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