src/HOL/Tools/quickcheck_generators.ML
author wenzelm
Wed Oct 28 16:28:12 2009 +0100 (2009-10-28)
changeset 33280 e3eaeba6ae28
parent 33243 17014b1b9353
child 33552 506f80a9afe8
permissions -rw-r--r--
tuned;
     1 (* Author: Florian Haftmann, TU Muenchen
     2 
     3 Quickcheck generators for various types.
     4 *)
     5 
     6 signature QUICKCHECK_GENERATORS =
     7 sig
     8   type seed = Random_Engine.seed
     9   val random_fun: typ -> typ -> ('a -> 'a -> bool) -> ('a -> term)
    10     -> (seed -> ('b * (unit -> term)) * seed) -> (seed -> seed * seed)
    11     -> seed -> (('a -> 'b) * (unit -> term)) * seed
    12   val ensure_random_typecopy: string -> theory -> theory
    13   val random_aux_specification: string -> string -> term list -> local_theory -> local_theory
    14   val mk_random_aux_eqs: theory -> Datatype.descr -> (string * sort) list
    15     -> string list -> string list * string list -> typ list * typ list
    16     -> term list * (term * term) list
    17   val ensure_random_datatype: Datatype.config -> string list -> theory -> theory
    18   val compile_generator_expr: theory -> term -> int -> term list option
    19   val eval_ref: (unit -> int -> seed -> term list option * seed) option Unsynchronized.ref
    20   val setup: theory -> theory
    21 end;
    22 
    23 structure Quickcheck_Generators : QUICKCHECK_GENERATORS =
    24 struct
    25 
    26 (** abstract syntax **)
    27 
    28 fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"})
    29 val size = @{term "i::code_numeral"};
    30 val size_pred = @{term "(i::code_numeral) - 1"};
    31 val size' = @{term "j::code_numeral"};
    32 val seed = @{term "s::Random.seed"};
    33 
    34 
    35 (** typ "'a => 'b" **)
    36 
    37 type seed = Random_Engine.seed;
    38 
    39 fun random_fun T1 T2 eq term_of random random_split seed =
    40   let
    41     val fun_upd = Const (@{const_name fun_upd},
    42       (T1 --> T2) --> T1 --> T2 --> T1 --> T2);
    43     val ((y, t2), seed') = random seed;
    44     val (seed'', seed''') = random_split seed';
    45 
    46     val state = Unsynchronized.ref (seed'', [], fn () => Abs ("x", T1, t2 ()));
    47     fun random_fun' x =
    48       let
    49         val (seed, fun_map, f_t) = ! state;
    50       in case AList.lookup (uncurry eq) fun_map x
    51        of SOME y => y
    52         | NONE => let
    53               val t1 = term_of x;
    54               val ((y, t2), seed') = random seed;
    55               val fun_map' = (x, y) :: fun_map;
    56               val f_t' = fn () => fun_upd $ f_t () $ t1 $ t2 ();
    57               val _ = state := (seed', fun_map', f_t');
    58             in y end
    59       end;
    60     fun term_fun' () = #3 (! state) ();
    61   in ((random_fun', term_fun'), seed''') end;
    62 
    63 
    64 (** type copies **)
    65 
    66 fun mk_random_typecopy tyco vs constr T' thy =
    67   let
    68     val Ts = map TFree vs;  
    69     val T = Type (tyco, Ts);
    70     val Tm = termifyT T;
    71     val Tm' = termifyT T';
    72     fun mk_const c Ts = Const (c, Sign.const_instance thy (c, Ts));
    73     val v = "x";
    74     val t_v = Free (v, Tm');
    75     val t_constr = mk_const constr Ts;
    76     val lhs = HOLogic.mk_random T size;
    77     val rhs = HOLogic.mk_ST [((HOLogic.mk_random T' size, @{typ Random.seed}), SOME (v, Tm'))]
    78       (HOLogic.mk_return Tm @{typ Random.seed}
    79       (mk_const "Code_Evaluation.valapp" [T', T]
    80         $ HOLogic.mk_prod (t_constr, Abs ("u", @{typ unit}, HOLogic.reflect_term t_constr)) $ t_v))
    81       @{typ Random.seed} (SOME Tm, @{typ Random.seed});
    82     val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
    83   in   
    84     thy
    85     |> TheoryTarget.instantiation ([tyco], vs, @{sort random})
    86     |> `(fn lthy => Syntax.check_term lthy eq)
    87     |-> (fn eq => Specification.definition (NONE, (apfst Binding.conceal Attrib.empty_binding, eq)))
    88     |> snd
    89     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
    90   end;
    91 
    92 fun ensure_random_typecopy tyco thy =
    93   let
    94     val SOME { vs = raw_vs, constr, typ = raw_T, ... } =
    95       Typecopy.get_info thy tyco;
    96     val constrain = curry (Sorts.inter_sort (Sign.classes_of thy));
    97     val T = map_atyps (fn TFree (v, sort) =>
    98       TFree (v, constrain sort @{sort random})) raw_T;
    99     val vs' = Term.add_tfreesT T [];
   100     val vs = map (fn (v, sort) =>
   101       (v, the_default (constrain sort @{sort typerep}) (AList.lookup (op =) vs' v))) raw_vs;
   102     val can_inst = Sign.of_sort thy (T, @{sort random});
   103   in if can_inst then mk_random_typecopy tyco vs constr T thy else thy end;
   104 
   105 
   106 (** datatypes **)
   107 
   108 (* definitional scheme for random instances on datatypes *)
   109 
   110 (*FIXME avoid this low-level proving*)
   111 local
   112 
   113 fun dest_ctyp_nth k cT = nth (Thm.dest_ctyp cT) k;
   114 val eq = Thm.cprop_of @{thm random_aux_rec} |> Thm.dest_arg |> Thm.dest_arg |> Thm.dest_arg;
   115 val lhs = eq |> Thm.dest_arg1;
   116 val pt_random_aux = lhs |> Thm.dest_fun;
   117 val ct_k = lhs |> Thm.dest_arg;
   118 val pt_rhs = eq |> Thm.dest_arg |> Thm.dest_fun;
   119 val aT = pt_random_aux |> Thm.ctyp_of_term |> dest_ctyp_nth 1;
   120 
   121 val rew_thms = map mk_meta_eq [@{thm code_numeral_zero_minus_one},
   122   @{thm Suc_code_numeral_minus_one}, @{thm select_weight_cons_zero}, @{thm beyond_zero}];
   123 val rew_ts = map (Logic.dest_equals o Thm.prop_of) rew_thms;
   124 val rew_ss = HOL_ss addsimps rew_thms;
   125 
   126 in
   127 
   128 fun random_aux_primrec eq lthy =
   129   let
   130     val thy = ProofContext.theory_of lthy;
   131     val ((t_random_aux as Free (random_aux, T)) $ (t_k as Free (v, _)), proto_t_rhs) =
   132       (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
   133     val Type (_, [_, iT]) = T;
   134     val icT = Thm.ctyp_of thy iT;
   135     val cert = Thm.cterm_of thy;
   136     val inst = Thm.instantiate_cterm ([(aT, icT)], []);
   137     fun subst_v t' = map_aterms (fn t as Free (w, _) => if v = w then t' else t | t => t);
   138     val t_rhs = lambda t_k proto_t_rhs;
   139     val eqs0 = [subst_v @{term "0::code_numeral"} eq,
   140       subst_v (@{term "Suc_code_numeral"} $ t_k) eq];
   141     val eqs1 = map (Pattern.rewrite_term thy rew_ts []) eqs0;
   142     val ((_, eqs2), lthy') = Primrec.add_primrec_simple
   143       [((Binding.conceal (Binding.name random_aux), T), NoSyn)] eqs1 lthy;
   144     val cT_random_aux = inst pt_random_aux;
   145     val cT_rhs = inst pt_rhs;
   146     val rule = @{thm random_aux_rec}
   147       |> Drule.instantiate ([(aT, icT)],
   148            [(cT_random_aux, cert t_random_aux), (cT_rhs, cert t_rhs)]);
   149     val tac = ALLGOALS (rtac rule)
   150       THEN ALLGOALS (simp_tac rew_ss)
   151       THEN (ALLGOALS (ProofContext.fact_tac (flat eqs2)))
   152     val simp = Skip_Proof.prove lthy' [v] [] eq (K tac);
   153   in (simp, lthy') end;
   154 
   155 end;
   156 
   157 fun random_aux_primrec_multi auxname [eq] lthy =
   158       lthy
   159       |> random_aux_primrec eq
   160       |>> (fn simp => [simp])
   161   | random_aux_primrec_multi auxname (eqs as _ :: _ :: _) lthy =
   162       let
   163         val thy = ProofContext.theory_of lthy;
   164         val (lhss, rhss) = map_split (HOLogic.dest_eq o HOLogic.dest_Trueprop) eqs;
   165         val (vs, (arg as Free (v, _)) :: _) = map_split (fn (t1 $ t2) => (t1, t2)) lhss;
   166         val Ts = map fastype_of lhss;
   167         val tupleT = foldr1 HOLogic.mk_prodT Ts;
   168         val aux_lhs = Free ("mutual_" ^ auxname, fastype_of arg --> tupleT) $ arg;
   169         val aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
   170           (aux_lhs, foldr1 HOLogic.mk_prod rhss);
   171         fun mk_proj t [T] = [t]
   172           | mk_proj t (Ts as T :: (Ts' as _ :: _)) =
   173               Const (@{const_name fst}, foldr1 HOLogic.mk_prodT Ts --> T) $ t
   174                 :: mk_proj (Const (@{const_name snd},
   175                   foldr1 HOLogic.mk_prodT Ts --> foldr1 HOLogic.mk_prodT Ts') $ t) Ts';
   176         val projs = mk_proj (aux_lhs) Ts;
   177         val proj_eqs = map2 (fn v => fn proj => (v, lambda arg proj)) vs projs;
   178         val proj_defs = map2 (fn Free (name, _) => fn (_, rhs) =>
   179           ((Binding.conceal (Binding.name name), NoSyn),
   180             (apfst Binding.conceal Attrib.empty_binding, rhs))) vs proj_eqs;
   181         val aux_eq' = Pattern.rewrite_term thy proj_eqs [] aux_eq;
   182         fun prove_eqs aux_simp proj_defs lthy = 
   183           let
   184             val proj_simps = map (snd o snd) proj_defs;
   185             fun tac { context = ctxt, prems = _ } =
   186               ALLGOALS (simp_tac (HOL_ss addsimps proj_simps))
   187               THEN ALLGOALS (EqSubst.eqsubst_tac ctxt [0] [aux_simp])
   188               THEN ALLGOALS (simp_tac (HOL_ss addsimps [fst_conv, snd_conv]));
   189           in (map (fn prop => Skip_Proof.prove lthy [v] [] prop tac) eqs, lthy) end;
   190       in
   191         lthy
   192         |> random_aux_primrec aux_eq'
   193         ||>> fold_map (LocalTheory.define Thm.definitionK) proj_defs
   194         |-> (fn (aux_simp, proj_defs) => prove_eqs aux_simp proj_defs)
   195       end;
   196 
   197 fun random_aux_specification prfx name eqs lthy =
   198   let
   199     val vs = fold Term.add_free_names ((snd o strip_comb o fst o HOLogic.dest_eq
   200       o HOLogic.dest_Trueprop o hd) eqs) [];
   201     fun mk_proto_eq eq =
   202       let
   203         val (head $ t $ u, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
   204       in ((HOLogic.mk_Trueprop o HOLogic.mk_eq) (head, lambda t (lambda u rhs))) end;
   205     val proto_eqs = map mk_proto_eq eqs;
   206     fun prove_simps proto_simps lthy =
   207       let
   208         val ext_simps = map (fn thm => fun_cong OF [fun_cong OF [thm]]) proto_simps;
   209         val tac = ALLGOALS (ProofContext.fact_tac ext_simps);
   210       in (map (fn prop => Skip_Proof.prove lthy vs [] prop (K tac)) eqs, lthy) end;
   211     val b = Binding.conceal (Binding.qualify true prfx
   212       (Binding.qualify true name (Binding.name "simps")));
   213   in
   214     lthy
   215     |> random_aux_primrec_multi (name ^ prfx) proto_eqs
   216     |-> (fn proto_simps => prove_simps proto_simps)
   217     |-> (fn simps => LocalTheory.note Thm.generatedK ((b,
   218            Code.add_default_eqn_attrib :: map (Attrib.internal o K)
   219           [Simplifier.simp_add, Nitpick_Simps.add, Quickcheck_RecFun_Simps.add]),
   220             simps))
   221     |> snd
   222   end
   223 
   224 
   225 (* constructing random instances on datatypes *)
   226 
   227 val random_auxN = "random_aux";
   228 
   229 fun mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us) =
   230   let
   231     val mk_const = curry (Sign.mk_const thy);
   232     val random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames);
   233     val rTs = Ts @ Us;
   234     fun random_resultT T = @{typ Random.seed}
   235       --> HOLogic.mk_prodT (termifyT T,@{typ Random.seed});
   236     val pTs = map random_resultT rTs;
   237     fun sizeT T = @{typ code_numeral} --> @{typ code_numeral} --> T;
   238     val random_auxT = sizeT o random_resultT;
   239     val random_auxs = map2 (fn s => fn rT => Free (s, random_auxT rT))
   240       random_auxsN rTs;
   241     fun mk_random_call T = (NONE, (HOLogic.mk_random T size', T));
   242     fun mk_random_aux_call fTs (k, _) (tyco, Ts) =
   243       let
   244         val T = Type (tyco, Ts);
   245         fun mk_random_fun_lift [] t = t
   246           | mk_random_fun_lift (fT :: fTs) t =
   247               mk_const @{const_name random_fun_lift} [fTs ---> T, fT] $
   248                 mk_random_fun_lift fTs t;
   249         val t = mk_random_fun_lift fTs (nth random_auxs k $ size_pred $ size');
   250         val size = Option.map snd (DatatypeCodegen.find_shortest_path descr k)
   251           |> the_default 0;
   252       in (SOME size, (t, fTs ---> T)) end;
   253     val tss = DatatypeAux.interpret_construction descr vs
   254       { atyp = mk_random_call, dtyp = mk_random_aux_call };
   255     fun mk_consexpr simpleT (c, xs) =
   256       let
   257         val (ks, simple_tTs) = split_list xs;
   258         val T = termifyT simpleT;
   259         val tTs = (map o apsnd) termifyT simple_tTs;
   260         val is_rec = exists is_some ks;
   261         val k = fold (fn NONE => I | SOME k => Integer.max k) ks 0;
   262         val vs = Name.names Name.context "x" (map snd simple_tTs);
   263         val vs' = (map o apsnd) termifyT vs;
   264         val tc = HOLogic.mk_return T @{typ Random.seed}
   265           (HOLogic.mk_valtermify_app c vs simpleT);
   266         val t = HOLogic.mk_ST (map (fn (t, _) => (t, @{typ Random.seed})) tTs ~~ map SOME vs')
   267           tc @{typ Random.seed} (SOME T, @{typ Random.seed});
   268         val tk = if is_rec
   269           then if k = 0 then size
   270             else @{term "Quickcheck.beyond :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"}
   271              $ HOLogic.mk_number @{typ code_numeral} k $ size
   272           else @{term "1::code_numeral"}
   273       in (is_rec, HOLogic.mk_prod (tk, t)) end;
   274     fun sort_rec xs =
   275       map_filter (fn (true, t) => SOME t | _ =>  NONE) xs
   276       @ map_filter (fn (false, t) => SOME t | _ =>  NONE) xs;
   277     val gen_exprss = tss
   278       |> (map o apfst) Type
   279       |> map (fn (T, cs) => (T, (sort_rec o map (mk_consexpr T)) cs));
   280     fun mk_select (rT, xs) =
   281       mk_const @{const_name Quickcheck.collapse} [@{typ "Random.seed"}, termifyT rT]
   282       $ (mk_const @{const_name Random.select_weight} [random_resultT rT]
   283         $ HOLogic.mk_list (HOLogic.mk_prodT (@{typ code_numeral}, random_resultT rT)) xs)
   284           $ seed;
   285     val auxs_lhss = map (fn t => t $ size $ size' $ seed) random_auxs;
   286     val auxs_rhss = map mk_select gen_exprss;
   287   in (random_auxs, auxs_lhss ~~ auxs_rhss) end;
   288 
   289 fun mk_random_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
   290   let
   291     val _ = DatatypeAux.message config "Creating quickcheck generators ...";
   292     val mk_prop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
   293     fun mk_size_arg k = case DatatypeCodegen.find_shortest_path descr k
   294      of SOME (_, l) => if l = 0 then size
   295           else @{term "max :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"}
   296             $ HOLogic.mk_number @{typ code_numeral} l $ size
   297       | NONE => size;
   298     val (random_auxs, auxs_eqs) = (apsnd o map) mk_prop_eq
   299       (mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us));
   300     val random_defs = map_index (fn (k, T) => mk_prop_eq
   301       (HOLogic.mk_random T size, nth random_auxs k $ mk_size_arg k $ size)) Ts;
   302   in
   303     thy
   304     |> TheoryTarget.instantiation (tycos, vs, @{sort random})
   305     |> random_aux_specification prfx random_auxN auxs_eqs
   306     |> `(fn lthy => map (Syntax.check_term lthy) random_defs)
   307     |-> (fn random_defs' => fold_map (fn random_def =>
   308           Specification.definition (NONE, (apfst Binding.conceal
   309             Attrib.empty_binding, random_def))) random_defs')
   310     |> snd
   311     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
   312   end;
   313 
   314 fun perhaps_constrain thy insts raw_vs =
   315   let
   316     fun meet_random (T, sort) = Sorts.meet_sort (Sign.classes_of thy) 
   317       (Logic.varifyT T, sort);
   318     val vtab = Vartab.empty
   319       |> fold (fn (v, sort) => Vartab.update ((v, 0), sort)) raw_vs
   320       |> fold meet_random insts;
   321   in SOME (fn (v, _) => (v, (the o Vartab.lookup vtab) (v, 0)))
   322   end handle Sorts.CLASS_ERROR _ => NONE;
   323 
   324 fun ensure_random_datatype config raw_tycos thy =
   325   let
   326     val algebra = Sign.classes_of thy;
   327     val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) =
   328       Datatype.the_descr thy raw_tycos;
   329     val typerep_vs = (map o apsnd)
   330       (curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs;
   331     val random_insts = (map (rpair @{sort random}) o flat o maps snd o maps snd)
   332       (DatatypeAux.interpret_construction descr typerep_vs
   333         { atyp = single, dtyp = (K o K o K) [] });
   334     val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd)
   335       (DatatypeAux.interpret_construction descr typerep_vs
   336         { atyp = K [], dtyp = K o K });
   337     val has_inst = exists (fn tyco =>
   338       can (Sorts.mg_domain algebra tyco) @{sort random}) tycos;
   339   in if has_inst then thy
   340     else case perhaps_constrain thy (random_insts @ term_of_insts) typerep_vs
   341      of SOME constrain => mk_random_datatype config descr
   342           (map constrain typerep_vs) tycos prfx (names, auxnames)
   343             ((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy
   344       | NONE => thy
   345   end;
   346 
   347 
   348 (** building and compiling generator expressions **)
   349 
   350 val eval_ref :
   351     (unit -> int -> int * int -> term list option * (int * int)) option Unsynchronized.ref =
   352   Unsynchronized.ref NONE;
   353 
   354 val target = "Quickcheck";
   355 
   356 fun mk_generator_expr thy prop Ts =
   357   let
   358     val bound_max = length Ts - 1;
   359     val bounds = map_index (fn (i, ty) =>
   360       (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
   361     val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
   362     val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
   363     val check = @{term "If :: bool => term list option => term list option => term list option"}
   364       $ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option "} $ terms);
   365     val return = @{term "Pair :: term list option => Random.seed => term list option * Random.seed"};
   366     fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
   367     fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"});
   368     fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
   369       liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
   370     fun mk_split T = Sign.mk_const thy
   371       (@{const_name split}, [T, @{typ "unit => term"}, liftT @{typ "term list option"} @{typ Random.seed}]);
   372     fun mk_scomp_split T t t' =
   373       mk_scomp (mk_termtyp T) @{typ "term list option"} @{typ Random.seed} t
   374         (mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t')));
   375     fun mk_bindclause (_, _, i, T) = mk_scomp_split T
   376       (Sign.mk_const thy (@{const_name Quickcheck.random}, [T]) $ Bound i);
   377   in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) end;
   378 
   379 fun compile_generator_expr thy t =
   380   let
   381     val Ts = (map snd o fst o strip_abs) t;
   382     val t' = mk_generator_expr thy t Ts;
   383     val compile = Code_ML.eval (SOME target) ("Quickcheck_Generators.eval_ref", eval_ref)
   384       (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' [];
   385   in compile #> Random_Engine.run end;
   386 
   387 
   388 (** setup **)
   389 
   390 val setup = Typecopy.interpretation ensure_random_typecopy
   391   #> Datatype.interpretation ensure_random_datatype
   392   #> Code_Target.extend_target (target, (Code_ML.target_Eval, K I))
   393   #> Quickcheck.add_generator ("code", compile_generator_expr o ProofContext.theory_of);
   394 
   395 end;