(* 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 timing : 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 quiet : bool Config.T
val timeout : real Config.T
val finite_types : bool Config.T
val finite_type_size : int Config.T
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 {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
val add_generator:
string * (Proof.context -> term -> int -> term list option * report option)
-> Context.generic -> Context.generic
(* testing terms and proof states *)
val test_term: Proof.context -> bool -> term ->
(string * term) list option * ((string * int) list * ((int * report) list) option)
val test_goal_terms:
Proof.context -> bool -> (string * typ) list -> term list
-> (string * term) list option * ((string * int) list * ((int * report) list) option) list
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
(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 }
(* 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 (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_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 -> int -> term list option * report option)) list
* test_params;
val empty = ([], Test_Params {default_type = [], expect = No_Expectation});
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 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 AList.update (op =);
(* generating tests *)
fun mk_tester ctxt t =
let
val name = Config.get ctxt tester
val tester = case AList.lookup (op =) ((fst o Data.get o Context.Proof) ctxt) name
of NONE => error ("No such quickcheck tester: " ^ name)
| SOME tester => tester ctxt;
in
if Config.get ctxt quiet then
try tester t
else
let
val tester = Exn.interruptible_capture tester t
in case Exn.get_result tester of
NONE => SOME (Exn.release tester)
| SOME tester => SOME tester
end
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 (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 limit ctxt is_interactive f exc () =
TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f ()
handle TimeLimit.TimeOut =>
if is_interactive then exc () else raise TimeLimit.TimeOut
fun test_term ctxt is_interactive t =
let
val (names, t') = apfst (map fst) (prep_test_term t);
val current_size = Unsynchronized.ref 0
fun excipit s =
"Quickcheck " ^ s ^ " while testing at size " ^ string_of_int (!current_size)
val (test_fun, comp_time) = cpu_time "quickcheck compilation" (fn () => mk_tester ctxt t');
fun with_size test_fun k reports =
if k > Config.get ctxt size then
(NONE, reports)
else
let
val _ = if Config.get ctxt quiet then () else Output.urgent_message
("Test data size: " ^ string_of_int k)
val _ = current_size := k
val ((result, new_report), timing) =
cpu_time ("size " ^ string_of_int k) (fn () => test_fun (k - 1))
val reports = case new_report of NONE => reports | SOME rep => (k, rep) :: reports
in
case result of NONE => with_size test_fun (k + 1) reports | SOME q => (SOME q, reports)
end;
in
case test_fun of NONE => (NONE, ([comp_time], NONE))
| SOME test_fun =>
limit ctxt is_interactive (fn () =>
let
val ((result, reports), exec_time) =
cpu_time "quickcheck execution" (fn () => with_size test_fun 1 [])
in
(case result of NONE => NONE | SOME ts => SOME (names ~~ ts),
([exec_time, comp_time],
if Config.get ctxt report andalso not (null reports) then SOME reports else NONE))
end) (fn () => error (excipit "ran out of time")) ()
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 is_interactive ts =
let
val thy = ProofContext.theory_of ctxt
val (freess, ts') = split_list (map prep_test_term ts)
val Ts = map snd (hd freess)
val (test_funs, comp_time) = cpu_time "quickcheck compilation"
(fn () => map (mk_tester ctxt) ts')
fun test_card_size (card, size) =
(* FIXME: why decrement size by one? *)
case fst (the (nth test_funs (card - 1)) (size - 1)) of
SOME ts => SOME (map fst (nth freess (card - 1)) ~~ ts)
| NONE => NONE
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
(NONE, ([comp_time], NONE))
else if (forall is_some test_funs) then
limit ctxt is_interactive (fn () =>
(get_first test_card_size enumeration_card_size, ([comp_time], NONE)))
(fn () => error "Quickcheck ran out of time") ()
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
fun test_goal_terms lthy is_interactive insts check_goals =
let
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 =>
if not (null (Term.add_tfree_names check_goal [])) then
map (fn T =>
(pair (SOME T) o Term o Object_Logic.atomize_term thy o monomorphic_term thy insts T)
check_goal
handle WELLSORTED s => (SOME T, Wellsorted_Error s)) default_insts
else
[(NONE, Term (Object_Logic.atomize_term thy check_goal))]) 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 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
fun test_term' goal =
case goal of
[(NONE, t)] => test_term lthy is_interactive t
| ts => test_term_with_increasing_cardinality lthy 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 is_interactive) [] (maps (map snd) correct_inst_goals)
end;
fun test_goal is_interactive 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 (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]
| SOME locale => map (fn (_, phi) => Morphism.term phi proto_goal)
(Locale.registrations_of (Context.Theory thy) (*FIXME*) locale);
in
test_goal_terms lthy 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) =
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));
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_counterex_and_reports ctxt auto (cex, timing_and_reports) =
Pretty.chunks (pretty_counterex ctxt auto cex ::
map (pretty_reports ctxt) (map snd timing_and_reports))
(* 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 [] 1);
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 true cex)])) 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 (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, ctxt) =
case try (ProofContext.read_typ ctxt) name
of SOME (TFree (v, _)) => (apfst o AList.update (op =))
(v, ProofContext.read_typ ctxt (the_single arg)) (insts, ctxt)
| _ => (apsnd o Context.proof_map o parse_test_param) (name, arg) (insts, ctxt);
fun quickcheck_params_cmd args = Context.theory_map (fold parse_test_param args);
fun gen_quickcheck args i state =
state
|> Proof.map_context_result (fn ctxt => fold parse_test_param_inst args ([], ctxt))
|> (fn (insts, state') => test_goal true insts i state'
|> tap (fn (SOME x, _) => if expect (Proof.context_of state') = No_Counterexample then
error ("quickcheck expected to find no counterexample but found one") else ()
| (NONE, _) => if expect (Proof.context_of state') = Counterexample then
error ("quickcheck expected to find a counterexample but did not find one") else ()))
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) 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;