val allow_existentials = Attrib.setup_config_bool \<^binding>\<open>quickcheck_allow_existentials\<close> (K true) val finite_functions = Attrib.setup_config_bool \<^binding>\<open>quickcheck_finite_functions\<close> (K true) val overlord = Attrib.setup_config_bool \<^binding>\<open>quickcheck_narrowing_overlord\<close> (K false) val ghc_options = Attrib.setup_config_string \<^binding>\<open>quickcheck_narrowing_ghc_options\<close> (K "")
(* partial_term_of instances *)
fun mk_partial_term_of (x, T) = Const (\<^const_name>\<open>Quickcheck_Narrowing.partial_term_of_class.partial_term_of\<close>,
Term.itselfT T --> \<^typ>\<open>narrowing_term\<close> --> \<^typ>\<open>Code_Evaluation.term\<close>) $ Logic.mk_type T $ x
(** formal definition **)
fun add_partial_term_of tyco raw_vs thy = let val vs = map (fn (v, _) => (v, \<^sort>\<open>typerep\<close>)) raw_vs val ty = Type (tyco, map TFree vs) val lhs = Const (\<^const_name>\<open>partial_term_of\<close>,
Term.itselfT ty --> \<^typ>\<open>narrowing_term\<close> --> \<^typ>\<open>Code_Evaluation.term\<close>) $
Free ("x", Term.itselfT ty) $ Free ("t", \<^typ>\<open>narrowing_term\<close>) val rhs = \<^term>\<open>undefined :: Code_Evaluation.term\<close> val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs)) fun triv_name_of t =
(fst o dest_Free o fst o strip_comb o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv" in
thy
|> Class.instantiation ([tyco], vs, \<^sort>\<open>partial_term_of\<close>)
|> `(fn lthy => Syntax.check_term lthy eq)
|-> (fn eq => Specification.definition NONE [] [] ((Binding.name (triv_name_of eq), []), eq))
|> snd
|> Class.prove_instantiation_exit (fn ctxt => Class.intro_classes_tac ctxt []) end
fun ensure_partial_term_of (tyco, (raw_vs, _)) thy = let val need_inst = not (Sorts.has_instance (Sign.classes_of thy) tyco \<^sort>\<open>partial_term_of\<close>)
andalso Sorts.has_instance (Sign.classes_of thy) tyco \<^sort>\<open>typerep\<close> inif need_inst then add_partial_term_of tyco raw_vs thy else thy end
(** code equations for datatypes **)
fun mk_partial_term_of_eq thy ty (i, (c, (_, tys))) = let val frees = map (fn a => Free (a, \<^typ>\<open>narrowing_term\<close>)) (Name.invent_global "a" (length tys)) val narrowing_term =
\<^term>\<open>Quickcheck_Narrowing.Narrowing_constructor\<close> $ HOLogic.mk_number \<^typ>\<open>integer\<close> i $
HOLogic.mk_list \<^typ>\<open>narrowing_term\<close> (rev frees) val rhs =
fold (fn u => fn t => \<^term>\<open>Code_Evaluation.App\<close> $ t $ u)
(map mk_partial_term_of (frees ~~ tys))
(\<^term>\<open>Code_Evaluation.Const\<close> $ HOLogic.mk_literal c $ HOLogic.mk_typerep (tys ---> ty)) val insts = map (SOME o Thm.global_cterm_of thy o Logic.unvarify_types_global o Logic.varify_global)
[Free ("ty", Term.itselfT ty), narrowing_term, rhs] val cty = Thm.global_ctyp_of thy ty in
@{thm partial_term_of_anything}
|> Thm.instantiate' [SOME cty] insts
|> Thm.varifyT_global end
fun add_partial_term_of_code tyco raw_vs raw_cs thy = let val algebra = Sign.classes_of thy val vs = map (fn (v, sort) => (v, curry (Sorts.inter_sort algebra) \<^sort>\<open>typerep\<close> sort)) raw_vs val ty = Type (tyco, map TFree vs) val cs =
(map o apsnd o apsnd o map o map_atyps)
(fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs valconst = Axclass.param_of_inst thy (\<^const_name>\<open>partial_term_of\<close>, tyco) val var_insts = map (SOME o Thm.global_cterm_of thy o Logic.unvarify_types_global o Logic.varify_global)
[Free ("ty", Term.itselfT ty), \<^term>\<open>Quickcheck_Narrowing.Narrowing_variable p tt\<close>,
\<^term>\<open>Code_Evaluation.Free (STR ''_'')\<close> $ HOLogic.mk_typerep ty] val var_eq =
@{thm partial_term_of_anything}
|> Thm.instantiate' [SOME (Thm.global_ctyp_of thy ty)] var_insts
|> Thm.varifyT_global val eqs = var_eq :: map_index (mk_partial_term_of_eq thy ty) cs in
thy
|> Code.declare_default_eqns_global (map (rpair true) eqs) end
fun ensure_partial_term_of_code (tyco, (raw_vs, cs)) thy = letval has_inst = Sorts.has_instance (Sign.classes_of thy) tyco \<^sort>\<open>partial_term_of\<close> inif has_inst then add_partial_term_of_code tyco raw_vs cs thy else thy end
(* narrowing generators *)
(** narrowing specific names and types **)
exception FUNCTION_TYPE
val narrowingN = "narrowing"
fun narrowingT T = \<^typ>\<open>integer\<close> --> Type (\<^type_name>\<open>Quickcheck_Narrowing.narrowing_cons\<close>, [T])
fun mk_cons c T = Const (\<^const_name>\<open>Quickcheck_Narrowing.cons\<close>, T --> narrowingT T) $ Const (c, T)
fun mk_apply (T, t) (U, u) = let val (_, U') = dest_funT U in
(U', Const (\<^const_name>\Quickcheck_Narrowing.apply\,
narrowingT U --> narrowingT T --> narrowingT U') $ u $ t) end
fun mk_sum (t, u) = letval T = fastype_of t inConst (\<^const_name>\<open>Quickcheck_Narrowing.sum\<close>, T --> T --> T) $ t $ u end
(** deriving narrowing instances **)
fun mk_equations descr vs narrowings = let fun mk_call T =
(T, Const (\<^const_name>\<open>Quickcheck_Narrowing.narrowing_class.narrowing\<close>, narrowingT T)) fun mk_aux_call fTs (k, _) (tyco, Ts) = let val T = Type (tyco, Ts) val _ = ifnot (null fTs) thenraise FUNCTION_TYPE else () in
(T, nth narrowings k) end fun mk_consexpr simpleT (c, xs) = letval Ts = map fst xs in snd (fold mk_apply xs (Ts ---> simpleT, mk_cons c (Ts ---> simpleT))) end fun mk_rhs exprs = foldr1 mk_sum exprs val rhss =
Old_Datatype_Aux.interpret_construction descr vs
{ atyp = mk_call, dtyp = mk_aux_call }
|> (map o apfst) Type
|> map (fn (T, cs) => map (mk_consexpr T) cs)
|> map mk_rhs val lhss = narrowings val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) in eqs end
fun with_overlord_dir name f =
(Path.explode "$ISABELLE_HOME_USER" + Path.basic (name ^ serial_string ()))
|> Isabelle_System.make_directory
|> f
fun value (contains_existentials, ((genuine_only, (quiet, verbose)), size))
ctxt cookie (code_modules_bytes, _) = let val code_modules = (map o apsnd) Bytes.content code_modules_bytes val ((is_genuine, counterexample_of), (get, put, put_ml)) = cookie fun message s = if quiet then () else writeln s fun verbose_message s = ifnot quiet andalso verbose then writeln s else () val current_size = Unsynchronized.ref 0 val current_result = Unsynchronized.ref Quickcheck.empty_result val tmp_prefix = "Quickcheck_Narrowing" val ghc_options = Config.get ctxt ghc_options val with_tmp_dir = if Config.get ctxt overlord then with_overlord_dir else Isabelle_System.with_tmp_dir fun run in_path = let fun mk_code_file module = let val (paths, base) = split_last module in Path.appends (in_path :: map Path.basic (paths @ [suffix ".hs" base])) end; val generatedN_suffix = suffix ".hs" Code_Target.generatedN; val includes = AList.delete (op =) [generatedN_suffix] code_modules
|> (map o apfst) mk_code_file val code = the (AList.lookup (op =) code_modules [generatedN_suffix]) val code_file = mk_code_file [Code_Target.generatedN] val narrowing_engine_file = mk_code_file ["Narrowing_Engine"] val main_file = mk_code_file ["Main"] val main = "module Main where {\n\n" ^ "import System.IO;\n" ^ "import System.Environment;\n" ^ "import Narrowing_Engine;\n" ^ "import " ^ Code_Target.generatedN ^ " ;\n\n" ^ "main = getArgs >>= \\[potential, size] -> " ^ "Narrowing_Engine.depthCheck (read potential) (read size) (" ^ Code_Target.generatedN ^ ".value ())\n\n}\n" val _ = map (uncurry File.write)
(includes @
[(narrowing_engine_file, if contains_existentials then pnf_narrowing_engine else narrowing_engine),
(code_file, code), (main_file, main)]) val executable = in_path + Path.basic "isabelle_quickcheck_narrowing" val cmd = "exec \"$ISABELLE_GHC\" " ^ Code_Haskell.language_params ^ " " ^ ghc_options ^ " " ^
(implode_space
(map File.bash_platform_path
(map fst includes @ [code_file, narrowing_engine_file, main_file]))) ^ " -o " ^ File.bash_platform_path executable ^ ";" val compilation_time =
Isabelle_System.bash_process (Bash.script cmd)
|> Process_Result.check
|> Process_Result.timing_elapsed |> Time.toMilliseconds handle ERROR msg => cat_error "Compilation with GHC failed" msg val _ = Quickcheck.add_timing ("Haskell compilation", compilation_time) current_result fun haskell_string_of_bool v = if v then"True"else"False" fun with_size genuine_only k = if k > sizethen (NONE, !current_result) else let val _ = verbose_message ("[Quickcheck-narrowing] Test data size: " ^ string_of_int k) val _ = current_size := k val res =
Isabelle_System.bash_process (Bash.script
(File.bash_path executable ^ " " ^ haskell_string_of_bool genuine_only ^ " " ^
string_of_int k))
|> Process_Result.check val response = Process_Result.out res val timing = res |> Process_Result.timing_elapsed |> Time.toMilliseconds; val _ =
Quickcheck.add_timing
("execution of size " ^ string_of_int k, timing) current_result in if response = "NONE"then with_size genuine_only (k + 1) else let val output_value = the_default "NONE"
(try (snd o split_last o filter_out (fn s => s = "") o split_lines) response) val ml_code = "\nval _ = Context.put_generic_context (SOME (Context.map_proof (" ^ put_ml
^ " (fn () => " ^ output_value ^ ")) (Context.the_generic_context ())))" val ctxt' = ctxt
|> put (fn () => error ("Bad evaluation for " ^ quote put_ml))
|> Context.proof_map (exec false ml_code) val counterexample = get ctxt' () in if is_genuine counterexample then
(counterexample, !current_result) else let val cex = Option.map (rpair []) (counterexample_of counterexample) val _ = message (Pretty.string_of (Quickcheck.pretty_counterex ctxt false cex)) val _ = message "Quickcheck continues to find a genuine counterexample..." in with_size true (k + 1) end end end in with_size genuine_only 0 end in with_tmp_dir tmp_prefix run end
fun dynamic_value_strict opts cookie ctxt postproc t = let fun evaluator program _ vs_ty_t deps =
Exn.result (value opts ctxt cookie)
(Code_Target.compilation_text ctxt target program deps true vs_ty_t) in Exn.release (Code_Thingol.dynamic_value ctxt (Exn.map_res o postproc) evaluator t) end
(** counterexample generator **)
datatype counterexample =
Universal_Counterexample of (term * counterexample)
| Existential_Counterexample of (term * counterexample) list
| Empty_Assignment
fun map_counterexample _ Empty_Assignment = Empty_Assignment
| map_counterexample f (Universal_Counterexample (t, c)) =
Universal_Counterexample (f t, map_counterexample f c)
| map_counterexample f (Existential_Counterexample cs) =
Existential_Counterexample (map (fn (t, c) => (f t, map_counterexample f c)) cs)
structure Data = Proof_Data
( type T =
(unit -> (bool * term list) option) *
(unit -> counterexample option) val empty: T =
(fn () => raise Fail "counterexample",
fn () => raise Fail "existential_counterexample") fun init _ = empty
)
val get_counterexample = #1 o Data.get; val get_existential_counterexample = #2 o Data.get;
val put_counterexample = Data.map o @{apply 2(1)} o K val put_existential_counterexample = Data.map o @{apply 2(2)} o K
fun finitize_functions (xTs, t) = let val (names, boundTs) = split_list xTs fun mk_eval_ffun dT rT = Const (\<^const_name>\<open>Quickcheck_Narrowing.eval_ffun\<close>, Type (\<^type_name>\<open>Quickcheck_Narrowing.ffun\<close>, [dT, rT]) --> dT --> rT) fun mk_eval_cfun dT rT = Const (\<^const_name>\<open>Quickcheck_Narrowing.eval_cfun\<close>, Type (\<^type_name>\<open>Quickcheck_Narrowing.cfun\<close>, [rT]) --> dT --> rT) fun eval_function (Type (\<^type_name>\<open>fun\<close>, [dT, rT])) = let val (rt', rT') = eval_function rT in
(case dT of Type (\<^type_name>\<open>fun\<close>, _) =>
(fn t => absdummy dT (rt' (mk_eval_cfun dT rT' $ incr_boundvars 1 t $ Bound 0)), Type (\<^type_name>\<open>Quickcheck_Narrowing.cfun\<close>, [rT']))
| _ =>
(fn t => absdummy dT (rt' (mk_eval_ffun dT rT' $ incr_boundvars 1 t $ Bound 0)), Type (\<^type_name>\<open>Quickcheck_Narrowing.ffun\<close>, [dT, rT']))) end
| eval_function (T as Type (\<^type_name>\<open>prod\<close>, [fT, sT])) = let val (ft', fT') = eval_function fT val (st', sT') = eval_function sT val T' = Type (\<^type_name>\prod\, [fT', sT']) val map_const = Const (\<^const_name>\<open>map_prod\<close>, (fT' --> fT) --> (sT' --> sT) --> T' --> T) fun apply_dummy T t = absdummy T (t (Bound 0)) in
(fn t => list_comb (map_const, [apply_dummy fT' ft', apply_dummy sT' st', t]), T') end
| eval_function T = (I, T) val (tt, boundTs') = split_list (map eval_function boundTs) val t' = subst_bounds (map2 (fn f => fn x => f x) (rev tt) (map_index (Bound o fst) boundTs), t) in
(names ~~ boundTs', t') end
fun dest_ffun (Type (\<^type_name>\<open>Quickcheck_Narrowing.ffun\<close>, [dT, rT])) = (dT, rT)
fun eval_finite_functions (Const (\<^const_name>\<open>Quickcheck_Narrowing.ffun.Constant\<close>, T) $ value) =
absdummy (fst (dest_ffun (body_type T))) (eval_finite_functions value)
| eval_finite_functions (Const (\<^const_name>\<open>Quickcheck_Narrowing.ffun.Update\<close>, T) $ a $ b $ f) = let val (T1, T2) = dest_ffun (body_type T) in
Quickcheck_Common.mk_fun_upd T1 T2
(eval_finite_functions a, eval_finite_functions b) (eval_finite_functions f) end
| eval_finite_functions t = t
(** tester **)
val rewrs = map (swap o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of)
(@{thms all_simps} @ @{thms ex_simps}) @ map (HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of)
[@{thm iff_conv_conj_imp}, @{thm not_ex}, @{thm not_all},
@{thm meta_eq_to_obj_eq [OF Ex1_def]}]
fun make_pnf_term thy t = Pattern.rewrite_term thy rewrs [] t
fun contains_existentials t = exists (fn (Q, _) => Q = \<^const_name>\<open>Ex\<close>) (fst (strip_quantifiers t))
fun mk_property qs t = let fun enclose (\<^const_name>\<open>Ex\<close>, (x, T)) t = Const (\<^const_name>\<open>Quickcheck_Narrowing.exists\<close>,
(T --> \<^typ>\<open>property\<close>) --> \<^typ>\<open>property\<close>) $ Abs (x, T, t)
| enclose (\<^const_name>\<open>All\<close>, (x, T)) t = Const (\<^const_name>\<open>Quickcheck_Narrowing.all\<close>,
(T --> \<^typ>\<open>property\<close>) --> \<^typ>\<open>property\<close>) $ Abs (x, T, t) in fold_rev enclose qs (\<^term>\<open>Quickcheck_Narrowing.Property\<close> $ t) end
fun mk_case_term ctxt p ((\<^const_name>\<open>Ex\<close>, (x, T)) :: qs') (Existential_Counterexample cs) =
Case_Translation.make_case ctxt Case_Translation.Quiet Name.context (Free (x, T)) (map (fn (t, c) =>
(t, mk_case_term ctxt (p - 1) qs' c)) cs)
| mk_case_term ctxt p ((\<^const_name>\<open>All\<close>, _) :: qs') (Universal_Counterexample (t, c)) = if p = 0 then t else mk_case_term ctxt (p - 1) qs' c
val post_process =
perhaps (try Quickcheck_Common.post_process_term) o eval_finite_functions
fun mk_terms ctxt qs result = let val ps = filter (fn (_, (\<^const_name>\<open>All\<close>, _)) => true | _ => false) (map_index I qs) in map (fn (p, (_, (x, _))) => (x, mk_case_term ctxt p qs result)) ps
|> map (apsnd post_process) end
fun test_term ctxt catch_code_errors (t, _) = let fun dest_result (Quickcheck.Result r) = r val opts =
((Config.get ctxt Quickcheck.genuine_only,
(Config.get ctxt Quickcheck.quiet, Config.get ctxt Quickcheck.verbose)),
Config.get ctxt Quickcheck.size) val thy = Proof_Context.theory_of ctxt val t' = fold_rev (fn (x, T) => fn t => HOLogic.mk_all (x, T, t)) (Term.add_frees t []) t val pnf_t = make_pnf_term thy t' in if Config.get ctxt allow_existentials andalso contains_existentials pnf_t then let fun wrap f (qs, t) = letval (qs1, qs2) = split_list qs in apfst (map2 pair qs1) (f (qs2, t)) end val finitize = if Config.get ctxt finite_functions then wrap finitize_functions else I val (qs, prop_t) = finitize (strip_quantifiers pnf_t) val act = if catch_code_errors thentryelse (fn f => SOME o f) val execute =
dynamic_value_strict (true, opts)
((K true, fn _ => error ""),
(get_existential_counterexample, put_existential_counterexample, "Narrowing_Generators.put_existential_counterexample"))
ctxt (apfst o Option.map o map_counterexample) in
(case act execute (mk_property qs prop_t) of
SOME (counterexample, result) => Quickcheck.Result
{counterexample = Option.map (pair true o mk_terms ctxt qs) counterexample,
evaluation_terms = Option.map (K []) counterexample,
timings = #timings (dest_result result), reports = #reports (dest_result result)}
| NONE =>
(Quickcheck.message ctxt "Conjecture is not executable with Quickcheck-narrowing";
Quickcheck.empty_result)) end else let val frees = Term.add_frees t [] val t' = fold_rev absfree frees t fun wrap f t = uncurry (fold_rev Term.abs) (f (strip_abs t)) val finitize = if Config.get ctxt finite_functions then wrap finitize_functions else I fun ensure_testable t = Const (\<^const_name>\<open>Quickcheck_Narrowing.ensure_testable\<close>,
fastype_of t --> fastype_of t) $ t fun is_genuine (SOME (true, _)) = true
| is_genuine _ = false val counterexample_of = Option.map (apsnd (curry (op ~~) (map fst frees) o map post_process)) val act = if catch_code_errors thentryelse (fn f => SOME o f) val execute =
dynamic_value_strict (false, opts)
((is_genuine, counterexample_of),
(get_counterexample, put_counterexample, "Narrowing_Generators.put_counterexample"))
ctxt (apfst o Option.map o apsnd o map) in
(case act execute (ensure_testable (finitize t')) of
SOME (counterexample, result) =>
Quickcheck.Result
{counterexample = counterexample_of counterexample,
evaluation_terms = Option.map (K []) counterexample,
timings = #timings (dest_result result),
reports = #reports (dest_result result)}
| NONE =>
(Quickcheck.message ctxt "Conjecture is not executable with Quickcheck-narrowing";
Quickcheck.empty_result)) end end
fun test_goals ctxt catch_code_errors insts goals = ifnot (getenv "ISABELLE_GHC" = "") then let val _ = Quickcheck.message ctxt "Testing conjecture with Quickcheck-narrowing..." val correct_inst_goals = Quickcheck_Common.instantiate_goals ctxt insts goals in
Quickcheck_Common.collect_results (test_term ctxt catch_code_errors)
(maps (map snd) correct_inst_goals) [] end else
(if Config.get ctxt Quickcheck.quiet then () else writeln
("Environment variable ISABELLE_GHC is not set. To use narrowing-based quickcheck, please set "
^ "this variable to your GHC Haskell compiler in your settings file. "
^ "To deactivate narrowing-based quickcheck, set quickcheck_narrowing_active to false.");
[Quickcheck.empty_result])
(* setup *)
val active = Attrib.setup_config_bool \<^binding>\<open>quickcheck_narrowing_active\<close> (K false)
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