src/HOL/Tools/quickcheck_generators.ML
author haftmann
Tue May 26 17:29:32 2009 +0200 (2009-05-26)
changeset 31260 4d273d043d59
child 31485 259a3c90016e
permissions -rw-r--r--
separate module for quickcheck generators
     1 (* Author: Florian Haftmann, TU Muenchen
     2 
     3 Quickcheck generators for various types.
     4 *)
     5 
     6 signature QUICKCHECK_GENERATORS =
     7 sig
     8   val compile_generator_expr: theory -> term -> int -> term list option
     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.term)) * seed
    13   val ensure_random_typecopy: string -> theory -> theory
    14   val eval_ref: (unit -> int -> int * int -> term list option * (int * int)) option ref
    15   val setup: theory -> theory
    16 end;
    17 
    18 structure Quickcheck_Generators : QUICKCHECK_GENERATORS =
    19 struct
    20 
    21 (** building and compiling generator expressions **)
    22 
    23 val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE;
    24 
    25 val target = "Quickcheck";
    26 
    27 fun mk_generator_expr thy prop tys =
    28   let
    29     val bound_max = length tys - 1;
    30     val bounds = map_index (fn (i, ty) =>
    31       (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) tys;
    32     val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
    33     val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
    34     val check = @{term "If :: bool => term list option => term list option => term list option"}
    35       $ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option "} $ terms);
    36     val return = @{term "Pair :: term list option => Random.seed => term list option * Random.seed"};
    37     fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
    38     fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit => term"});
    39     fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
    40       liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
    41     fun mk_split ty = Sign.mk_const thy
    42       (@{const_name split}, [ty, @{typ "unit => term"}, liftT @{typ "term list option"} @{typ Random.seed}]);
    43     fun mk_scomp_split ty t t' =
    44       mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t
    45         (mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit => term"}, t')));
    46     fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty
    47       (Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i);
    48   in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) end;
    49 
    50 fun compile_generator_expr thy t =
    51   let
    52     val tys = (map snd o fst o strip_abs) t;
    53     val t' = mk_generator_expr thy t tys;
    54     val f = Code_ML.eval (SOME target) ("Quickcheck_Generators.eval_ref", eval_ref)
    55       (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' [];
    56   in f #> Random_Engine.run end;
    57 
    58 
    59 (** typ "'a => 'b" **)
    60 
    61 type seed = Random_Engine.seed;
    62 
    63 fun random_fun (T1 : typ) (T2 : typ) (eq : 'a -> 'a -> bool) (term_of : 'a -> term)
    64     (random : seed -> ('b * (unit -> term)) * seed)
    65     (random_split : seed -> seed * seed)
    66     (seed : seed) =
    67   let
    68     val (seed', seed'') = random_split seed;
    69     val state = ref (seed', [], Const (@{const_name undefined}, T1 --> T2));
    70     val fun_upd = Const (@{const_name fun_upd},
    71       (T1 --> T2) --> T1 --> T2 --> T1 --> T2);
    72     fun random_fun' x =
    73       let
    74         val (seed, fun_map, f_t) = ! state;
    75       in case AList.lookup (uncurry eq) fun_map x
    76        of SOME y => y
    77         | NONE => let
    78               val t1 = term_of x;
    79               val ((y, t2), seed') = random seed;
    80               val fun_map' = (x, y) :: fun_map;
    81               val f_t' = fun_upd $ f_t $ t1 $ t2 ();
    82               val _ = state := (seed', fun_map', f_t');
    83             in y end
    84       end;
    85     fun term_fun' () = #3 (! state);
    86   in ((random_fun', term_fun'), seed'') end;
    87 
    88 
    89 (** type copies **)
    90 
    91 fun mk_random_typecopy tyco vs constr typ thy =
    92   let
    93     val Ts = map TFree vs;  
    94     val T = Type (tyco, Ts);
    95     fun mk_termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"})
    96     val Ttm = mk_termifyT T;
    97     val typtm = mk_termifyT typ;
    98     fun mk_const c Ts = Const (c, Sign.const_instance thy (c, Ts));
    99     fun mk_random T = mk_const @{const_name random} [T];
   100     val size = @{term "j::code_numeral"};
   101     val v = "x";
   102     val t_v = Free (v, typtm);
   103     val t_constr = mk_const constr Ts;
   104     val lhs = mk_random T $ size;
   105     val rhs = HOLogic.mk_ST [(((mk_random typ) $ size, @{typ Random.seed}), SOME (v, typtm))]
   106       (HOLogic.mk_return Ttm @{typ Random.seed}
   107       (mk_const "Code_Eval.valapp" [typ, T]
   108         $ HOLogic.mk_prod (t_constr, Abs ("u", @{typ unit}, HOLogic.reflect_term t_constr)) $ t_v))
   109       @{typ Random.seed} (SOME Ttm, @{typ Random.seed});
   110     val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
   111   in   
   112     thy
   113     |> TheoryTarget.instantiation ([tyco], vs, @{sort random})
   114     |> `(fn lthy => Syntax.check_term lthy eq)
   115     |-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))
   116     |> snd
   117     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
   118   end;
   119 
   120 fun ensure_random_typecopy tyco thy =
   121   let
   122     val SOME { vs = raw_vs, constr, typ = raw_typ, ... } =
   123       TypecopyPackage.get_info thy tyco;
   124     val constrain = curry (Sorts.inter_sort (Sign.classes_of thy));
   125     val typ = map_atyps (fn TFree (v, sort) =>
   126       TFree (v, constrain sort @{sort random})) raw_typ;
   127     val vs' = Term.add_tfreesT typ [];
   128     val vs = map (fn (v, sort) =>
   129       (v, the_default (constrain sort @{sort typerep}) (AList.lookup (op =) vs' v))) raw_vs;
   130     val do_inst = Sign.of_sort thy (typ, @{sort random});
   131   in if do_inst then mk_random_typecopy tyco vs constr typ thy else thy end;
   132 
   133 
   134 (** datatypes **)
   135 
   136 (* still under construction *)
   137 
   138 
   139 (** setup **)
   140 
   141 val setup = Code_Target.extend_target (target, (Code_ML.target_Eval, K I))
   142   #> Quickcheck.add_generator ("code", compile_generator_expr o ProofContext.theory_of)
   143   #> TypecopyPackage.interpretation ensure_random_typecopy;
   144 
   145 end;