(* Title: HOL/Tools/Quickcheck/random_generators.ML
Author: Florian Haftmann, TU Muenchen
Random generators for various types.
*)
signature RANDOM_GENERATORS =
sig
type seed = Random_Engine.seed
val random_plugin: string
val random_fun: typ -> typ -> ('a -> 'a -> bool) -> ('a -> term)
-> (seed -> ('b * (unit -> term)) * seed) -> (seed -> seed * seed)
-> seed -> (('a -> 'b) * (unit -> term)) * seed
val compile_generator_expr:
Proof.context -> (term * term list) list -> bool -> int list -> (bool * term list) option * Quickcheck.report option
val put_counterexample: (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> seed -> (bool * term list) option * seed)
-> Proof.context -> Proof.context
val put_counterexample_report: (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> seed -> ((bool * term list) option * (bool list * bool)) * seed)
-> Proof.context -> Proof.context
val instantiate_random_datatype : Old_Datatype_Aux.config -> Old_Datatype_Aux.descr ->
(string * sort) list -> string list -> string -> string list * string list -> typ list * typ list -> theory -> theory
val setup: theory -> theory
end;
structure Random_Generators : RANDOM_GENERATORS =
struct
val random_plugin = "quickcheck_random";
(** abstract syntax **)
fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"})
val size = @{term "i::natural"};
val size_pred = @{term "(i::natural) - 1"};
val size' = @{term "j::natural"};
val seed = @{term "s::Random.seed"};
val resultT = @{typ "(bool * term list) option"};
(** typ "'a => 'b" **)
type seed = Random_Engine.seed;
fun random_fun T1 T2 eq term_of random random_split seed =
let
val fun_upd = Const (@{const_name fun_upd},
(T1 --> T2) --> T1 --> T2 --> T1 --> T2);
val ((_, t2), seed') = random seed;
val (seed'', seed''') = random_split seed';
val state = Unsynchronized.ref (seed'', [], fn () => Abs ("x", T1, t2 ()));
fun random_fun' x =
let
val (seed, fun_map, f_t) = ! state;
in case AList.lookup (uncurry eq) fun_map x
of SOME y => y
| NONE => let
val t1 = term_of x;
val ((y, t2), seed') = random seed;
val fun_map' = (x, y) :: fun_map;
val f_t' = fn () => fun_upd $ f_t () $ t1 $ t2 ();
val _ = state := (seed', fun_map', f_t');
in y end
end;
fun term_fun' () = #3 (! state) ();
in ((random_fun', term_fun'), seed''') end;
(** datatypes **)
(* definitional scheme for random instances on datatypes *)
local
fun dest_ctyp_nth k cT = nth (Thm.dest_ctyp cT) k;
val eq = Thm.cprop_of @{thm random_aux_rec} |> Thm.dest_arg |> Thm.dest_arg |> Thm.dest_arg;
val lhs = eq |> Thm.dest_arg1;
val pt_random_aux = lhs |> Thm.dest_fun;
val pt_rhs = eq |> Thm.dest_arg |> Thm.dest_fun;
val aT = pt_random_aux |> Thm.ctyp_of_term |> dest_ctyp_nth 1;
val rew_thms = map mk_meta_eq [@{thm natural_zero_minus_one},
@{thm Suc_natural_minus_one}, @{thm select_weight_cons_zero}, @{thm beyond_zero}];
val rew_ts = map (Logic.dest_equals o Thm.prop_of) rew_thms;
val rew_ss = simpset_of (put_simpset HOL_ss @{context} addsimps rew_thms);
in
fun random_aux_primrec eq lthy =
let
val thy = Proof_Context.theory_of lthy;
val ((t_random_aux as Free (random_aux, T)) $ (t_k as Free (v, _)), proto_t_rhs) =
(HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
val Type (_, [_, iT]) = T;
val icT = Thm.ctyp_of thy iT;
val cert = Thm.cterm_of thy;
val inst = Thm.instantiate_cterm ([(aT, icT)], []);
fun subst_v t' = map_aterms (fn t as Free (w, _) => if v = w then t' else t | t => t);
val t_rhs = lambda t_k proto_t_rhs;
val eqs0 = [subst_v @{term "0::natural"} eq,
subst_v (@{const Code_Numeral.Suc} $ t_k) eq];
val eqs1 = map (Pattern.rewrite_term thy rew_ts []) eqs0;
val ((_, (_, eqs2)), lthy') = BNF_LFP_Compat.add_primrec_simple
[((Binding.conceal (Binding.name random_aux), T), NoSyn)] eqs1 lthy;
val cT_random_aux = inst pt_random_aux;
val cT_rhs = inst pt_rhs;
val rule = @{thm random_aux_rec}
|> Drule.instantiate_normalize ([(aT, icT)],
[(cT_random_aux, cert t_random_aux), (cT_rhs, cert t_rhs)]);
fun tac ctxt =
ALLGOALS (rtac rule)
THEN ALLGOALS (simp_tac (put_simpset rew_ss ctxt))
THEN (ALLGOALS (Proof_Context.fact_tac ctxt eqs2))
val simp = Goal.prove_sorry lthy' [v] [] eq (tac o #context);
in (simp, lthy') end;
end;
fun random_aux_primrec_multi auxname [eq] lthy =
lthy
|> random_aux_primrec eq
|>> (fn simp => [simp])
| random_aux_primrec_multi auxname (eqs as _ :: _ :: _) lthy =
let
val thy = Proof_Context.theory_of lthy;
val (lhss, rhss) = map_split (HOLogic.dest_eq o HOLogic.dest_Trueprop) eqs;
val (vs, (arg as Free (v, _)) :: _) = map_split (fn (t1 $ t2) => (t1, t2)) lhss;
val Ts = map fastype_of lhss;
val tupleT = foldr1 HOLogic.mk_prodT Ts;
val aux_lhs = Free ("mutual_" ^ auxname, fastype_of arg --> tupleT) $ arg;
val aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
(aux_lhs, foldr1 HOLogic.mk_prod rhss);
fun mk_proj t [T] = [t]
| mk_proj t (Ts as T :: (Ts' as _ :: _)) =
Const (@{const_name fst}, foldr1 HOLogic.mk_prodT Ts --> T) $ t
:: mk_proj (Const (@{const_name snd},
foldr1 HOLogic.mk_prodT Ts --> foldr1 HOLogic.mk_prodT Ts') $ t) Ts';
val projs = mk_proj (aux_lhs) Ts;
val proj_eqs = map2 (fn v => fn proj => (v, lambda arg proj)) vs projs;
val proj_defs = map2 (fn Free (name, _) => fn (_, rhs) =>
((Binding.conceal (Binding.name name), NoSyn),
(apfst Binding.conceal Attrib.empty_binding, rhs))) vs proj_eqs;
val aux_eq' = Pattern.rewrite_term thy proj_eqs [] aux_eq;
fun prove_eqs aux_simp proj_defs lthy =
let
val proj_simps = map (snd o snd) proj_defs;
fun tac { context = ctxt, prems = _ } =
ALLGOALS (simp_tac (put_simpset HOL_ss ctxt addsimps proj_simps))
THEN ALLGOALS (EqSubst.eqsubst_tac ctxt [0] [aux_simp])
THEN ALLGOALS (simp_tac
(put_simpset HOL_ss ctxt addsimps [@{thm fst_conv}, @{thm snd_conv}]));
in (map (fn prop => Goal.prove_sorry lthy [v] [] prop tac) eqs, lthy) end;
in
lthy
|> random_aux_primrec aux_eq'
||>> fold_map Local_Theory.define proj_defs
|-> (fn (aux_simp, proj_defs) => prove_eqs aux_simp proj_defs)
end;
fun random_aux_specification prfx name eqs lthy =
let
val vs = fold Term.add_free_names ((snd o strip_comb o fst o HOLogic.dest_eq
o HOLogic.dest_Trueprop o hd) eqs) [];
fun mk_proto_eq eq =
let
val (head $ t $ u, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
in ((HOLogic.mk_Trueprop o HOLogic.mk_eq) (head, lambda t (lambda u rhs))) end;
val proto_eqs = map mk_proto_eq eqs;
fun prove_simps proto_simps lthy =
let
val ext_simps = map (fn thm => fun_cong OF [fun_cong OF [thm]]) proto_simps;
val tac = ALLGOALS (Proof_Context.fact_tac lthy ext_simps);
in (map (fn prop => Goal.prove_sorry lthy vs [] prop (K tac)) eqs, lthy) end;
val b = Binding.conceal (Binding.qualify true prfx
(Binding.qualify true name (Binding.name "simps")));
in
lthy
|> random_aux_primrec_multi (name ^ prfx) proto_eqs
|-> (fn proto_simps => prove_simps proto_simps)
|-> (fn simps => Local_Theory.note
((b, Code.add_default_eqn_attrib :: @{attributes [simp, nitpick_simp]}), simps))
|> snd
end
(* constructing random instances on datatypes *)
val random_auxN = "random_aux";
fun mk_random_aux_eqs thy descr vs (names, auxnames) (Ts, Us) =
let
val mk_const = curry (Sign.mk_const thy);
val random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames);
val rTs = Ts @ Us;
fun random_resultT T = @{typ Random.seed}
--> HOLogic.mk_prodT (termifyT T,@{typ Random.seed});
fun sizeT T = @{typ natural} --> @{typ natural} --> T;
val random_auxT = sizeT o random_resultT;
val random_auxs = map2 (fn s => fn rT => Free (s, random_auxT rT))
random_auxsN rTs;
fun mk_random_call T = (NONE, (HOLogic.mk_random T size', T));
fun mk_random_aux_call fTs (k, _) (tyco, Ts) =
let
val T = Type (tyco, Ts);
fun mk_random_fun_lift [] t = t
| mk_random_fun_lift (fT :: fTs) t =
mk_const @{const_name random_fun_lift} [fTs ---> T, fT] $
mk_random_fun_lift fTs t;
val t = mk_random_fun_lift fTs (nth random_auxs k $ size_pred $ size');
val size = Option.map snd (Old_Datatype_Aux.find_shortest_path descr k)
|> the_default 0;
in (SOME size, (t, fTs ---> T)) end;
val tss = Old_Datatype_Aux.interpret_construction descr vs
{ atyp = mk_random_call, dtyp = mk_random_aux_call };
fun mk_consexpr simpleT (c, xs) =
let
val (ks, simple_tTs) = split_list xs;
val T = termifyT simpleT;
val tTs = (map o apsnd) termifyT simple_tTs;
val is_rec = exists is_some ks;
val k = fold (fn NONE => I | SOME k => Integer.max k) ks 0;
val vs = Name.invent_names Name.context "x" (map snd simple_tTs);
val tc = HOLogic.mk_return T @{typ Random.seed}
(HOLogic.mk_valtermify_app c vs simpleT);
val t = HOLogic.mk_ST
(map2 (fn (t, _) => fn (v, T') => ((t, @{typ Random.seed}), SOME ((v, termifyT T')))) tTs vs)
tc @{typ Random.seed} (SOME T, @{typ Random.seed});
val tk = if is_rec
then if k = 0 then size
else @{term "Quickcheck_Random.beyond :: natural \<Rightarrow> natural \<Rightarrow> natural"}
$ HOLogic.mk_number @{typ natural} k $ size
else @{term "1::natural"}
in (is_rec, HOLogic.mk_prod (tk, t)) end;
fun sort_rec xs =
map_filter (fn (true, t) => SOME t | _ => NONE) xs
@ map_filter (fn (false, t) => SOME t | _ => NONE) xs;
val gen_exprss = tss
|> (map o apfst) Type
|> map (fn (T, cs) => (T, (sort_rec o map (mk_consexpr T)) cs));
fun mk_select (rT, xs) =
mk_const @{const_name Quickcheck_Random.collapse} [@{typ Random.seed}, termifyT rT]
$ (mk_const @{const_name Random.select_weight} [random_resultT rT]
$ HOLogic.mk_list (HOLogic.mk_prodT (@{typ natural}, random_resultT rT)) xs)
$ seed;
val auxs_lhss = map (fn t => t $ size $ size' $ seed) random_auxs;
val auxs_rhss = map mk_select gen_exprss;
in (random_auxs, auxs_lhss ~~ auxs_rhss) end;
fun instantiate_random_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
let
val _ = Old_Datatype_Aux.message config "Creating quickcheck generators ...";
val mk_prop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
fun mk_size_arg k = case Old_Datatype_Aux.find_shortest_path descr k
of SOME (_, l) => if l = 0 then size
else @{term "max :: natural \<Rightarrow> natural \<Rightarrow> natural"}
$ HOLogic.mk_number @{typ natural} l $ size
| NONE => size;
val (random_auxs, auxs_eqs) = (apsnd o map) mk_prop_eq
(mk_random_aux_eqs thy descr vs (names, auxnames) (Ts, Us));
val random_defs = map_index (fn (k, T) => mk_prop_eq
(HOLogic.mk_random T size, nth random_auxs k $ mk_size_arg k $ size)) Ts;
in
thy
|> Class.instantiation (tycos, vs, @{sort random})
|> random_aux_specification prfx random_auxN auxs_eqs
|> `(fn lthy => map (Syntax.check_term lthy) random_defs)
|-> (fn random_defs' => fold_map (fn random_def =>
Specification.definition (NONE, (apfst Binding.conceal
Attrib.empty_binding, random_def))) random_defs')
|> snd
|> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
end;
(** building and compiling generator expressions **)
(* FIXME just one data slot (record) per program unit *)
structure Counterexample = Proof_Data
(
type T = unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> seed -> (bool * term list) option * seed
(* FIXME avoid user error with non-user text *)
fun init _ () = error "Counterexample"
);
val put_counterexample = Counterexample.put;
structure Counterexample_Report = Proof_Data
(
type T = unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> seed -> ((bool * term list) option * (bool list * bool)) * seed
(* FIXME avoid user error with non-user text *)
fun init _ () = error "Counterexample_Report"
);
val put_counterexample_report = Counterexample_Report.put;
val target = "Quickcheck";
fun mk_generator_expr ctxt (t, _) =
let
val thy = Proof_Context.theory_of ctxt
val prop = fold_rev absfree (Term.add_frees t []) t
val Ts = (map snd o fst o strip_abs) prop
val bound_max = length Ts - 1;
val bounds = map_index (fn (i, ty) =>
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
val ([genuine_only_name], _) = Variable.variant_fixes ["genuine_only"] ctxt
val genuine_only = Free (genuine_only_name, @{typ bool})
val none_t = Const (@{const_name "None"}, resultT)
val check = Quickcheck_Common.mk_safe_if genuine_only none_t (result, none_t,
fn genuine => @{term "Some :: bool * term list => (bool * term list) option"} $
HOLogic.mk_prod (Quickcheck_Common.reflect_bool genuine, terms))
val return = HOLogic.pair_const resultT @{typ Random.seed};
fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"});
fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
fun mk_split T = Sign.mk_const thy
(@{const_name case_prod}, [T, @{typ "unit => term"}, liftT resultT @{typ Random.seed}]);
fun mk_scomp_split T t t' =
mk_scomp (mk_termtyp T) resultT @{typ Random.seed} t
(mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t')));
fun mk_bindclause (_, _, i, T) = mk_scomp_split T
(Sign.mk_const thy (@{const_name Quickcheck_Random.random}, [T]) $ Bound i);
in
lambda genuine_only
(Abs ("n", @{typ natural}, fold_rev mk_bindclause bounds (return $ check true)))
end;
fun mk_reporting_generator_expr ctxt (t, _) =
let
val thy = Proof_Context.theory_of ctxt
val resultT = @{typ "(bool * term list) option * (bool list * bool)"}
val prop = fold_rev absfree (Term.add_frees t []) t
val Ts = (map snd o fst o strip_abs) prop
val bound_max = length Ts - 1
val bounds = map_index (fn (i, ty) =>
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
val prop' = betapplys (prop, map (fn (i, _, _, _) => Bound i) bounds);
val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds)
val (assms, concl) = Quickcheck_Common.strip_imp prop'
val return = HOLogic.pair_const resultT @{typ Random.seed};
fun mk_assms_report i =
HOLogic.mk_prod (@{term "None :: (bool * term list) option"},
HOLogic.mk_prod (HOLogic.mk_list HOLogic.boolT
(replicate i @{term True} @ replicate (length assms - i) @{term False}),
@{term False}))
fun mk_concl_report b =
HOLogic.mk_prod (HOLogic.mk_list HOLogic.boolT (replicate (length assms) @{term True}),
Quickcheck_Common.reflect_bool b)
val ([genuine_only_name], _) = Variable.variant_fixes ["genuine_only"] ctxt
val genuine_only = Free (genuine_only_name, @{typ bool})
val none_t = HOLogic.mk_prod (@{term "None :: (bool * term list) option"}, mk_concl_report true)
val concl_check = Quickcheck_Common.mk_safe_if genuine_only none_t (concl, none_t,
fn genuine => HOLogic.mk_prod (@{term "Some :: bool * term list => (bool * term list) option"} $
HOLogic.mk_prod (Quickcheck_Common.reflect_bool genuine, terms), mk_concl_report false))
val check = fold_rev (fn (i, assm) => fn t => Quickcheck_Common.mk_safe_if genuine_only
(mk_assms_report i) (HOLogic.mk_not assm, mk_assms_report i, t))
(map_index I assms) concl_check
fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"});
fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
fun mk_split T = Sign.mk_const thy
(@{const_name case_prod}, [T, @{typ "unit => term"}, liftT resultT @{typ Random.seed}]);
fun mk_scomp_split T t t' =
mk_scomp (mk_termtyp T) resultT @{typ Random.seed} t
(mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t')));
fun mk_bindclause (_, _, i, T) = mk_scomp_split T
(Sign.mk_const thy (@{const_name Quickcheck_Random.random}, [T]) $ Bound i);
in
lambda genuine_only
(Abs ("n", @{typ natural}, fold_rev mk_bindclause bounds (return $ check true)))
end
val mk_parametric_generator_expr = Quickcheck_Common.gen_mk_parametric_generator_expr
((mk_generator_expr,
absdummy @{typ bool} (absdummy @{typ natural}
@{term "Pair None :: Random.seed => (bool * term list) option * Random.seed"})),
@{typ "bool => natural => Random.seed => (bool * term list) option * Random.seed"})
val mk_parametric_reporting_generator_expr = Quickcheck_Common.gen_mk_parametric_generator_expr
((mk_reporting_generator_expr,
absdummy @{typ bool} (absdummy @{typ natural}
@{term "Pair (None, ([], False)) :: Random.seed =>
((bool * term list) option * (bool list * bool)) * Random.seed"})),
@{typ "bool => natural => Random.seed => ((bool * term list) option * (bool list * bool)) * Random.seed"})
(* single quickcheck report *)
datatype single_report = Run of bool list * bool | MatchExc
fun collect_single_report single_report
(Quickcheck.Report {iterations = iterations, raised_match_errors = raised_match_errors,
satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =
case single_report
of MatchExc =>
Quickcheck.Report {iterations = iterations + 1, raised_match_errors = raised_match_errors + 1,
satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}
| Run (assms, concl) =>
Quickcheck.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}
val empty_report = Quickcheck.Report { iterations = 0, raised_match_errors = 0,
satisfied_assms = [], positive_concl_tests = 0 }
fun compile_generator_expr_raw ctxt ts =
let
val iterations = Config.get ctxt Quickcheck.iterations
in
if Config.get ctxt Quickcheck.report then
let
val t' = mk_parametric_reporting_generator_expr ctxt ts;
val compile = Code_Runtime.dynamic_value_strict
(Counterexample_Report.get, put_counterexample_report, "Random_Generators.put_counterexample_report")
ctxt (SOME target)
(fn proc => fn g => fn c => fn b => fn s => g c b s
#>> (apfst o Option.map o apsnd o map) proc) t' [];
fun single_tester c b s = compile c b s |> Random_Engine.run
fun iterate_and_collect _ _ 0 report = (NONE, report)
| iterate_and_collect genuine_only (card, size) j report =
let
val (test_result, single_report) = apsnd Run (single_tester card genuine_only size)
val report = collect_single_report single_report report
in
case test_result of NONE => iterate_and_collect genuine_only (card, size) (j - 1) report
| SOME q => (SOME q, report)
end
in
fn genuine_only => fn [card, size] =>
apsnd SOME (iterate_and_collect genuine_only (card, size) iterations empty_report)
end
else
let
val t' = mk_parametric_generator_expr ctxt ts;
val compile = Code_Runtime.dynamic_value_strict
(Counterexample.get, put_counterexample, "Random_Generators.put_counterexample")
ctxt (SOME target)
(fn proc => fn g => fn c => fn b => fn s => g c b s
#>> (Option.map o apsnd o map) proc) t' [];
fun single_tester c b s = compile c b s |> Random_Engine.run
fun iterate _ _ 0 = NONE
| iterate genuine_only (card, size) j =
case single_tester card genuine_only size of
NONE => iterate genuine_only (card, size) (j - 1)
| SOME q => SOME q
in
fn genuine_only => fn [card, size] =>
(rpair NONE (iterate genuine_only (card, size) iterations))
end
end;
fun compile_generator_expr ctxt ts =
let
val compiled = compile_generator_expr_raw ctxt ts
in fn genuine_only => fn [card, size] =>
compiled genuine_only [Code_Numeral.natural_of_integer card, Code_Numeral.natural_of_integer size]
end;
val size_types = [@{type_name Enum.finite_1}, @{type_name Enum.finite_2},
@{type_name Enum.finite_3}, @{type_name Enum.finite_4}, @{type_name Enum.finite_5}];
fun size_matters_for _ Ts =
not (forall (fn Type (tyco, []) => member (op =) size_types tyco | _ => false) Ts);
val test_goals =
Quickcheck_Common.generator_test_goal_terms ("random", (size_matters_for, compile_generator_expr));
(** setup **)
val active = Attrib.setup_config_bool @{binding quickcheck_random_active} (K false);
val setup =
Quickcheck_Common.datatype_interpretation random_plugin
(@{sort random}, instantiate_random_datatype)
#> Context.theory_map (Quickcheck.add_tester ("random", (active, test_goals)));
end;