primitive definitions of bot/top/inf/sup for bool and fun are named with canonical suffix `_def` rather than `_eq`
1 (* Title: HOL/Tools/quickcheck_generators.ML
2 Author: Florian Haftmann, TU Muenchen
4 Quickcheck generators for various types.
7 signature QUICKCHECK_GENERATORS =
9 type seed = Random_Engine.seed
10 val random_fun: typ -> typ -> ('a -> 'a -> bool) -> ('a -> term)
11 -> (seed -> ('b * (unit -> term)) * seed) -> (seed -> seed * seed)
12 -> seed -> (('a -> 'b) * (unit -> term)) * seed
13 val perhaps_constrain: theory -> (typ * sort) list -> (string * sort) list
14 -> (string * sort -> string * sort) option
15 val ensure_sort_datatype:
16 sort * (Datatype.config -> Datatype.descr -> (string * sort) list -> string list -> string ->
17 string list * string list -> typ list * typ list -> theory -> theory)
18 -> Datatype.config -> string list -> theory -> theory
19 val compile_generator_expr:
20 Proof.context -> term -> int -> term list option * Quickcheck.report option
21 val put_counterexample: (unit -> int -> seed -> term list option * seed)
22 -> Proof.context -> Proof.context
23 val put_counterexample_report: (unit -> int -> seed -> (term list option * (bool list * bool)) * seed)
24 -> Proof.context -> Proof.context
25 val setup: theory -> theory
28 structure Quickcheck_Generators : QUICKCHECK_GENERATORS =
31 (** abstract syntax **)
33 fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"})
34 val size = @{term "i::code_numeral"};
35 val size_pred = @{term "(i::code_numeral) - 1"};
36 val size' = @{term "j::code_numeral"};
37 val seed = @{term "s::Random.seed"};
40 (** typ "'a => 'b" **)
42 type seed = Random_Engine.seed;
44 fun random_fun T1 T2 eq term_of random random_split seed =
46 val fun_upd = Const (@{const_name fun_upd},
47 (T1 --> T2) --> T1 --> T2 --> T1 --> T2);
48 val ((y, t2), seed') = random seed;
49 val (seed'', seed''') = random_split seed';
51 val state = Unsynchronized.ref (seed'', [], fn () => Abs ("x", T1, t2 ()));
54 val (seed, fun_map, f_t) = ! state;
55 in case AList.lookup (uncurry eq) fun_map x
59 val ((y, t2), seed') = random seed;
60 val fun_map' = (x, y) :: fun_map;
61 val f_t' = fn () => fun_upd $ f_t () $ t1 $ t2 ();
62 val _ = state := (seed', fun_map', f_t');
65 fun term_fun' () = #3 (! state) ();
66 in ((random_fun', term_fun'), seed''') end;
71 (* definitional scheme for random instances on datatypes *)
75 fun dest_ctyp_nth k cT = nth (Thm.dest_ctyp cT) k;
76 val eq = Thm.cprop_of @{thm random_aux_rec} |> Thm.dest_arg |> Thm.dest_arg |> Thm.dest_arg;
77 val lhs = eq |> Thm.dest_arg1;
78 val pt_random_aux = lhs |> Thm.dest_fun;
79 val ct_k = lhs |> Thm.dest_arg;
80 val pt_rhs = eq |> Thm.dest_arg |> Thm.dest_fun;
81 val aT = pt_random_aux |> Thm.ctyp_of_term |> dest_ctyp_nth 1;
83 val rew_thms = map mk_meta_eq [@{thm code_numeral_zero_minus_one},
84 @{thm Suc_code_numeral_minus_one}, @{thm select_weight_cons_zero}, @{thm beyond_zero}];
85 val rew_ts = map (Logic.dest_equals o Thm.prop_of) rew_thms;
86 val rew_ss = HOL_ss addsimps rew_thms;
90 fun random_aux_primrec eq lthy =
92 val thy = ProofContext.theory_of lthy;
93 val ((t_random_aux as Free (random_aux, T)) $ (t_k as Free (v, _)), proto_t_rhs) =
94 (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
95 val Type (_, [_, iT]) = T;
96 val icT = Thm.ctyp_of thy iT;
97 val cert = Thm.cterm_of thy;
98 val inst = Thm.instantiate_cterm ([(aT, icT)], []);
99 fun subst_v t' = map_aterms (fn t as Free (w, _) => if v = w then t' else t | t => t);
100 val t_rhs = lambda t_k proto_t_rhs;
101 val eqs0 = [subst_v @{term "0::code_numeral"} eq,
102 subst_v (@{term "Suc_code_numeral"} $ t_k) eq];
103 val eqs1 = map (Pattern.rewrite_term thy rew_ts []) eqs0;
104 val ((_, (_, eqs2)), lthy') = Primrec.add_primrec_simple
105 [((Binding.conceal (Binding.name random_aux), T), NoSyn)] eqs1 lthy;
106 val cT_random_aux = inst pt_random_aux;
107 val cT_rhs = inst pt_rhs;
108 val rule = @{thm random_aux_rec}
109 |> Drule.instantiate ([(aT, icT)],
110 [(cT_random_aux, cert t_random_aux), (cT_rhs, cert t_rhs)]);
111 val tac = ALLGOALS (rtac rule)
112 THEN ALLGOALS (simp_tac rew_ss)
113 THEN (ALLGOALS (ProofContext.fact_tac eqs2))
114 val simp = Skip_Proof.prove lthy' [v] [] eq (K tac);
115 in (simp, lthy') end;
119 fun random_aux_primrec_multi auxname [eq] lthy =
121 |> random_aux_primrec eq
122 |>> (fn simp => [simp])
123 | random_aux_primrec_multi auxname (eqs as _ :: _ :: _) lthy =
125 val thy = ProofContext.theory_of lthy;
126 val (lhss, rhss) = map_split (HOLogic.dest_eq o HOLogic.dest_Trueprop) eqs;
127 val (vs, (arg as Free (v, _)) :: _) = map_split (fn (t1 $ t2) => (t1, t2)) lhss;
128 val Ts = map fastype_of lhss;
129 val tupleT = foldr1 HOLogic.mk_prodT Ts;
130 val aux_lhs = Free ("mutual_" ^ auxname, fastype_of arg --> tupleT) $ arg;
131 val aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
132 (aux_lhs, foldr1 HOLogic.mk_prod rhss);
133 fun mk_proj t [T] = [t]
134 | mk_proj t (Ts as T :: (Ts' as _ :: _)) =
135 Const (@{const_name fst}, foldr1 HOLogic.mk_prodT Ts --> T) $ t
136 :: mk_proj (Const (@{const_name snd},
137 foldr1 HOLogic.mk_prodT Ts --> foldr1 HOLogic.mk_prodT Ts') $ t) Ts';
138 val projs = mk_proj (aux_lhs) Ts;
139 val proj_eqs = map2 (fn v => fn proj => (v, lambda arg proj)) vs projs;
140 val proj_defs = map2 (fn Free (name, _) => fn (_, rhs) =>
141 ((Binding.conceal (Binding.name name), NoSyn),
142 (apfst Binding.conceal Attrib.empty_binding, rhs))) vs proj_eqs;
143 val aux_eq' = Pattern.rewrite_term thy proj_eqs [] aux_eq;
144 fun prove_eqs aux_simp proj_defs lthy =
146 val proj_simps = map (snd o snd) proj_defs;
147 fun tac { context = ctxt, prems = _ } =
148 ALLGOALS (simp_tac (HOL_ss addsimps proj_simps))
149 THEN ALLGOALS (EqSubst.eqsubst_tac ctxt [0] [aux_simp])
150 THEN ALLGOALS (simp_tac (HOL_ss addsimps [@{thm fst_conv}, @{thm snd_conv}]));
151 in (map (fn prop => Skip_Proof.prove lthy [v] [] prop tac) eqs, lthy) end;
154 |> random_aux_primrec aux_eq'
155 ||>> fold_map Local_Theory.define proj_defs
156 |-> (fn (aux_simp, proj_defs) => prove_eqs aux_simp proj_defs)
159 fun random_aux_specification prfx name eqs lthy =
161 val vs = fold Term.add_free_names ((snd o strip_comb o fst o HOLogic.dest_eq
162 o HOLogic.dest_Trueprop o hd) eqs) [];
165 val (head $ t $ u, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
166 in ((HOLogic.mk_Trueprop o HOLogic.mk_eq) (head, lambda t (lambda u rhs))) end;
167 val proto_eqs = map mk_proto_eq eqs;
168 fun prove_simps proto_simps lthy =
170 val ext_simps = map (fn thm => fun_cong OF [fun_cong OF [thm]]) proto_simps;
171 val tac = ALLGOALS (ProofContext.fact_tac ext_simps);
172 in (map (fn prop => Skip_Proof.prove lthy vs [] prop (K tac)) eqs, lthy) end;
173 val b = Binding.conceal (Binding.qualify true prfx
174 (Binding.qualify true name (Binding.name "simps")));
177 |> random_aux_primrec_multi (name ^ prfx) proto_eqs
178 |-> (fn proto_simps => prove_simps proto_simps)
179 |-> (fn simps => Local_Theory.note
180 ((b, Code.add_default_eqn_attrib :: map (Attrib.internal o K)
181 [Simplifier.simp_add, Nitpick_Simps.add]), simps))
186 (* constructing random instances on datatypes *)
188 val random_auxN = "random_aux";
190 fun mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us) =
192 val mk_const = curry (Sign.mk_const thy);
193 val random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames);
195 fun random_resultT T = @{typ Random.seed}
196 --> HOLogic.mk_prodT (termifyT T,@{typ Random.seed});
197 val pTs = map random_resultT rTs;
198 fun sizeT T = @{typ code_numeral} --> @{typ code_numeral} --> T;
199 val random_auxT = sizeT o random_resultT;
200 val random_auxs = map2 (fn s => fn rT => Free (s, random_auxT rT))
202 fun mk_random_call T = (NONE, (HOLogic.mk_random T size', T));
203 fun mk_random_aux_call fTs (k, _) (tyco, Ts) =
205 val T = Type (tyco, Ts);
206 fun mk_random_fun_lift [] t = t
207 | mk_random_fun_lift (fT :: fTs) t =
208 mk_const @{const_name random_fun_lift} [fTs ---> T, fT] $
209 mk_random_fun_lift fTs t;
210 val t = mk_random_fun_lift fTs (nth random_auxs k $ size_pred $ size');
211 val size = Option.map snd (Datatype_Aux.find_shortest_path descr k)
213 in (SOME size, (t, fTs ---> T)) end;
214 val tss = Datatype_Aux.interpret_construction descr vs
215 { atyp = mk_random_call, dtyp = mk_random_aux_call };
216 fun mk_consexpr simpleT (c, xs) =
218 val (ks, simple_tTs) = split_list xs;
219 val T = termifyT simpleT;
220 val tTs = (map o apsnd) termifyT simple_tTs;
221 val is_rec = exists is_some ks;
222 val k = fold (fn NONE => I | SOME k => Integer.max k) ks 0;
223 val vs = Name.names Name.context "x" (map snd simple_tTs);
224 val tc = HOLogic.mk_return T @{typ Random.seed}
225 (HOLogic.mk_valtermify_app c vs simpleT);
226 val t = HOLogic.mk_ST
227 (map2 (fn (t, _) => fn (v, T') => ((t, @{typ Random.seed}), SOME ((v, termifyT T')))) tTs vs)
228 tc @{typ Random.seed} (SOME T, @{typ Random.seed});
230 then if k = 0 then size
231 else @{term "Quickcheck.beyond :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"}
232 $ HOLogic.mk_number @{typ code_numeral} k $ size
233 else @{term "1::code_numeral"}
234 in (is_rec, HOLogic.mk_prod (tk, t)) end;
236 map_filter (fn (true, t) => SOME t | _ => NONE) xs
237 @ map_filter (fn (false, t) => SOME t | _ => NONE) xs;
239 |> (map o apfst) Type
240 |> map (fn (T, cs) => (T, (sort_rec o map (mk_consexpr T)) cs));
241 fun mk_select (rT, xs) =
242 mk_const @{const_name Quickcheck.collapse} [@{typ "Random.seed"}, termifyT rT]
243 $ (mk_const @{const_name Random.select_weight} [random_resultT rT]
244 $ HOLogic.mk_list (HOLogic.mk_prodT (@{typ code_numeral}, random_resultT rT)) xs)
246 val auxs_lhss = map (fn t => t $ size $ size' $ seed) random_auxs;
247 val auxs_rhss = map mk_select gen_exprss;
248 in (random_auxs, auxs_lhss ~~ auxs_rhss) end;
250 fun instantiate_random_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
252 val _ = Datatype_Aux.message config "Creating quickcheck generators ...";
253 val mk_prop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
254 fun mk_size_arg k = case Datatype_Aux.find_shortest_path descr k
255 of SOME (_, l) => if l = 0 then size
256 else @{term "max :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"}
257 $ HOLogic.mk_number @{typ code_numeral} l $ size
259 val (random_auxs, auxs_eqs) = (apsnd o map) mk_prop_eq
260 (mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us));
261 val random_defs = map_index (fn (k, T) => mk_prop_eq
262 (HOLogic.mk_random T size, nth random_auxs k $ mk_size_arg k $ size)) Ts;
265 |> Class.instantiation (tycos, vs, @{sort random})
266 |> random_aux_specification prfx random_auxN auxs_eqs
267 |> `(fn lthy => map (Syntax.check_term lthy) random_defs)
268 |-> (fn random_defs' => fold_map (fn random_def =>
269 Specification.definition (NONE, (apfst Binding.conceal
270 Attrib.empty_binding, random_def))) random_defs')
272 |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
275 fun perhaps_constrain thy insts raw_vs =
277 fun meet (T, sort) = Sorts.meet_sort (Sign.classes_of thy)
278 (Logic.varifyT_global T, sort);
279 val vtab = Vartab.empty
280 |> fold (fn (v, sort) => Vartab.update ((v, 0), sort)) raw_vs
282 in SOME (fn (v, _) => (v, (the o Vartab.lookup vtab) (v, 0)))
283 end handle Sorts.CLASS_ERROR _ => NONE;
285 fun ensure_sort_datatype (sort, instantiate_datatype) config raw_tycos thy =
287 val algebra = Sign.classes_of thy;
288 val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) =
289 Datatype.the_descr thy raw_tycos;
290 val typerep_vs = (map o apsnd)
291 (curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs;
292 val sort_insts = (map (rpair sort) o flat o maps snd o maps snd)
293 (Datatype_Aux.interpret_construction descr typerep_vs
294 { atyp = single, dtyp = (K o K o K) [] });
295 val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd)
296 (Datatype_Aux.interpret_construction descr typerep_vs
297 { atyp = K [], dtyp = K o K });
298 val has_inst = exists (fn tyco =>
299 can (Sorts.mg_domain algebra tyco) sort) tycos;
300 in if has_inst then thy
301 else case perhaps_constrain thy (sort_insts @ term_of_insts) typerep_vs
302 of SOME constrain => instantiate_datatype config descr
303 (map constrain typerep_vs) tycos prfx (names, auxnames)
304 ((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy
308 (** building and compiling generator expressions **)
310 structure Counterexample = Proof_Data (
311 type T = unit -> int -> int * int -> term list option * (int * int)
312 fun init _ () = error "Counterexample"
314 val put_counterexample = Counterexample.put;
316 structure Counterexample_Report = Proof_Data (
317 type T = unit -> int -> seed -> (term list option * (bool list * bool)) * seed
318 fun init _ () = error "Counterexample_Report"
320 val put_counterexample_report = Counterexample_Report.put;
322 val target = "Quickcheck";
324 fun mk_generator_expr thy prop Ts =
326 val bound_max = length Ts - 1;
327 val bounds = map_index (fn (i, ty) =>
328 (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
329 val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
330 val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
331 val check = @{term "If :: bool => term list option => term list option => term list option"}
332 $ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option"} $ terms);
333 val return = @{term "Pair :: term list option => Random.seed => term list option * Random.seed"};
334 fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
335 fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"});
336 fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
337 liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
338 fun mk_split T = Sign.mk_const thy
339 (@{const_name prod_case}, [T, @{typ "unit => term"}, liftT @{typ "term list option"} @{typ Random.seed}]);
340 fun mk_scomp_split T t t' =
341 mk_scomp (mk_termtyp T) @{typ "term list option"} @{typ Random.seed} t
342 (mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t')));
343 fun mk_bindclause (_, _, i, T) = mk_scomp_split T
344 (Sign.mk_const thy (@{const_name Quickcheck.random}, [T]) $ Bound i);
345 in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) end;
347 fun mk_reporting_generator_expr thy prop Ts =
349 val bound_max = length Ts - 1;
350 val bounds = map_index (fn (i, ty) =>
351 (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
352 fun strip_imp (Const(@{const_name HOL.implies},_) $ A $ B) = apfst (cons A) (strip_imp B)
353 | strip_imp A = ([], A)
354 val prop' = betapplys (prop, map (fn (i, _, _, _) => Bound i) bounds);
355 val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds)
356 val (assms, concl) = strip_imp prop'
358 @{term "Pair :: term list option * (bool list * bool) => Random.seed => (term list option * (bool list * bool)) * Random.seed"};
359 fun mk_assms_report i =
360 HOLogic.mk_prod (@{term "None :: term list option"},
361 HOLogic.mk_prod (HOLogic.mk_list HOLogic.boolT
362 (replicate i @{term True} @ replicate (length assms - i) @{term False}),
364 fun mk_concl_report b =
365 HOLogic.mk_prod (HOLogic.mk_list HOLogic.boolT (replicate (length assms) @{term True}),
366 if b then @{term True} else @{term False})
368 @{term "If :: bool => term list option * (bool list * bool) => term list option * (bool list * bool) => term list option * (bool list * bool)"}
369 val concl_check = If $ concl $
370 HOLogic.mk_prod (@{term "None :: term list option"}, mk_concl_report true) $
371 HOLogic.mk_prod (@{term "Some :: term list => term list option"} $ terms, mk_concl_report false)
372 val check = fold_rev (fn (i, assm) => fn t => If $ assm $ t $ mk_assms_report i)
373 (map_index I assms) concl_check
374 fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
375 fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"});
376 fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
377 liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
378 fun mk_split T = Sign.mk_const thy
379 (@{const_name prod_case}, [T, @{typ "unit => term"},
380 liftT @{typ "term list option * (bool list * bool)"} @{typ Random.seed}]);
381 fun mk_scomp_split T t t' =
382 mk_scomp (mk_termtyp T) @{typ "term list option * (bool list * bool)"} @{typ Random.seed} t
383 (mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t')));
384 fun mk_bindclause (_, _, i, T) = mk_scomp_split T
385 (Sign.mk_const thy (@{const_name Quickcheck.random}, [T]) $ Bound i);
387 Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check))
390 (* single quickcheck report *)
392 datatype single_report = Run of bool list * bool | MatchExc
394 fun collect_single_report single_report
395 (Quickcheck.Report {iterations = iterations, raised_match_errors = raised_match_errors,
396 satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}) =
399 Quickcheck.Report {iterations = iterations + 1, raised_match_errors = raised_match_errors + 1,
400 satisfied_assms = satisfied_assms, positive_concl_tests = positive_concl_tests}
401 | Run (assms, concl) =>
402 Quickcheck.Report {iterations = iterations + 1, raised_match_errors = raised_match_errors,
404 map2 (fn b => fn s => if b then s + 1 else s) assms
405 (if null satisfied_assms then replicate (length assms) 0 else satisfied_assms),
406 positive_concl_tests = if concl then positive_concl_tests + 1 else positive_concl_tests}
408 val empty_report = Quickcheck.Report { iterations = 0, raised_match_errors = 0,
409 satisfied_assms = [], positive_concl_tests = 0 }
411 fun compile_generator_expr ctxt t =
413 val Ts = (map snd o fst o strip_abs) t;
414 val thy = ProofContext.theory_of ctxt
415 val iterations = Config.get ctxt Quickcheck.iterations
417 if Config.get ctxt Quickcheck.report then
419 val t' = mk_reporting_generator_expr thy t Ts;
420 val compile = Code_Runtime.dynamic_value_strict
421 (Counterexample_Report.get, put_counterexample_report, "Quickcheck_Generators.put_counterexample_report")
422 thy (SOME target) (fn proc => fn g => fn s => g s #>> (apfst o Option.map o map) proc) t' [];
423 val single_tester = compile #> Random_Engine.run
424 fun iterate_and_collect size 0 report = (NONE, report)
425 | iterate_and_collect size j report =
427 val (test_result, single_report) = apsnd Run (single_tester size) handle Match =>
428 (if Config.get ctxt Quickcheck.quiet then ()
429 else warning "Exception Match raised during quickcheck"; (NONE, MatchExc))
430 val report = collect_single_report single_report report
432 case test_result of NONE => iterate_and_collect size (j - 1) report
433 | SOME q => (SOME q, report)
436 fn size => apsnd SOME (iterate_and_collect size iterations empty_report)
440 val t' = mk_generator_expr thy t Ts;
441 val compile = Code_Runtime.dynamic_value_strict
442 (Counterexample.get, put_counterexample, "Quickcheck_Generators.put_counterexample")
443 thy (SOME target) (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) t' [];
444 val single_tester = compile #> Random_Engine.run
445 fun iterate size 0 = NONE
448 val result = single_tester size handle Match =>
449 (if Config.get ctxt Quickcheck.quiet then ()
450 else warning "Exception Match raised during quickcheck"; NONE)
452 case result of NONE => iterate size (j - 1) | SOME q => SOME q
455 fn size => (rpair NONE (iterate size iterations))
463 Datatype.interpretation (ensure_sort_datatype (@{sort random}, instantiate_random_datatype))
464 #> Code_Target.extend_target (target, (Code_Runtime.target, K I))
465 #> Context.theory_map
466 (Quickcheck.add_generator ("random", compile_generator_expr));