author | haftmann |
Fri, 17 Apr 2009 14:29:54 +0200 | |
changeset 30945 | 0418e9bffbba |
parent 29823 | 0ab754d13ccd |
child 30970 | 3fe2e418a071 |
permissions | -rw-r--r-- |
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(* Author: Florian Haftmann, TU Muenchen *) |
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header {* A simple counterexample generator *} |
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theory Quickcheck |
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imports Random Code_Eval Map |
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begin |
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subsection {* The @{text random} class *} |
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class random = typerep + |
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fixes random :: "index \<Rightarrow> seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> seed" |
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text {* Type @{typ "'a itself"} *} |
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instantiation itself :: ("{type, typerep}") random |
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begin |
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definition |
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"random _ = Pair (TYPE('a), \<lambda>u. Code_Eval.Const (STR ''TYPE'') TYPEREP('a))" |
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instance .. |
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end |
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subsection {* Quickcheck generator *} |
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ML {* |
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structure StateMonad = |
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struct |
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fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT); |
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fun liftT' sT = sT --> sT; |
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split of already properly working part of Quickcheck infrastructure
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fun return T sT x = Const (@{const_name Pair}, T --> liftT T sT) $ x; |
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fun scomp T1 T2 sT f g = Const (@{const_name scomp}, |
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liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g; |
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end; |
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structure Quickcheck = |
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struct |
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open Quickcheck; |
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val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE; |
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val target = "Quickcheck"; |
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fun mk_generator_expr thy prop tys = |
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let |
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val bound_max = length tys - 1; |
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val bounds = map_index (fn (i, ty) => |
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(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) tys; |
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val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds); |
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val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds); |
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val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"} |
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$ result $ @{term "None \<Colon> term list option"} $ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} $ terms); |
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val return = @{term "Pair \<Colon> term list option \<Rightarrow> seed \<Rightarrow> term list option \<times> seed"}; |
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fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"}); |
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fun mk_split ty = Sign.mk_const thy |
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(@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, StateMonad.liftT @{typ "term list option"} @{typ seed}]); |
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fun mk_scomp_split ty t t' = |
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StateMonad.scomp (mk_termtyp ty) @{typ "term list option"} @{typ seed} t (*FIXME*) |
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(mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t'))); |
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fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty |
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(Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i) |
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val t = fold_rev mk_bindclause bounds (return $ check); |
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in Abs ("n", @{typ index}, t) end; |
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fun compile_generator_expr thy t = |
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let |
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val tys = (map snd o fst o strip_abs) t; |
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val t' = mk_generator_expr thy t tys; |
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val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref) thy t' []; |
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in f #> Random_Engine.run #> (Option.map o map) (Code.postprocess_term thy) end; |
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end |
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*} |
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setup {* |
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Code_Target.extend_target (Quickcheck.target, (Code_ML.target_Eval, K I)) |
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#> Quickcheck.add_generator ("code", Quickcheck.compile_generator_expr o ProofContext.theory_of) |
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*} |
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subsection {* Type @{typ "'a \<Rightarrow> 'b"} *} |
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ML {* |
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structure Random_Engine = |
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struct |
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open Random_Engine; |
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fun random_fun (T1 : typ) (T2 : typ) (eq : 'a -> 'a -> bool) (term_of : 'a -> term) |
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(random : Random_Engine.seed -> ('b * (unit -> term)) * Random_Engine.seed) |
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(random_split : Random_Engine.seed -> Random_Engine.seed * Random_Engine.seed) |
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(seed : Random_Engine.seed) = |
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let |
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val (seed', seed'') = random_split seed; |
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val state = ref (seed', [], Const (@{const_name undefined}, T1 --> T2)); |
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val fun_upd = Const (@{const_name fun_upd}, |
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(T1 --> T2) --> T1 --> T2 --> T1 --> T2); |
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fun random_fun' x = |
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let |
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val (seed, fun_map, f_t) = ! state; |
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in case AList.lookup (uncurry eq) fun_map x |
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of SOME y => y |
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| NONE => let |
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val t1 = term_of x; |
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val ((y, t2), seed') = random seed; |
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val fun_map' = (x, y) :: fun_map; |
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val f_t' = fun_upd $ f_t $ t1 $ t2 (); |
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val _ = state := (seed', fun_map', f_t'); |
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in y end |
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end; |
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fun term_fun' () = #3 (! state); |
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in ((random_fun', term_fun'), seed'') end; |
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end |
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*} |
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axiomatization |
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random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term) |
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\<Rightarrow> (seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> seed) \<Rightarrow> (seed \<Rightarrow> seed \<times> seed) |
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\<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed" |
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code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun") |
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-- {* With enough criminal energy this can be abused to derive @{prop False}; |
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for this reason we use a distinguished target @{text Quickcheck} |
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not spoiling the regular trusted code generation *} |
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instantiation "fun" :: ("{eq, term_of}", "{type, random}") random |
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begin |
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definition random_fun :: "index \<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed" where |
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"random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) split_seed" |
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instance .. |
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end |
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code_reserved Quickcheck Random_Engine |
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end |