author | haftmann |
Tue, 23 Jun 2009 16:27:12 +0200 | |
changeset 31784 | bd3486c57ba3 |
parent 31744 | dc3c2d52b642 |
child 31785 | 9db4e79c91cf |
permissions | -rw-r--r-- |
31260 | 1 |
(* Author: Florian Haftmann, TU Muenchen |
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Quickcheck generators for various types. |
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*) |
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signature QUICKCHECK_GENERATORS = |
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sig |
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val compile_generator_expr: theory -> term -> int -> term list option |
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type seed = Random_Engine.seed |
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val random_fun: typ -> typ -> ('a -> 'a -> bool) -> ('a -> term) |
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-> (seed -> ('b * (unit -> term)) * seed) -> (seed -> seed * seed) |
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-> seed -> (('a -> 'b) * (unit -> Term.term)) * seed |
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val ensure_random_typecopy: string -> theory -> theory |
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val random_aux_specification: string -> term list -> local_theory -> local_theory |
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val mk_random_aux_eqs: theory -> Datatype.descr -> (string * sort) list |
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-> string list -> string list * string list -> typ list * typ list |
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-> string * (term list * (term * term) list) |
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val ensure_random_datatype: Datatype.config -> string list -> theory -> theory |
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val eval_ref: (unit -> int -> seed -> term list option * seed) option ref |
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val setup: theory -> theory |
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end; |
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structure Quickcheck_Generators : QUICKCHECK_GENERATORS = |
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struct |
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(** building and compiling generator expressions **) |
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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 :: bool => term list option => term list option => term list option"} |
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$ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option "} $ terms); |
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val return = @{term "Pair :: term list option => Random.seed => term list option * Random.seed"}; |
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fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT); |
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fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit => term"}); |
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fun mk_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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fun mk_split ty = Sign.mk_const thy |
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(@{const_name split}, [ty, @{typ "unit => term"}, liftT @{typ "term list option"} @{typ Random.seed}]); |
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fun mk_scomp_split ty t t' = |
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mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t |
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(mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit => 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 Quickcheck.random}, [ty]) $ Bound i); |
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in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) 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_Generators.eval_ref", eval_ref) |
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(fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' []; |
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in f #> Random_Engine.run end; |
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(** typ "'a => 'b" **) |
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type seed = Random_Engine.seed; |
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fun random_fun T1 T2 eq term_of random random_split 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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(** type copies **) |
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fun mk_random_typecopy tyco vs constr typ thy = |
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let |
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val Ts = map TFree vs; |
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val T = Type (tyco, Ts); |
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fun mk_termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"}) |
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val Ttm = mk_termifyT T; |
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val typtm = mk_termifyT typ; |
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fun mk_const c Ts = Const (c, Sign.const_instance thy (c, Ts)); |
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fun mk_random T = mk_const @{const_name Quickcheck.random} [T]; |
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val size = @{term "j::code_numeral"}; |
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val v = "x"; |
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val t_v = Free (v, typtm); |
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val t_constr = mk_const constr Ts; |
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val lhs = mk_random T $ size; |
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val rhs = HOLogic.mk_ST [(((mk_random typ) $ size, @{typ Random.seed}), SOME (v, typtm))] |
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(HOLogic.mk_return Ttm @{typ Random.seed} |
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(mk_const "Code_Eval.valapp" [typ, T] |
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$ HOLogic.mk_prod (t_constr, Abs ("u", @{typ unit}, HOLogic.reflect_term t_constr)) $ t_v)) |
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@{typ Random.seed} (SOME Ttm, @{typ Random.seed}); |
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val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs)); |
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in |
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thy |
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|> TheoryTarget.instantiation ([tyco], vs, @{sort random}) |
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|> `(fn lthy => Syntax.check_term lthy eq) |
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|-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq))) |
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|> snd |
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|> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) |
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end; |
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fun ensure_random_typecopy tyco thy = |
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let |
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val SOME { vs = raw_vs, constr, typ = raw_typ, ... } = |
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Typecopy.get_info thy tyco; |
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val constrain = curry (Sorts.inter_sort (Sign.classes_of thy)); |
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val typ = map_atyps (fn TFree (v, sort) => |
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TFree (v, constrain sort @{sort random})) raw_typ; |
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val vs' = Term.add_tfreesT typ []; |
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val vs = map (fn (v, sort) => |
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(v, the_default (constrain sort @{sort typerep}) (AList.lookup (op =) vs' v))) raw_vs; |
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val do_inst = Sign.of_sort thy (typ, @{sort random}); |
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in if do_inst then mk_random_typecopy tyco vs constr typ thy else thy end; |
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(** datatypes **) |
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(* definitional scheme for random instances on datatypes *) |
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(*FIXME avoid this low-level proving*) |
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local |
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fun dest_ctyp_nth k cT = nth (Thm.dest_ctyp cT) k; |
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val eq = Thm.cprop_of @{thm random_aux_rec} |> Thm.dest_arg |> Thm.dest_arg |> Thm.dest_arg; |
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val lhs = eq |> Thm.dest_arg1; |
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val pt_random_aux = lhs |> Thm.dest_fun; |
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val ct_k = lhs |> Thm.dest_arg; |
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val pt_rhs = eq |> Thm.dest_arg |> Thm.dest_fun; |
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val aT = pt_random_aux |> Thm.ctyp_of_term |> dest_ctyp_nth 1; |
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val rew_thms = map mk_meta_eq [@{thm code_numeral_zero_minus_one}, |
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@{thm Suc_code_numeral_minus_one}, @{thm select_weight_cons_zero}, @{thm beyond_zero}]; |
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val rew_ts = map (Logic.dest_equals o Thm.prop_of) rew_thms; |
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val rew_ss = HOL_ss addsimps rew_thms; |
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in |
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fun random_aux_primrec eq lthy = |
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let |
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val thy = ProofContext.theory_of lthy; |
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val ((t_random_aux as Free (random_aux, T)) $ (t_k as Free (v, _)), proto_t_rhs) = |
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(HOLogic.dest_eq o HOLogic.dest_Trueprop) eq; |
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val Type (_, [_, iT]) = T; |
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val icT = Thm.ctyp_of thy iT; |
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val cert = Thm.cterm_of thy; |
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val inst = Thm.instantiate_cterm ([(aT, icT)], []); |
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fun subst_v t' = map_aterms (fn t as Free (w, _) => if v = w then t' else t | t => t); |
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val t_rhs = lambda t_k proto_t_rhs; |
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val eqs0 = [subst_v @{term "0::code_numeral"} eq, subst_v (@{term "Suc_code_numeral"} $ t_k) eq]; |
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val eqs1 = map (Pattern.rewrite_term thy rew_ts []) eqs0; |
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val ((_, eqs2), lthy') = Primrec.add_primrec_simple |
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[((Binding.name random_aux, T), NoSyn)] eqs1 lthy; |
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val eq_tac = ALLGOALS (simp_tac rew_ss) |
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THEN (ALLGOALS (ProofContext.fact_tac (flat eqs2))); |
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val eqs3 = map (fn prop => SkipProof.prove lthy' [v] [] prop (K eq_tac)) eqs0; |
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val cT_random_aux = inst pt_random_aux; |
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val cT_rhs = inst pt_rhs; |
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val rule = @{thm random_aux_rec} |
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|> Drule.instantiate ([(aT, icT)], |
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[(cT_random_aux, cert t_random_aux), (cT_rhs, cert t_rhs)]) |
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|> (fn thm => thm OF eqs3); |
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val tac = ALLGOALS (rtac rule); |
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val simp = SkipProof.prove lthy' [v] [] eq (K tac); |
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in (simp, lthy') end; |
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end; |
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fun random_aux_primrec_multi prefix [eq] lthy = |
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lthy |
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|> random_aux_primrec eq |
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|>> (fn simp => [simp]) |
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| random_aux_primrec_multi prefix (eqs as _ :: _ :: _) lthy = |
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let |
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val thy = ProofContext.theory_of lthy; |
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val (lhss, rhss) = map_split (HOLogic.dest_eq o HOLogic.dest_Trueprop) eqs; |
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val (vs, (arg as Free (v, _)) :: _) = map_split (fn (t1 $ t2) => (t1, t2)) lhss; |
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val Ts = map fastype_of lhss; |
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val tupleT = foldr1 HOLogic.mk_prodT Ts; |
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val aux_lhs = Free ("mutual_" ^ prefix, fastype_of arg --> tupleT) $ arg; |
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val aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq) |
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(aux_lhs, foldr1 HOLogic.mk_prod rhss); |
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fun mk_proj t [T] = [t] |
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| mk_proj t (Ts as T :: (Ts' as _ :: _)) = |
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Const (@{const_name fst}, foldr1 HOLogic.mk_prodT Ts --> T) $ t |
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:: mk_proj (Const (@{const_name snd}, |
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foldr1 HOLogic.mk_prodT Ts --> foldr1 HOLogic.mk_prodT Ts') $ t) Ts'; |
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val projs = mk_proj (aux_lhs) Ts; |
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val proj_eqs = map2 (fn v => fn proj => (v, lambda arg proj)) vs projs; |
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val proj_defs = map2 (fn Free (name, _) => fn (_, rhs) => |
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((Binding.name name, NoSyn), (Attrib.empty_binding, rhs))) vs proj_eqs; |
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val aux_eq' = Pattern.rewrite_term thy proj_eqs [] aux_eq; |
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fun prove_eqs aux_simp proj_defs lthy = |
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let |
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val proj_simps = map (snd o snd) proj_defs; |
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fun tac { context = ctxt, prems = _ } = |
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ALLGOALS (simp_tac (HOL_ss addsimps proj_simps)) |
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THEN ALLGOALS (EqSubst.eqsubst_tac ctxt [0] [aux_simp]) |
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THEN ALLGOALS (simp_tac (HOL_ss addsimps [fst_conv, snd_conv])); |
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in (map (fn prop => SkipProof.prove lthy [v] [] prop tac) eqs, lthy) end; |
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in |
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lthy |
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|> random_aux_primrec aux_eq' |
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||>> fold_map (LocalTheory.define Thm.definitionK) proj_defs |
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|-> (fn (aux_simp, proj_defs) => prove_eqs aux_simp proj_defs) |
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end; |
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|
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fun random_aux_specification prefix eqs lthy = |
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let |
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val vs = fold Term.add_free_names ((snd o strip_comb o fst o HOLogic.dest_eq |
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o HOLogic.dest_Trueprop o hd) eqs) []; |
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fun mk_proto_eq eq = |
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let |
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val (head $ t $ u, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq; |
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in ((HOLogic.mk_Trueprop o HOLogic.mk_eq) (head, lambda t (lambda u rhs))) end; |
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val proto_eqs = map mk_proto_eq eqs; |
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fun prove_simps proto_simps lthy = |
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let |
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val ext_simps = map (fn thm => fun_cong OF [fun_cong OF [thm]]) proto_simps; |
239 |
val tac = ALLGOALS (ProofContext.fact_tac ext_simps); |
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in (map (fn prop => SkipProof.prove lthy vs [] prop (K tac)) eqs, lthy) end; |
|
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val b = Binding.qualify true prefix (Binding.name "simps"); |
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in |
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lthy |
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|> random_aux_primrec_multi prefix proto_eqs |
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|-> (fn proto_simps => prove_simps proto_simps) |
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|-> (fn simps => LocalTheory.note Thm.generatedK ((b, |
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Code.add_default_eqn_attrib :: map (Attrib.internal o K) |
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[Simplifier.simp_add, Nitpick_Const_Simp_Thms.add, Quickcheck_RecFun_Simp_Thms.add]), |
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simps)) |
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|> snd |
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end |
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|
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|
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(* constructing random instances on datatypes *) |
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|
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fun mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us) = |
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let |
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val mk_const = curry (Sign.mk_const thy); |
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val i = @{term "i\<Colon>code_numeral"}; |
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val i1 = @{term "(i\<Colon>code_numeral) - 1"}; |
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val j = @{term "j\<Colon>code_numeral"}; |
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val seed = @{term "s\<Colon>Random.seed"}; |
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val random_auxN = "random_aux"; |
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val random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames); |
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fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit \<Rightarrow> term"}); |
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val rTs = Ts @ Us; |
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fun random_resultT T = @{typ Random.seed} |
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--> HOLogic.mk_prodT (termifyT T,@{typ Random.seed}); |
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val pTs = map random_resultT rTs; |
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fun sizeT T = @{typ code_numeral} --> @{typ code_numeral} --> T; |
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val random_auxT = sizeT o random_resultT; |
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val random_auxs = map2 (fn s => fn rT => Free (s, random_auxT rT)) |
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random_auxsN rTs; |
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fun mk_random_call T = (NONE, (HOLogic.mk_random T j, T)); |
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fun mk_random_aux_call fTs (k, _) (tyco, Ts) = |
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let |
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val T = Type (tyco, Ts); |
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fun mk_random_fun_lift [] t = t |
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| mk_random_fun_lift (fT :: fTs) t = |
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mk_const @{const_name random_fun_lift} [fTs ---> T, fT] $ |
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mk_random_fun_lift fTs t; |
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val t = mk_random_fun_lift fTs (nth random_auxs k $ i1 $ j); |
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val size = Option.map snd (DatatypeCodegen.find_shortest_path descr k) |
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|> the_default 0; |
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in (SOME size, (t, fTs ---> T)) end; |
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val tss = DatatypeAux.interpret_construction descr vs |
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{ atyp = mk_random_call, dtyp = mk_random_aux_call }; |
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fun mk_consexpr simpleT (c, xs) = |
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let |
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val (ks, simple_tTs) = split_list xs; |
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val T = termifyT simpleT; |
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val tTs = (map o apsnd) termifyT simple_tTs; |
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val is_rec = exists is_some ks; |
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val k = fold (fn NONE => I | SOME k => curry Int.max k) ks 0; |
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val vs = Name.names Name.context "x" (map snd simple_tTs); |
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val vs' = (map o apsnd) termifyT vs; |
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val tc = HOLogic.mk_return T @{typ Random.seed} |
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(HOLogic.mk_valtermify_app c vs simpleT); |
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val t = HOLogic.mk_ST (map (fn (t, _) => (t, @{typ Random.seed})) tTs ~~ map SOME vs') |
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tc @{typ Random.seed} (SOME T, @{typ Random.seed}); |
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val tk = if is_rec |
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then if k = 0 then i |
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else @{term "Quickcheck.beyond :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"} |
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$ HOLogic.mk_number @{typ code_numeral} k $ i |
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else @{term "1::code_numeral"} |
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in (is_rec, HOLogic.mk_prod (tk, t)) end; |
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fun sort_rec xs = |
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map_filter (fn (true, t) => SOME t | _ => NONE) xs |
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@ map_filter (fn (false, t) => SOME t | _ => NONE) xs; |
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val gen_exprss = tss |
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|> (map o apfst) Type |
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|> map (fn (T, cs) => (T, (sort_rec o map (mk_consexpr T)) cs)); |
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fun mk_select (rT, xs) = |
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mk_const @{const_name Quickcheck.collapse} [@{typ "Random.seed"}, termifyT rT] |
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$ (mk_const @{const_name Random.select_weight} [random_resultT rT] |
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$ HOLogic.mk_list (HOLogic.mk_prodT (@{typ code_numeral}, random_resultT rT)) xs) |
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$ seed; |
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val auxs_lhss = map (fn t => t $ i $ j $ seed) random_auxs; |
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val auxs_rhss = map mk_select gen_exprss; |
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val prefix = space_implode "_" (random_auxN :: names); |
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in (prefix, (random_auxs, auxs_lhss ~~ auxs_rhss)) end; |
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322 |
|
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fun mk_random_datatype config descr vs tycos (names, auxnames) (Ts, Us) thy = |
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324 |
let |
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val _ = DatatypeAux.message config "Creating quickcheck generators ..."; |
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val i = @{term "i\<Colon>code_numeral"}; |
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val mk_prop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq; |
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fun mk_size_arg k = case DatatypeCodegen.find_shortest_path descr k |
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of SOME (_, l) => if l = 0 then i |
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else @{term "max :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"} |
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$ HOLogic.mk_number @{typ code_numeral} l $ i |
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| NONE => i; |
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val (prefix, (random_auxs, auxs_eqs)) = (apsnd o apsnd o map) mk_prop_eq |
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(mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us)); |
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val random_defs = map_index (fn (k, T) => mk_prop_eq |
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(HOLogic.mk_random T i, nth random_auxs k $ mk_size_arg k $ i)) Ts; |
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in |
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thy |
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|> TheoryTarget.instantiation (tycos, vs, @{sort random}) |
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|> random_aux_specification prefix auxs_eqs |
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|> `(fn lthy => map (Syntax.check_term lthy) random_defs) |
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|-> (fn random_defs' => fold_map (fn random_def => |
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Specification.definition (NONE, (Attrib.empty_binding, |
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random_def))) random_defs') |
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|> snd |
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|> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) |
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end; |
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|
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fun perhaps_constrain thy insts raw_vs = |
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let |
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fun meet_random (T, sort) = Sorts.meet_sort (Sign.classes_of thy) |
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(Logic.varifyT T, sort); |
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val vtab = Vartab.empty |
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|> fold (fn (v, sort) => Vartab.update ((v, 0), sort)) raw_vs |
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|> fold meet_random insts; |
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in SOME (fn (v, _) => (v, (the o Vartab.lookup vtab) (v, 0))) |
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end handle CLASS_ERROR => NONE; |
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fun ensure_random_datatype config raw_tycos thy = |
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let |
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val pp = Syntax.pp_global thy; |
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val algebra = Sign.classes_of thy; |
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val (descr, raw_vs, tycos, (names, auxnames), raw_TUs) = |
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Datatype.the_descr thy raw_tycos; |
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val typrep_vs = (map o apsnd) |
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(curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs; |
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val random_insts = (map (rpair @{sort random}) o flat o maps snd o maps snd) |
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(DatatypeAux.interpret_construction descr typrep_vs |
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{ atyp = single, dtyp = (K o K o K) [] }); |
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val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd) |
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(DatatypeAux.interpret_construction descr typrep_vs |
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{ atyp = K [], dtyp = K o K }); |
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val has_inst = exists (fn tyco => |
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can (Sorts.mg_domain algebra tyco) @{sort random}) tycos; |
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in if has_inst then thy |
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else case perhaps_constrain thy (random_insts @ term_of_insts) typrep_vs |
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of SOME constrain => mk_random_datatype config descr |
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(map constrain typrep_vs) tycos (names, auxnames) |
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((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy |
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| NONE => thy |
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end; |
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383 |
||
384 |
(** setup **) |
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||
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val setup = Code_Target.extend_target (target, (Code_ML.target_Eval, K I)) |
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#> Quickcheck.add_generator ("code", compile_generator_expr o ProofContext.theory_of) |
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#> Typecopy.interpretation ensure_random_typecopy |
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#> Datatype.interpretation ensure_random_datatype; |
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end; |