src/HOL/Quickcheck.thy
author haftmann
Tue May 19 13:57:32 2009 +0200 (2009-05-19)
changeset 31203 5c8fb4fd67e0
parent 31194 1d6926f96440
child 31205 98370b26c2ce
permissions -rw-r--r--
moved Code_Index, Random and Quickcheck before Main
     1 (* Author: Florian Haftmann, TU Muenchen *)
     2 
     3 header {* A simple counterexample generator *}
     4 
     5 theory Quickcheck
     6 imports Random Code_Eval
     7 begin
     8 
     9 notation fcomp (infixl "o>" 60)
    10 notation scomp (infixl "o\<rightarrow>" 60)
    11 
    12 
    13 subsection {* The @{text random} class *}
    14 
    15 class random = typerep +
    16   fixes random :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
    17 
    18 
    19 subsection {* Quickcheck generator *}
    20 
    21 ML {*
    22 structure Quickcheck =
    23 struct
    24 
    25 open Quickcheck;
    26 
    27 val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE;
    28 
    29 val target = "Quickcheck";
    30 
    31 fun mk_generator_expr thy prop tys =
    32   let
    33     val bound_max = length tys - 1;
    34     val bounds = map_index (fn (i, ty) =>
    35       (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) tys;
    36     val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
    37     val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
    38     val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"}
    39       $ result $ @{term "None \<Colon> term list option"} $ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} $ terms);
    40     val return = @{term "Pair \<Colon> term list option \<Rightarrow> Random.seed \<Rightarrow> term list option \<times> Random.seed"};
    41     fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
    42     fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});
    43     fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
    44       liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
    45     fun mk_split ty = Sign.mk_const thy
    46       (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, liftT @{typ "term list option"} @{typ Random.seed}]);
    47     fun mk_scomp_split ty t t' =
    48       mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t
    49         (mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')));
    50     fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty
    51       (Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i);
    52   in Abs ("n", @{typ index}, fold_rev mk_bindclause bounds (return $ check)) end;
    53 
    54 fun compile_generator_expr thy t =
    55   let
    56     val tys = (map snd o fst o strip_abs) t;
    57     val t' = mk_generator_expr thy t tys;
    58     val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref)
    59       (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' [];
    60   in f #> Random_Engine.run end;
    61 
    62 end
    63 *}
    64 
    65 setup {*
    66   Code_Target.extend_target (Quickcheck.target, (Code_ML.target_Eval, K I))
    67   #> Quickcheck.add_generator ("code", Quickcheck.compile_generator_expr o ProofContext.theory_of)
    68 *}
    69 
    70 
    71 subsection {* Fundamental types*}
    72 
    73 instantiation bool :: random
    74 begin
    75 
    76 definition
    77   "random i = Random.range i o\<rightarrow>
    78     (\<lambda>k. Pair (if (k div 2 = 0) then Code_Eval.valtermify True else Code_Eval.valtermify False))"
    79 
    80 instance ..
    81 
    82 end
    83 
    84 instantiation itself :: (typerep) random
    85 begin
    86 
    87 definition random_itself :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
    88   "random_itself _ = Pair (Code_Eval.valtermify TYPE('a))"
    89 
    90 instance ..
    91 
    92 end
    93 
    94 text {* Type @{typ "'a \<Rightarrow> 'b"} *}
    95 
    96 ML {*
    97 structure Random_Engine =
    98 struct
    99 
   100 open Random_Engine;
   101 
   102 fun random_fun (T1 : typ) (T2 : typ) (eq : 'a -> 'a -> bool) (term_of : 'a -> term)
   103     (random : Random_Engine.seed -> ('b * (unit -> term)) * Random_Engine.seed)
   104     (random_split : Random_Engine.seed -> Random_Engine.seed * Random_Engine.seed)
   105     (seed : Random_Engine.seed) =
   106   let
   107     val (seed', seed'') = random_split seed;
   108     val state = ref (seed', [], Const (@{const_name undefined}, T1 --> T2));
   109     val fun_upd = Const (@{const_name fun_upd},
   110       (T1 --> T2) --> T1 --> T2 --> T1 --> T2);
   111     fun random_fun' x =
   112       let
   113         val (seed, fun_map, f_t) = ! state;
   114       in case AList.lookup (uncurry eq) fun_map x
   115        of SOME y => y
   116         | NONE => let
   117               val t1 = term_of x;
   118               val ((y, t2), seed') = random seed;
   119               val fun_map' = (x, y) :: fun_map;
   120               val f_t' = fun_upd $ f_t $ t1 $ t2 ();
   121               val _ = state := (seed', fun_map', f_t');
   122             in y end
   123       end;
   124     fun term_fun' () = #3 (! state);
   125   in ((random_fun', term_fun'), seed'') end;
   126 
   127 end
   128 *}
   129 
   130 axiomatization random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)
   131   \<Rightarrow> (Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed) \<Rightarrow> (Random.seed \<Rightarrow> Random.seed \<times> Random.seed)
   132   \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
   133 
   134 code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun")
   135   -- {* With enough criminal energy this can be abused to derive @{prop False};
   136   for this reason we use a distinguished target @{text Quickcheck}
   137   not spoiling the regular trusted code generation *}
   138 
   139 instantiation "fun" :: ("{eq, term_of}", "{type, random}") random
   140 begin
   141 
   142 definition random_fun :: "index \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
   143   "random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) Random.split_seed"
   144 
   145 instance ..
   146 
   147 end
   148 
   149 code_reserved Quickcheck Random_Engine
   150 
   151 
   152 subsection {* Numeric types *}
   153 
   154 instantiation nat :: random
   155 begin
   156 
   157 definition random_nat :: "index \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Eval.term)) \<times> Random.seed" where
   158   "random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (
   159      let n = Code_Index.nat_of k
   160      in (n, \<lambda>_. Code_Eval.term_of n)))"
   161 
   162 instance ..
   163 
   164 end
   165 
   166 instantiation int :: random
   167 begin
   168 
   169 definition
   170   "random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (
   171      let j = (if k \<ge> i then Code_Index.int_of (k - i) else - Code_Index.int_of (i - k))
   172      in (j, \<lambda>_. Code_Eval.term_of j)))"
   173 
   174 instance ..
   175 
   176 end
   177 
   178 
   179 no_notation fcomp (infixl "o>" 60)
   180 no_notation scomp (infixl "o\<rightarrow>" 60)
   181 
   182 end