(* Author: Florian Haftmann, TU Muenchen *)
header {* A simple counterexample generator *}
theory Quickcheck
imports Random Code_Eval Map
begin
subsection {* The @{text random} class *}
class random = typerep +
fixes random :: "index \<Rightarrow> seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> seed"
text {* Type @{typ "'a itself"} *}
instantiation itself :: ("{type, typerep}") random
begin
definition
"random _ = Pair (TYPE('a), \<lambda>u. Code_Eval.Const (STR ''TYPE'') TYPEREP('a))"
instance ..
end
subsection {* Quickcheck generator *}
ML {*
structure StateMonad =
struct
fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
fun liftT' sT = sT --> sT;
fun return T sT x = Const (@{const_name Pair}, T --> liftT T sT) $ x;
fun scomp T1 T2 sT f g = Const (@{const_name scomp},
liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
end;
structure Quickcheck =
struct
open Quickcheck;
val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE;
val target = "Quickcheck";
fun mk_generator_expr thy prop tys =
let
val bound_max = length tys - 1;
val bounds = map_index (fn (i, ty) =>
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) tys;
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 check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"}
$ result $ @{term "None \<Colon> term list option"} $ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} $ terms);
val return = @{term "Pair \<Colon> term list option \<Rightarrow> seed \<Rightarrow> term list option \<times> seed"};
fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});
fun mk_split ty = Sign.mk_const thy
(@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, StateMonad.liftT @{typ "term list option"} @{typ seed}]);
fun mk_scomp_split ty t t' =
StateMonad.scomp (mk_termtyp ty) @{typ "term list option"} @{typ seed} t (*FIXME*)
(mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')));
fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty
(Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i)
val t = fold_rev mk_bindclause bounds (return $ check);
in Abs ("n", @{typ index}, t) end;
fun compile_generator_expr thy t =
let
val tys = (map snd o fst o strip_abs) t;
val t' = mk_generator_expr thy t tys;
val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref) thy t' [];
in f #> Random_Engine.run #> (Option.map o map) (Code.postprocess_term thy) end;
end
*}
setup {*
Code_Target.extend_target (Quickcheck.target, (Code_ML.target_Eval, K I))
#> Quickcheck.add_generator ("code", Quickcheck.compile_generator_expr o ProofContext.theory_of)
*}
subsection {* Type @{typ "'a \<Rightarrow> 'b"} *}
ML {*
structure Random_Engine =
struct
open Random_Engine;
fun random_fun (T1 : typ) (T2 : typ) (eq : 'a -> 'a -> bool) (term_of : 'a -> term)
(random : Random_Engine.seed -> ('b * (unit -> term)) * Random_Engine.seed)
(random_split : Random_Engine.seed -> Random_Engine.seed * Random_Engine.seed)
(seed : Random_Engine.seed) =
let
val (seed', seed'') = random_split seed;
val state = ref (seed', [], Const (@{const_name undefined}, T1 --> T2));
val fun_upd = Const (@{const_name fun_upd},
(T1 --> T2) --> T1 --> T2 --> 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' = 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;
end
*}
axiomatization
random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)
\<Rightarrow> (seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> seed) \<Rightarrow> (seed \<Rightarrow> seed \<times> seed)
\<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed"
code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun")
-- {* With enough criminal energy this can be abused to derive @{prop False};
for this reason we use a distinguished target @{text Quickcheck}
not spoiling the regular trusted code generation *}
instantiation "fun" :: ("{eq, term_of}", "{type, random}") random
begin
definition random_fun :: "index \<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed" where
"random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) split_seed"
instance ..
end
code_reserved Quickcheck Random_Engine
end