src/Tools/quickcheck.ML

+(*  Title:      Pure/Tools/quickcheck.ML
+    Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen
+
+Generic counterexample search engine.
+*)
+
+signature QUICKCHECK =
+sig
+  val test_term: Proof.context -> bool -> string option -> int -> int -> term -> (string * term) list option;
+  val add_generator: string * (Proof.context -> term -> int -> term list option) -> theory -> theory
+  val auto: bool ref
+  val auto_time_limit: int ref
+end;
+
+structure Quickcheck : QUICKCHECK =
+struct
+
+(* quickcheck configuration -- default parameters, test generators *)
+
+datatype test_params = Test_Params of
+  { size: int, iterations: int, default_type: typ option };
+
+fun dest_test_params (Test_Params { size, iterations, default_type}) =
+  ((size, iterations), default_type);
+fun mk_test_params ((size, iterations), default_type) =
+  Test_Params { size = size, iterations = iterations, default_type = default_type };
+fun map_test_params f (Test_Params { size, iterations, default_type}) =
+  mk_test_params (f ((size, iterations), default_type));
+fun merge_test_params (Test_Params {size = size1, iterations = iterations1, default_type = default_type1},
+  Test_Params {size = size2, iterations = iterations2, default_type = default_type2}) =
+  mk_test_params ((Int.max (size1, size2), Int.max (iterations1, iterations2)),
+    case default_type1 of NONE => default_type2 | _ => default_type1);
+
+structure Data = TheoryDataFun(
+  type T = (string * (Proof.context -> term -> int -> term list option)) list
+    * test_params;
+  val empty = ([], Test_Params { size = 10, iterations = 100, default_type = NONE });
+  val copy = I;
+  val extend = I;
+  fun merge pp ((generators1, params1), (generators2, params2)) =
+    (AList.merge (op = : string * string -> bool) (K true) (generators1, generators2),
+      merge_test_params (params1, params2));
+)
+
+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 t =
+  (map snd o fst o Data.get o ProofContext.theory_of) ctxt
+  |> map_filter (fn generator => try (generator ctxt) t);
+
+fun mk_testers_strict ctxt 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) 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_tvars t) andalso null (term_tfrees t)) orelse
+      error "Term to be tested contains type variables";
+    val _ = null (term_vars t) orelse
+      error "Term to be tested contains schematic variables";
+    val frees = map dest_Free (term_frees t);
+  in (map fst frees, list_abs_free (frees, t)) end
+
+fun test_term ctxt quiet generator_name size i t =
+  let
+    val (names, t') = prep_test_term t;
+    val testers = case generator_name
+     of NONE => if quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'
+      | SOME name => [mk_tester_select name ctxt t'];
+    fun iterate f 0 = NONE
+      | iterate f k = case f () handle Match => (if quiet then ()
+             else warning "Exception Match raised during quickcheck"; NONE)
+          of NONE => iterate f (k - 1) | SOME q => SOME q;
+    fun with_testers k [] = NONE
+      | with_testers k (tester :: testers) =
+          case iterate (fn () => tester k) i
+           of NONE => with_testers k testers
+            | SOME q => SOME q;
+    fun with_size k = if k > size then NONE
+      else (if quiet then () else priority ("Test data size: " ^ string_of_int k);
+        case with_testers k testers
+         of NONE => with_size (k + 1) | SOME q => SOME q);
+  in case with_size 1
+   of NONE => NONE
+    | SOME ts => SOME (names ~~ ts)
+  end;
+
+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 (the_default T default_T)
+          in if Sign.of_sort thy (T, S) then T'
+            else error ("Type " ^ Syntax.string_of_typ_global thy T ^
+              " to be substituted for variable " ^
+              Syntax.string_of_typ_global thy T ^ "\ndoes not have sort " ^
+              Syntax.string_of_sort_global thy S)
+          end
+      | subst T = T;
+  in (map_types o map_atyps) subst end;
+
+fun test_goal quiet generator_name size iterations default_T insts i assms state =
+  let
+    val ctxt = Proof.context_of state;
+    val thy = Proof.theory_of state;
+    fun strip (Const ("all", _) $ Abs (_, _, t)) = strip t
+      | strip t = t;
+    val (_, (_, st)) = Proof.get_goal state;
+    val (gi, frees) = Logic.goal_params (prop_of st) i;
+    val gi' = Logic.list_implies (assms, subst_bounds (frees, strip gi))
+      |> monomorphic_term thy insts default_T
+      |> ObjectLogic.atomize_term thy;
+  in test_term ctxt quiet generator_name size iterations gi' end;
+
+fun pretty_counterex ctxt NONE = Pretty.str "No counterexamples found."
+  | pretty_counterex ctxt (SOME cex) =
+      Pretty.chunks (Pretty.str "Counterexample found:\n" ::
+        map (fn (s, t) =>
+          Pretty.block [Pretty.str (s ^ " ="), Pretty.brk 1, Syntax.pretty_term ctxt t]) cex);
+
+
+(* automatic testing *)
+
+val auto = ref false;
+val auto_time_limit = ref 5000;
+
+fun test_goal_auto int state =
+  let
+    val ctxt = Proof.context_of state;
+    val assms = map term_of (Assumption.assms_of ctxt);
+    val Test_Params { size, iterations, default_type } =
+      (snd o Data.get o Proof.theory_of) state;
+    fun test () =
+      let
+        val res = TimeLimit.timeLimit (Time.fromMilliseconds (!auto_time_limit))
+          (try (test_goal true NONE size iterations default_type [] 1 assms)) state;
+      in
+        case res of
+          NONE => state
+        | SOME NONE => state
+        | SOME cex => Proof.goal_message (fn () => Pretty.chunks [Pretty.str "",
+            Pretty.mark Markup.hilite (pretty_counterex ctxt cex)]) state
+      end handle TimeLimit.TimeOut => (warning "Auto quickcheck: timeout."; state);
+  in
+    if int andalso !auto andalso not (!Toplevel.quiet)
+    then test ()
+    else state
+  end;
+
+val _ = Context.>> (Specification.add_theorem_hook test_goal_auto);
+
+
+(* Isar interfaces *)
+
+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 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 K o SOME) (ProofContext.read_typ ctxt arg)
+  | parse_test_param ctxt (name, _) =
+      error ("Bad 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 arg)
+        | _ => (apfst o parse_test_param ctxt) (name, arg);
+
+fun quickcheck_params_cmd args thy =
+  let
+    val ctxt = ProofContext.init thy;
+    val f = fold (parse_test_param ctxt) args;
+  in
+    thy
+    |> (Data.map o apsnd o map_test_params) f
+  end;
+
+fun quickcheck_cmd args i state =
+  let
+    val prf = Toplevel.proof_of state;
+    val thy = Toplevel.theory_of state;
+    val ctxt = Toplevel.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), (generator_name, insts)) =
+      f (default_params, (NONE, []));
+    val counterex = test_goal false generator_name size iterations
+      default_type insts i [] prf;
+  in (Pretty.writeln o pretty_counterex ctxt) counterex end;
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val parse_arg = P.name --| P.$$$ "=" -- P.name;
+val parse_args = P.$$$ "[" |-- P.list1 parse_arg --| P.$$$ "]"
+  || Scan.succeed [];
+
+val _ = OuterSyntax.command "quickcheck_params" "set parameters for random testing" K.thy_decl
+  (parse_args >> (fn args => Toplevel.theory (quickcheck_params_cmd args)));
+
+val _ = OuterSyntax.improper_command "quickcheck" "try to find counterexample for subgoal" K.diag
+  (parse_args -- Scan.optional P.nat 1
+    >> (fn (args, i) => Toplevel.no_timing o Toplevel.keep (quickcheck_cmd args i)));
+
+end; (*local*)
+
+end;
+
+
+val auto_quickcheck = Quickcheck.auto;
+val auto_quickcheck_time_limit = Quickcheck.auto_time_limit;