author | haftmann |
Mon, 07 Dec 2009 16:27:48 +0100 | |
changeset 34028 | 1e6206763036 |
parent 33968 | f94fb13ecbb3 |
child 34969 | acd6b305ffb5 |
permissions | -rw-r--r-- |
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(* 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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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)) * seed |
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val ensure_random_typecopy: string -> theory -> theory |
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val random_aux_specification: string -> 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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-> term list * (term * term) list |
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val ensure_random_datatype: Datatype.config -> string list -> theory -> theory |
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val compile_generator_expr: theory -> term -> int -> term list option |
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val eval_ref: (unit -> int -> seed -> term list option * seed) option Unsynchronized.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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(** abstract syntax **) |
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fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"}) |
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val size = @{term "i::code_numeral"}; |
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val size_pred = @{term "(i::code_numeral) - 1"}; |
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val size' = @{term "j::code_numeral"}; |
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val seed = @{term "s::Random.seed"}; |
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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 fun_upd = Const (@{const_name fun_upd}, |
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(T1 --> T2) --> T1 --> T2 --> T1 --> T2); |
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val ((y, t2), seed') = random seed; |
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val (seed'', seed''') = random_split seed'; |
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val state = Unsynchronized.ref (seed'', [], fn () => Abs ("x", 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' = fn () => 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 T' 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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val Tm = termifyT T; |
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val Tm' = termifyT T'; |
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fun mk_const c Ts = Const (c, Sign.const_instance thy (c, Ts)); |
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val v = "x"; |
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val t_v = Free (v, Tm'); |
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val t_constr = mk_const constr Ts; |
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val lhs = HOLogic.mk_random T size; |
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val rhs = HOLogic.mk_ST [((HOLogic.mk_random T' size, @{typ Random.seed}), SOME (v, Tm'))] |
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(HOLogic.mk_return Tm @{typ Random.seed} |
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(mk_const "Code_Evaluation.valapp" [T', 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 Tm, @{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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|> Theory_Target.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, (apfst Binding.conceal 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_T, ... } = |
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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 T = map_atyps (fn TFree (v, sort) => |
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TFree (v, constrain sort @{sort random})) raw_T; |
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val vs' = Term.add_tfreesT T []; |
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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 can_inst = Sign.of_sort thy (T, @{sort random}); |
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in if can_inst then mk_random_typecopy tyco vs constr T 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, |
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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.conceal (Binding.name random_aux), T), NoSyn)] eqs1 lthy; |
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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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val tac = ALLGOALS (rtac rule) |
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THEN ALLGOALS (simp_tac rew_ss) |
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THEN (ALLGOALS (ProofContext.fact_tac (flat eqs2))) |
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val simp = Skip_Proof.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 auxname [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 auxname (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_" ^ auxname, 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.conceal (Binding.name name), NoSyn), |
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(apfst Binding.conceal 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 => Skip_Proof.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 Local_Theory.define 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 prfx name 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; |
209 |
val tac = ALLGOALS (ProofContext.fact_tac ext_simps); |
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in (map (fn prop => Skip_Proof.prove lthy vs [] prop (K tac)) eqs, lthy) end; |
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val b = Binding.conceal (Binding.qualify true prfx |
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(Binding.qualify true name (Binding.name "simps"))); |
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in |
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lthy |
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|> random_aux_primrec_multi (name ^ prfx) proto_eqs |
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|-> (fn proto_simps => prove_simps proto_simps) |
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|-> (fn simps => Local_Theory.note |
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((b, Code.add_default_eqn_attrib :: map (Attrib.internal o K) |
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[Simplifier.simp_add, Nitpick_Simps.add]), simps)) |
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|> snd |
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end |
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|
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223 |
|
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(* constructing random instances on datatypes *) |
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225 |
|
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val random_auxN = "random_aux"; |
227 |
||
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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 random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames); |
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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; |
31950 | 240 |
fun mk_random_call T = (NONE, (HOLogic.mk_random T size', 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 $ size_pred $ size'); |
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val size = Option.map snd (Datatype_Aux.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 = Datatype_Aux.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; |
33029 | 260 |
val k = fold (fn NONE => I | SOME k => Integer.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 |
31950 | 268 |
then if k = 0 then size |
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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 $ size |
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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; |
31950 | 284 |
val auxs_lhss = map (fn t => t $ size $ size' $ seed) random_auxs; |
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val auxs_rhss = map mk_select gen_exprss; |
31868 | 286 |
in (random_auxs, auxs_lhss ~~ auxs_rhss) end; |
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287 |
|
31868 | 288 |
fun mk_random_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy = |
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let |
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val _ = Datatype_Aux.message config "Creating quickcheck generators ..."; |
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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 Datatype_Aux.find_shortest_path descr k |
31950 | 293 |
of SOME (_, l) => if l = 0 then size |
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else @{term "max :: code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"} |
31950 | 295 |
$ HOLogic.mk_number @{typ code_numeral} l $ size |
296 |
| NONE => size; |
|
31868 | 297 |
val (random_auxs, auxs_eqs) = (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 |
31950 | 300 |
(HOLogic.mk_random T size, nth random_auxs k $ mk_size_arg k $ size)) Ts; |
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301 |
in |
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thy |
33553 | 303 |
|> Theory_Target.instantiation (tycos, vs, @{sort random}) |
31868 | 304 |
|> random_aux_specification prfx random_auxN 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 => |
33280 | 307 |
Specification.definition (NONE, (apfst Binding.conceal |
33205 | 308 |
Attrib.empty_binding, 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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312 |
|
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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 Sorts.CLASS_ERROR _ => NONE; |
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322 |
|
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fun ensure_random_datatype config raw_tycos thy = |
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324 |
let |
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325 |
val algebra = Sign.classes_of thy; |
31868 | 326 |
val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) = |
31784 | 327 |
Datatype.the_descr thy raw_tycos; |
32378 | 328 |
val typerep_vs = (map o apsnd) |
31744 | 329 |
(curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs; |
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quickcheck generators for datatypes with functions
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val random_insts = (map (rpair @{sort random}) o flat o maps snd o maps snd) |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
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331 |
(Datatype_Aux.interpret_construction descr typerep_vs |
31744 | 332 |
{ atyp = single, dtyp = (K o K o K) [] }); |
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quickcheck generators for datatypes with functions
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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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f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33766
diff
changeset
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334 |
(Datatype_Aux.interpret_construction descr typerep_vs |
31744 | 335 |
{ atyp = K [], dtyp = K o K }); |
31608 | 336 |
val has_inst = exists (fn tyco => |
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bd2f7211a420
first running version of qc generators for datatypes
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337 |
can (Sorts.mg_domain algebra tyco) @{sort random}) tycos; |
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quickcheck generators for datatypes with functions
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diff
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in if has_inst then thy |
32378 | 339 |
else case perhaps_constrain thy (random_insts @ term_of_insts) typerep_vs |
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datatype packages: record datatype_config for configuration flags; less verbose signatures
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of SOME constrain => mk_random_datatype config descr |
32378 | 341 |
(map constrain typerep_vs) tycos prfx (names, auxnames) |
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quickcheck generators for datatypes with functions
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parents:
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diff
changeset
|
342 |
((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy |
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quickcheck generators for datatypes with functions
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parents:
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343 |
| NONE => thy |
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quickcheck generators for datatypes with functions
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parents:
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diff
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344 |
end; |
31260 | 345 |
|
346 |
||
31950 | 347 |
(** building and compiling generator expressions **) |
348 |
||
32740 | 349 |
val eval_ref : |
350 |
(unit -> int -> int * int -> term list option * (int * int)) option Unsynchronized.ref = |
|
351 |
Unsynchronized.ref NONE; |
|
31950 | 352 |
|
353 |
val target = "Quickcheck"; |
|
354 |
||
355 |
fun mk_generator_expr thy prop Ts = |
|
356 |
let |
|
357 |
val bound_max = length Ts - 1; |
|
358 |
val bounds = map_index (fn (i, ty) => |
|
359 |
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts; |
|
360 |
val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds); |
|
361 |
val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds); |
|
362 |
val check = @{term "If :: bool => term list option => term list option => term list option"} |
|
363 |
$ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option "} $ terms); |
|
364 |
val return = @{term "Pair :: term list option => Random.seed => term list option * Random.seed"}; |
|
365 |
fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT); |
|
366 |
fun mk_termtyp T = HOLogic.mk_prodT (T, @{typ "unit => term"}); |
|
367 |
fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp}, |
|
368 |
liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g; |
|
369 |
fun mk_split T = Sign.mk_const thy |
|
370 |
(@{const_name split}, [T, @{typ "unit => term"}, liftT @{typ "term list option"} @{typ Random.seed}]); |
|
371 |
fun mk_scomp_split T t t' = |
|
372 |
mk_scomp (mk_termtyp T) @{typ "term list option"} @{typ Random.seed} t |
|
373 |
(mk_split T $ Abs ("", T, Abs ("", @{typ "unit => term"}, t'))); |
|
374 |
fun mk_bindclause (_, _, i, T) = mk_scomp_split T |
|
375 |
(Sign.mk_const thy (@{const_name Quickcheck.random}, [T]) $ Bound i); |
|
376 |
in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) end; |
|
377 |
||
378 |
fun compile_generator_expr thy t = |
|
379 |
let |
|
380 |
val Ts = (map snd o fst o strip_abs) t; |
|
381 |
val t' = mk_generator_expr thy t Ts; |
|
34028
1e6206763036
split off evaluation mechanisms in separte module Code_Eval
haftmann
parents:
33968
diff
changeset
|
382 |
val compile = Code_Eval.eval (SOME target) ("Quickcheck_Generators.eval_ref", eval_ref) |
31950 | 383 |
(fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' []; |
384 |
in compile #> Random_Engine.run end; |
|
385 |
||
386 |
||
31260 | 387 |
(** setup **) |
388 |
||
31950 | 389 |
val setup = Typecopy.interpretation ensure_random_typecopy |
390 |
#> Datatype.interpretation ensure_random_datatype |
|
34028
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split off evaluation mechanisms in separte module Code_Eval
haftmann
parents:
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diff
changeset
|
391 |
#> Code_Target.extend_target (target, (Code_Eval.target, K I)) |
31950 | 392 |
#> Quickcheck.add_generator ("code", compile_generator_expr o ProofContext.theory_of); |
31260 | 393 |
|
394 |
end; |