(* Title: Tools/quickcheck.ML
Author: Stefan Berghofer, Florian Haftmann, Lukas Bulwahn, TU Muenchen
Generic counterexample search engine.
*)
signature QUICKCHECK =
sig
val setup: theory -> theory
(* configuration *)
val auto: bool Unsynchronized.ref
val tester : string Config.T
val size : int Config.T
val iterations : int Config.T
val no_assms : bool Config.T
val report : bool Config.T
val timing : bool Config.T
val quiet : bool Config.T
val timeout : real Config.T
val finite_types : bool Config.T
val finite_type_size : int Config.T
datatype expectation = No_Expectation | No_Counterexample | Counterexample;
datatype test_params = Test_Params of {default_type: typ list, expect : expectation};
val test_params_of : Proof.context -> test_params
val map_test_params : (typ list * expectation -> typ list * expectation)
-> Context.generic -> Context.generic
datatype report = Report of
{ iterations : int, raised_match_errors : int,
satisfied_assms : int list, positive_concl_tests : int }
(* registering generators *)
val add_generator:
string * (Proof.context -> term * term list -> int -> term list option * report option)
-> Context.generic -> Context.generic
val add_batch_generator:
string * (Proof.context -> term list -> (int -> term list option) list)
-> Context.generic -> Context.generic
(* quickcheck's result *)
datatype result =
Result of
{counterexample : (string * term) list option,
evaluation_terms : (term * term) list option,
timings : (string * int) list,
reports : (int * report) list}
val counterexample_of : result -> (string * term) list option
val timings_of : result -> (string * int) list
(* testing terms and proof states *)
val test_term: Proof.context -> bool * bool -> term * term list -> result
val test_goal_terms:
Proof.context -> bool * bool -> (string * typ) list -> (term * term list) list
-> result list
val quickcheck: (string * string list) list -> int -> Proof.state -> (string * term) list option
(* testing a batch of terms *)
val test_terms: Proof.context -> term list -> (string * term) list option list option
end;
structure Quickcheck : QUICKCHECK =
struct
(* preferences *)
val auto = Unsynchronized.ref false;
val _ =
ProofGeneralPgip.add_preference Preferences.category_tracing
(Unsynchronized.setmp auto true (fn () =>
Preferences.bool_pref auto
"auto-quickcheck"
"Run Quickcheck automatically.") ());
(* quickcheck report *)
datatype report = Report of
{ iterations : int, raised_match_errors : int,
satisfied_assms : int list, positive_concl_tests : int }
(* Quickcheck Result *)
datatype result = Result of
{ counterexample : (string * term) list option, evaluation_terms : (term * term) list option,
timings : (string * int) list, reports : (int * report) list}
val empty_result =
Result {counterexample = NONE, evaluation_terms = NONE, timings = [], reports = []}
fun counterexample_of (Result r) = #counterexample r
fun found_counterexample (Result r) = is_some (#counterexample r)
fun response_of (Result r) = case (#counterexample r, #evaluation_terms r) of
(SOME ts, SOME evals) => SOME (ts, evals)
| (NONE, NONE) => NONE
fun timings_of (Result r) = #timings r
fun set_reponse names eval_terms (SOME ts) (Result r) =
let
val (ts1, ts2) = chop (length names) ts
in
Result {counterexample = SOME (names ~~ ts1), evaluation_terms = SOME (eval_terms ~~ ts2),
timings = #timings r, reports = #reports r}
end
| set_reponse _ _ NONE result = result
fun cons_timing timing (Result r) =
Result {counterexample = #counterexample r, evaluation_terms = #evaluation_terms r,
timings = cons timing (#timings r), reports = #reports r}
fun cons_report size (SOME report) (Result r) =
Result {counterexample = #counterexample r, evaluation_terms = #evaluation_terms r,
timings = #timings r, reports = cons (size, report) (#reports r)}
| cons_report _ NONE result = result
fun add_timing timing result_ref = (result_ref := cons_timing timing (!result_ref))
fun add_report size report result_ref = (result_ref := cons_report size report (!result_ref))
fun add_response names eval_terms response result_ref =
(result_ref := set_reponse names eval_terms response (!result_ref))
(* 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 *)
val (tester, setup_tester) = Attrib.config_string "quickcheck_tester" (K "")
val (size, setup_size) = Attrib.config_int "quickcheck_size" (K 10)
val (iterations, setup_iterations) = Attrib.config_int "quickcheck_iterations" (K 100)
val (no_assms, setup_no_assms) = Attrib.config_bool "quickcheck_no_assms" (K false)
val (report, setup_report) = Attrib.config_bool "quickcheck_report" (K true)
val (timing, setup_timing) = Attrib.config_bool "quickcheck_timing" (K false)
val (quiet, setup_quiet) = Attrib.config_bool "quickcheck_quiet" (K false)
val (timeout, setup_timeout) = Attrib.config_real "quickcheck_timeout" (K 30.0)
val (finite_types, setup_finite_types) = Attrib.config_bool "quickcheck_finite_types" (K true)
val (finite_type_size, setup_finite_type_size) =
Attrib.config_int "quickcheck_finite_type_size" (K 3)
val setup_config =
setup_tester #> setup_size #> setup_iterations #> setup_no_assms #> setup_report #> setup_timing
#> setup_quiet #> setup_timeout #> setup_finite_types #> setup_finite_type_size
datatype test_params = Test_Params of
{default_type: typ list, expect : expectation};
fun dest_test_params (Test_Params {default_type, expect}) = (default_type, expect);
fun make_test_params (default_type, expect) =
Test_Params {default_type = default_type, expect = expect};
fun map_test_params' f (Test_Params {default_type, expect}) =
make_test_params (f (default_type, expect));
fun merge_test_params
(Test_Params {default_type = default_type1, expect = expect1},
Test_Params {default_type = default_type2, expect = expect2}) =
make_test_params
(merge (op =) (default_type1, default_type2), merge_expectation (expect1, expect2));
structure Data = Generic_Data
(
type T =
((string * (Proof.context -> term * term list -> int -> term list option * report option)) list
* (string * (Proof.context -> term list -> (int -> term list option) list)) list)
* test_params;
val empty = (([], []), Test_Params {default_type = [], expect = No_Expectation});
val extend = I;
fun merge (((generators1, batch_generators1), params1), ((generators2, batch_generators2), params2)) : T =
((AList.merge (op =) (K true) (generators1, generators2),
AList.merge (op =) (K true) (batch_generators1, batch_generators2)),
merge_test_params (params1, params2));
);
val test_params_of = snd o Data.get o Context.Proof;
val default_type = fst o dest_test_params o test_params_of
val expect = snd o dest_test_params o test_params_of
val map_test_params = Data.map o apsnd o map_test_params'
val add_generator = Data.map o apfst o apfst o AList.update (op =);
val add_batch_generator = Data.map o apfst o apsnd o AList.update (op =);
(* generating tests *)
fun gen_mk_tester lookup ctxt v =
let
val name = Config.get ctxt tester
val tester = case lookup ctxt name
of NONE => error ("No such quickcheck tester: " ^ name)
| SOME tester => tester ctxt;
in
if Config.get ctxt quiet then
try tester v
else
let
val tester = Exn.interruptible_capture tester v
in case Exn.get_result tester of
NONE => SOME (Exn.release tester)
| SOME tester => SOME tester
end
end
val mk_tester = gen_mk_tester (fn ctxt =>
AList.lookup (op =) ((fst o fst o Data.get o Context.Proof) ctxt))
val mk_batch_tester = gen_mk_tester (fn ctxt => AList.lookup (op =) ((snd o fst o Data.get o Context.Proof) ctxt))
(* testing propositions *)
fun check_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";
in () end
fun cpu_time description e =
let val ({cpu, ...}, result) = Timing.timing e ()
in (result, (description, Time.toMilliseconds cpu)) end
fun limit ctxt (limit_time, is_interactive) f exc () =
if limit_time then
TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f ()
handle TimeLimit.TimeOut =>
if is_interactive then exc () else raise TimeLimit.TimeOut
else
f ()
fun test_term ctxt (limit_time, is_interactive) (t, eval_terms) =
let
fun message s = if Config.get ctxt quiet then () else Output.urgent_message s
val _ = check_test_term t
val names = Term.add_free_names t []
val current_size = Unsynchronized.ref 0
val current_result = Unsynchronized.ref empty_result
fun excipit () =
"Quickcheck ran out of time while testing at size " ^ string_of_int (!current_size)
val (test_fun, comp_time) = cpu_time "quickcheck compilation"
(fn () => mk_tester ctxt (t, eval_terms));
val _ = add_timing comp_time current_result
fun with_size test_fun k =
if k > Config.get ctxt size then
NONE
else
let
val _ = message ("Test data size: " ^ string_of_int k)
val _ = current_size := k
val ((result, report), timing) =
cpu_time ("size " ^ string_of_int k) (fn () => test_fun (k - 1))
val _ = add_timing timing current_result
val _ = add_report k report current_result
in
case result of NONE => with_size test_fun (k + 1) | SOME q => SOME q
end;
in
case test_fun of NONE => !current_result
| SOME test_fun =>
limit ctxt (limit_time, is_interactive) (fn () =>
let
val (response, exec_time) =
cpu_time "quickcheck execution" (fn () => with_size test_fun 1)
val _ = add_response names eval_terms response current_result
val _ = add_timing exec_time current_result
in
!current_result
end) (fn () => (message (excipit ()); !current_result)) ()
end;
fun test_terms ctxt ts =
let
val _ = map check_test_term ts
val namess = map (fn t => Term.add_free_names t []) ts
val test_funs = mk_batch_tester ctxt ts
fun with_size tester k =
if k > Config.get ctxt size then NONE
else case tester k of SOME ts => SOME ts | NONE => with_size tester (k + 1)
val results =
Option.map (map (fn test_fun => TimeLimit.timeLimit (seconds (Config.get ctxt timeout))
(fn () => with_size test_fun 1) ()
handle TimeLimit.TimeOut => NONE)) test_funs
in
Option.map (map2 (fn names => Option.map (fn ts => names ~~ ts)) namess) results
end
(* FIXME: this function shows that many assumptions are made upon the generation *)
(* In the end there is probably no generic quickcheck interface left... *)
fun test_term_with_increasing_cardinality ctxt (limit_time, is_interactive) ts =
let
val thy = ProofContext.theory_of ctxt
fun message s = if Config.get ctxt quiet then () else Output.urgent_message s
val (ts, eval_terms) = split_list ts
val _ = map check_test_term ts
val names = Term.add_free_names (hd ts) []
val Ts = map snd (Term.add_frees (hd ts) [])
val current_result = Unsynchronized.ref empty_result
val (test_funs, comp_time) = cpu_time "quickcheck compilation"
(fn () => map (mk_tester ctxt) (ts ~~ eval_terms))
val _ = add_timing comp_time current_result
fun test_card_size (card, size) =
(* FIXME: why decrement size by one? *)
let
val (ts, timing) = cpu_time ("size " ^ string_of_int size ^ " and card " ^ string_of_int card)
(fn () => fst (the (nth test_funs (card - 1)) (size - 1)))
val _ = add_timing timing current_result
in
Option.map (pair card) ts
end
val enumeration_card_size =
if forall (fn T => Sign.of_sort thy (T, ["Enum.enum"])) Ts then
(* size does not matter *)
map (rpair 0) (1 upto (length ts))
else
(* size does matter *)
map_product pair (1 upto (length ts)) (1 upto (Config.get ctxt size))
|> sort (fn ((c1, s1), (c2, s2)) => int_ord ((c1 + s1), (c2 + s2)))
in
if (forall is_none test_funs) then !current_result
else if (forall is_some test_funs) then
limit ctxt (limit_time, is_interactive) (fn () =>
let
val _ = case get_first test_card_size enumeration_card_size of
SOME (card, ts) => add_response names (nth eval_terms (card - 1)) (SOME ts) current_result
| NONE => ()
in !current_result end)
(fn () => (message "Quickcheck ran out of time"; !current_result)) ()
else
error "Unexpectedly, testers of some cardinalities are executable but others are not"
end
fun get_finite_types ctxt =
fst (chop (Config.get ctxt finite_type_size)
(map (Type o rpair []) ["Enum.finite_1", "Enum.finite_2", "Enum.finite_3",
"Enum.finite_4", "Enum.finite_5"]))
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 * term list
fun test_goal_terms lthy (limit_time, is_interactive) insts check_goals =
let
fun map_goal_and_eval_terms f (check_goal, eval_terms) = (f check_goal, map f eval_terms)
val thy = ProofContext.theory_of lthy
val default_insts =
if Config.get lthy finite_types then (get_finite_types lthy) else (default_type lthy)
val inst_goals =
map (fn (check_goal, eval_terms) =>
if not (null (Term.add_tfree_names check_goal [])) then
map (fn T =>
(pair (SOME T) o Term o apfst (Object_Logic.atomize_term thy))
(map_goal_and_eval_terms (monomorphic_term thy insts T) (check_goal, eval_terms))
handle WELLSORTED s => (SOME T, Wellsorted_Error s)) default_insts
else
[(NONE, Term (Object_Logic.atomize_term thy check_goal, eval_terms))]) check_goals
val error_msg =
cat_lines
(maps (map_filter (fn (_, Term t) => NONE | (_, Wellsorted_Error s) => SOME s)) inst_goals)
fun is_wellsorted_term (T, Term t) = SOME (T, t)
| is_wellsorted_term (_, Wellsorted_Error s) = NONE
val correct_inst_goals =
case map (map_filter is_wellsorted_term) inst_goals of
[[]] => error error_msg
| xs => xs
val _ = if Config.get lthy quiet then () else warning error_msg
fun collect_results f [] results = results
| collect_results f (t :: ts) results =
let
val result = f t
in
if found_counterexample result then
(result :: results)
else
collect_results f ts (result :: results)
end
fun test_term' goal =
case goal of
[(NONE, t)] => test_term lthy (limit_time, is_interactive) t
| ts => test_term_with_increasing_cardinality lthy (limit_time, is_interactive) (map snd ts)
in
if Config.get lthy finite_types then
collect_results test_term' correct_inst_goals []
else
collect_results (test_term lthy (limit_time, is_interactive)) (maps (map snd) correct_inst_goals) []
end;
fun test_goal (time_limit, is_interactive) (insts, eval_terms) 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 (Option.map #target o Named_Target.peek) lthy
of NONE => NONE
| SOME "" => NONE
| SOME locale => SOME locale;
val assms = if Config.get lthy 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, eval_terms)]
| SOME locale =>
map (fn (_, phi) => (Morphism.term phi proto_goal, map (Morphism.term phi) eval_terms))
(Locale.registrations_of (Context.Theory thy) (*FIXME*) locale);
in
test_goal_terms lthy (time_limit, is_interactive) insts check_goals
end
(* pretty printing *)
fun tool_name auto = (if auto then "Auto " else "") ^ "Quickcheck"
fun pretty_counterex ctxt auto NONE = Pretty.str (tool_name auto ^ " found no counterexample.")
| pretty_counterex ctxt auto (SOME (cex, eval_terms)) =
Pretty.chunks ((Pretty.str (tool_name auto ^ " found a counterexample:\n") ::
map (fn (s, t) =>
Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) (rev cex))
@ (Pretty.str ("Evaluated terms:\n") ::
map (fn (t, u) =>
Pretty.block [Syntax.pretty_term ctxt t, Pretty.str " =", Pretty.brk 1, Syntax.pretty_term ctxt u])
(rev eval_terms)));
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 ctxt (SOME reports) =
Pretty.chunks (Pretty.fbrk :: Pretty.str "Quickcheck report:" ::
maps (fn (size, report) =>
Pretty.str ("size " ^ string_of_int size ^ ":") :: pretty_report report @ [Pretty.brk 1])
(rev reports))
| pretty_reports ctxt NONE = Pretty.str ""
fun pretty_timings timings =
Pretty.chunks (Pretty.fbrk :: Pretty.str "timings:" ::
maps (fn (label, time) =>
Pretty.str (label ^ ": " ^ string_of_int time ^ " ms") :: Pretty.brk 1 :: []) (rev timings))
fun pretty_counterex_and_reports ctxt auto (result :: _) =
Pretty.chunks (pretty_counterex ctxt auto (response_of result) ::
(* map (pretty_reports ctxt) (reports_of result) :: *)
(if Config.get ctxt timing then cons (pretty_timings (timings_of result)) else I) [])
(* automatic testing *)
fun auto_quickcheck state =
let
val ctxt = Proof.context_of state;
val res =
state
|> Proof.map_context (Config.put report false #> Config.put quiet true)
|> try (test_goal (false, false) ([], []) 1);
in
case res of
NONE => (false, state)
| SOME (result :: _) => if found_counterexample result then
(true, Proof.goal_message (K (Pretty.chunks [Pretty.str "",
Pretty.mark Markup.hilite (pretty_counterex ctxt true (response_of result))])) state)
else
(false, state)
end
val setup = Auto_Tools.register_tool (auto, auto_quickcheck)
#> setup_config
(* 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_real s =
case (Real.fromString s) of
SOME s => s
| NONE => error ("Not a real number: " ^ 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 valid_tester_name genctxt = AList.defined (op =) (fst (fst (Data.get genctxt)))
fun parse_tester name genctxt =
if valid_tester_name genctxt name then
Config.put_generic tester name genctxt
else
error ("Unknown tester: " ^ name)
fun parse_test_param ("tester", [arg]) = parse_tester arg
| parse_test_param ("size", [arg]) = Config.put_generic size (read_nat arg)
| parse_test_param ("iterations", [arg]) = Config.put_generic iterations (read_nat arg)
| parse_test_param ("default_type", arg) = (fn gen_ctxt =>
map_test_params
((apfst o K) (map (ProofContext.read_typ (Context.proof_of gen_ctxt)) arg)) gen_ctxt)
| parse_test_param ("no_assms", [arg]) = Config.put_generic no_assms (read_bool arg)
| parse_test_param ("expect", [arg]) = map_test_params ((apsnd o K) (read_expectation arg))
| parse_test_param ("report", [arg]) = Config.put_generic report (read_bool arg)
| parse_test_param ("quiet", [arg]) = Config.put_generic quiet (read_bool arg)
| parse_test_param ("timeout", [arg]) = Config.put_generic timeout (read_real arg)
| parse_test_param ("finite_types", [arg]) = Config.put_generic finite_types (read_bool arg)
| parse_test_param ("finite_type_size", [arg]) =
Config.put_generic finite_type_size (read_nat arg)
| parse_test_param (name, _) = fn genctxt =>
if valid_tester_name genctxt name then
Config.put_generic tester name genctxt
else error ("Unknown tester or test parameter: " ^ name);
fun parse_test_param_inst (name, arg) ((insts, eval_terms), ctxt) =
case try (ProofContext.read_typ ctxt) name
of SOME (TFree (v, _)) =>
((AList.update (op =) (v, ProofContext.read_typ ctxt (the_single arg)) insts, eval_terms), ctxt)
| NONE => (case name of
"eval" => ((insts, eval_terms @ map (Syntax.read_term ctxt) arg), ctxt)
| _ => ((insts, eval_terms), Context.proof_map (parse_test_param (name, arg)) ctxt));
fun quickcheck_params_cmd args = Context.theory_map (fold parse_test_param args);
fun check_expectation state results =
(if found_counterexample (hd results) andalso expect (Proof.context_of state) = No_Counterexample
then
error ("quickcheck expected to find no counterexample but found one")
else
(if not (found_counterexample (hd results)) andalso expect (Proof.context_of state) = Counterexample
then
error ("quickcheck expected to find a counterexample but did not find one")
else ()))
fun gen_quickcheck args i state =
state
|> Proof.map_context_result (fn ctxt => fold parse_test_param_inst args (([], []), ctxt))
|> (fn ((insts, eval_terms), state') => test_goal (true, true) (insts, eval_terms) i state'
|> tap (check_expectation state'))
fun quickcheck args i state = counterexample_of (hd (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) false;
val parse_arg =
Parse.name --
(Scan.optional (Parse.$$$ "=" |--
(((Parse.name || Parse.float_number) >> single) ||
(Parse.$$$ "[" |-- 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;