parse.name --| Parse.$$$ "]"))) ["true"]);
436 val parse_args = Parse.$$$ "[" |-- Parse.list1 parse_arg --| Parse.$$$ "]"
440 Outer_Syntax.command "quickcheck_params" "set parameters for random testing" Keyword.thy_decl
441 (parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));
444 Outer_Syntax.improper_command "quickcheck" "try to find counterexample for subgoal" Keyword.diag
445 (parse_args -- Scan.optional Parse.nat 1
446 >> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));
451 val auto_quickcheck = Quickcheck.auto;